Daniel Salós

Anaïs Martineau

Christophe Macabiau

Bernard Bonhoure

Damien Kubrak

Receiver Autonomous Integrity Monitoring of GNSS Signals for Electronic Toll Collection

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Abstract-Various Road User Charging (RUC) mechanisms are used to control the traffic and its resulting pollution, as well as revenue sources for reinvestment in the road infrastructure. Among them, Electronic Toll Collection (ETC) systems based on user positions estimated with Global Navigation Satellite Systems (GNSS) are particularly attractive due to their flexibility and reduced roadside infrastructure in comparison to other systems like tollbooths. Because GNSS positioning may be perturbed by different errors and failures, ETC systems, as liability critical applications, should monitor the integrity of GNSS signals in order to limit the use of faulty positions and the consequent charging errors. The integrity monitoring systems have been originally designed for civil aviation, so they need to be adapted to the ETC requirements. This paper studies the use of Receiver Autonomous Integrity Monitoring (RAIM), which are algorithms run within the GNSS receiver, and therefore easier to tune to ETC needs than other systems based on external information. The Weighted Least Squares Residuals (WLSR) RAIM used in civil aviation is analyzed, and an algorithm modification for ETC is proposed. Simulations demonstrate that the proposed RAIM algorithm has a superior level of availability over civil aviation based RAIM procedures, particularly in urban environments.

Index Terms-Electronic Toll Collection (ETC), Global Navigation Satellite Systems (GNSS), Receiver Autonomous

Integrity Monitoring (RAIM), urban environment.

I. INTRODUCTION

NTEGRITY of Global Navigation Satellite Systems (GNSS) is defined as a measure of the trust that can be placed in the correctness of the information supplied by the navigation system [START_REF]International Standards and Recommended Practices, Annex 10 to the Convention on International Civil Aviation, Aeronautical Telecommunications, Volume I, Radio Navigation Aids[END_REF]. The concept of GNSS integrity was originally developed in the civil aviation framework as part of the International Civil Aviation Organization (ICAO) requirements for using GNSS in the Communications, Navigation and Surveillance / Air Traffic Management (CNS/ATM) system. In particular, civil aviation standards specify a set of minimum accuracy, availability, integrity and continuity performance on the GNSS Signal-in-Space (SIS) for each operation and phase of flight [START_REF] Rtca | Minimum Operational Performance Standards for Global Positioning System / Wide Area Augmentation System Airborne Equipment[END_REF]. Nevertheless, Manuscript received December 19, 2012. This work was supported in part by the Centre National d'Etudes Spatiales (CNES) and Thales Alenia Space. D. Salós, A. Martineau, and C. Macabiau are with the Ecole Nationale de l'Aviation Civile (ENAC), Toulouse, France (e-mail: salos, martineau, macabiau @ recherche.enac.fr).

B. Bonhoure is with the CNES, Toulouse, France. D. Kubrak is with Thales Alenia Space, Toulouse, France.

standalone GPS cannot meet the stringent civil aviation requirements, and, specifically, the GPS SIS integrity standard [START_REF]Global Positioning Service Standard Positioning Service Performance Standard[END_REF] does not assure integrity as specified by the ICAO. For this reason, various augmentation systems have been developed to allow the use of GPS within the ICAO requirements. These systems are classified according to their infrastructure into Ground, Satellite, and Aircraft Based Augmentation Systems (GBAS, SBAS and ABAS).

The need for reliable satellite navigation with integrity monitoring is not limited to the civil aviation field. Two types of applications need GNSS integrity: Safety-of-Life (SoL) applications, in which undetected navigation errors may endanger life, and liability critical applications, in which positioning errors may have negative legal or economic consequences [START_REF] Cosmen-Schortmann | Integrity in Urban and Road Environments and its use in Liability Critical Applications[END_REF]. A number of integrity-driven positioning applications have vehicular or pedestrian users and take place in urban and rural environments [START_REF] Tracs | Galileo Overall Architecture Definition (GALA). Definition and Sizing For The Safety of Life Market[END_REF]. A few examples of these applications are Electronic Toll Collection (ETC), train control, dangerous or valuable goods transport survey and emergency calls.

Each application has its own integrity constraints and needs an integrity monitoring technique adapted to its specifications. This paper focuses on Electronic Toll Collection (ETC) systems in urban and rural environments based on GNSS positioning. GNSS-based ETC schemes are particularly interesting because they are free-flow (pay-as-you-drive), highly flexible systems with a reduced quantity of roadside infrastructure. Moreover, satellite navigation is, together with 5.8 GHz microwave and GSM-GPRS communication systems, one of the technologies the European Union recommends for the European Electronic Toll Service (EETS) [6]. As of 2012, toll systems for freight transport using GPS as primary positioning technology are already operational in German and Slovak highways and national roads [START_REF] Pfitzinger | Analysis and Evaluation of the German Toll System Using a Holistic Executable Specification[END_REF] [START_REF] Vargic | On self-similarity in service triggering in NGN networks using satellite based tolling systems[END_REF].

GNSS-based ETC systems are liability critical applications because excessive and uncontrolled positioning errors may lead to incorrect toll invoices. The act of levying a toll lower than it should be is denoted undercharging and implies a loss of revenue, whereas the act of levying a toll higher than it should is known as overcharging and may originate user claims. Thus, ETC specifications should bound the maximum acceptable rate of undercharging and overcharging errors in order to assure the quality of the service to both users and the toll operator. For this reason, GNSS integrity monitoring is a key element of ETC systems which assures that positioning errors are below the specified limits, detecting unacceptably large errors.

Different solutions have been studied to monitor the navigation integrity in urban environments, often hybridizing GNSS with dead-reckoning and map-matching techniques [START_REF] Velaga | Map-Aided Integrity Monitoring of a Land Vehicle Navigation System[END_REF][10] [START_REF] Toledo-Moreo | High-Integrity IMM-EKF-Based Road Vehicle Navigation With Low-Cost GPS/SBAS/INS[END_REF]. The aim of this paper is to present an integrity monitoring algorithm that only uses GNSS measurements, consisting of a snapshot RAIM tailored to the needs of ETC in urban environments. This approach reduces the complexity of the on-board equipment and avoids memory problems due to error propagation in recursive loops, as well as the thorough characterization of errors due to non-GNSS components required by integrity mechanisms. The Least Squares Residuals (LSR) RAIM has been chosen because it is well known in civil aviation and is commonly taken as baseline algorithm [START_REF] Van Graas | Baseline Fault Detection and Exclusion Algorithm[END_REF]. A digital map is used to charge the user, but not in the integrity monitoring process.

The paper is organized as follows. First, the GNSS-based ETC scheme with integrity monitoring is explained in section II. Afterwards, the WLSR RAIM used in civil aviation and a modified version adapted to the ETC needs in urban environments are analyzed in Sections III and IV. The characteristics of both RAIM algorithms are compared in section V, and, finally, section VI presents their performance calculated via simulations.

II. GNSS-BASED ELECTRONIC TOLL COLLECTION SYSTEMS

The discrete road links charging toll scheme defined in the ISO standard [START_REF]Electronic fee collection -Charging performance -Part 1: Metrics[END_REF] is studied. The geo-fencing approach is followed, in which the tolled road network is split into segments defined by virtual perimeters. The areas within the perimeters are denoted geo-objects and constitute the basic charging units, that is, users are charged the price associated to a geo-object whenever they are detected inside it. Each geoobject's fee is set individually and can be designed according to different factors like the user category, the time of the day or the traffic state. Moreover, distance-based charge is possible when geo-objects are defined as road portions between intersections, with only one entrance and one exit. Geo-fencing is an appropriate approach for GNSS-based ETC applications that allows highly flexible systems with a low number of roadside infrastructures.

The main task of the ETC system is to decide whether a user has driven through a road segment or not, and charge him if he has. This decision, known as geo-object recognition, can be taken as a function of the number of user positions lying inside the geo-object boundaries. In order to bound the maximum rate of erroneous geo-object recognitions (i.e. erroneously charged segments), only positions declared valid by the integrity monitoring system are used. Moreover, only independent positions are taken to eliminate the effects of the positioning error temporal correlation. In this context, two position estimates are independent when they produce independent integrity monitoring outputs. The correlation time depends on the GNSS receiver type as well as other constraints within the local environment. Summarizing, the proposed road segment charging algorithm is:

Th INSIDE valid N N   segment charge (1)
where N valid INSIDE is the number of valid and independent positions inside the geo-object, and N Th is the geo-object recognition threshold.

The integrity monitoring systems have been originally designed to meet the civil aviation requirements, so they need to be adapted to the ETC specifications. From the various possible integrity monitoring systems, this work studies the Receiver Autonomous Integrity Monitoring (RAIM), which are algorithms run within the GNSS receiver that monitor integrity thanks to redundant pseudorange measurements. Since RAIM algorithms, as opposed to GBAS or SBAS, do not rely on external information, they can be easily adapted to the ETC requirements and to the multi-frequency, multiconstellation case. This paper considers the use of SBAS corrections, but not of its integrity service because it has been designed mainly to assure the civil aviation requirements.

Only the integrity of the horizontal positioning is required to be monitored for ETC application. For each estimated position, RAIM provides a Horizontal Protection Level (HPL), defined as a circular area centered at the user real position that is assured to contain the estimated position with a probability equal to or higher than (1-P MD ), where the maximum allowed probability of missed detection P MD is a design parameter. The Horizontal Alert Limit (HAL) is the maximum allowed HPL and depends on the road network topography, and can be set as the half of the distance between roads [START_REF] Salós | Integrity monitoring applied to the reception of GNSS signals in urban environments[END_REF].

III. WLSR RAIM FOR CIVIL AVIATION

A. Introduction

The Least Squares Residuals (LSR) RAIM [START_REF] Parkinson | Autonomous GPS Integrity Monitoring using the Pseudorange Residual[END_REF], together with the solution separation method [START_REF] Brown | Self-Contained GPS Integrity Check Using Maximum Solution Separation[END_REF], is one of the RAIM algorithms most frequently used in civil aviation. Moreover, the parity matrix RAIM [START_REF] Sturza | Navigation System Integrity Monitoring using Redundant Measurements[END_REF] and the range comparison technique [START_REF] Lee | Analysis of range and position comparison methods as a means to provide GPS integrity in the user receiver[END_REF] are equivalent to the LSR RAIM [START_REF] Grover Brown | A Baseline GPS RAIM Scheme and a Note on the Equivalence of Three RAIM Methods[END_REF].

The design of the LSR RAIM assumes that pseudorange nominal errors are modeled as independent zero-mean Gaussian distributions with the same variance. This was an acceptable condition when pseudorange errors were dominated by the Selective Availability (SA), but at present pseudorange errors are better described as independent zero-mean Gaussian distributions with variance dependent upon several factors like the signal modulation or the satellite elevation angle. In this case, the Weighted Least Squares Residuals (WLSR) RAIM is used [START_REF] Walter | Weighted RAIM for Precision Approach[END_REF].

B. Algorithm Design

The WLSR RAIM considers the following linear pseurorange measurement model:

E X H Y      (2)
where ΔY [N s x 1] is the linearized measured pseudorange vector, H [N s x N u ] is the observation matrix, ΔX [N u x 1] is the linearized navigation state vector, and E [N s x 1] is the pseudorange error vector. N s is the number of pseudoranges, and N u is the number of unknowns in ΔX.

Two possible pseudorange error scenarios are assumed, namely fault-free and faulty. In the fault-free case, pseudorange measurements are disturbed only by nominal errors, modeled as zero-mean independent Gaussian distributions with covariance matrix Σ. In the faulty case, apart from nominal errors, there is one biased pseudorange measurement:

B E    (3)
where ε [N s x 1] is the nominal error vector and B [N s x 1] is the bias vector:

  T i b B 0 , , 0 , , , 0    (4)
with b i =0 in the fault-free case. The probability of simultaneous faulty pseudoranges is assumed to be negligible.

The WLSR RAIM monitors the integrity of the navigation state vector calculated with the Weighted Least Squares Estimator (WLSE):

Y A X     ˆ (5)
 

1 1 1       T T H H H A (6)
The aim of RAIM algorithms is to detect positioning errors exceeding the alert limit within the required probabilities of missed and false alarm. Since positioning errors are not directly measurable, the WLSR RAIM calculates, thanks to the residual vector (R), a measurable scalar test statistic (t) that provides information about pseudorange measurement errors. The test statistic is computed as the Weighted Sum of Squared Errors (WSSE):

  Y B I Y R R WSSE t T T           1 1 (7)    E B I Y B I X H Y R           (8)
 

1 1 1       T T H H H H B ( 9
)
The test statistic calculated in [START_REF] Pfitzinger | Analysis and Evaluation of the German Toll System Using a Holistic Executable Specification[END_REF] follows a chi-squared distribution in the fault free case, and a non-central chisquared one in the faulty case:

           , ~, 0 22 , B N E if N E if t k k    (10)
In both fault-free and faulty scenarios the test statistic's number of degrees of freedom (k) is the number of redundant pseudorange measurements:

u s N N k   (11)
The chi-squared non-centrality parameter (λ) introduced by a faulty measurement, which depends on the bias magnitude and on the nominal errors, is:

  2 2 i i ii b B I      (12)
where σ i 2 is the nominal error variance of the biased pseudorange, and (•) ii is the i th element of the i th row.

Because we are interested in the protection against positioning failures, but the WLSR RAIM detects faults via the test statistic, the relationship between the horizontal positioning error |e H | and t needs to be investigated. In the faulty case, there is a linear relationship between the pseudorange bias projection in the horizontal error domain (|b H |) and the square root of the test statistic λ, characterized by the slope parameter:

   i H slope b (13)     ii i E i N i i B I A A slope     2 , 2 ,  (14)
where A 2 N,i and A 2 E,i are the i th element of the rows of matrix A in (6) corresponding to the state vector horizontal position components. The slope, which varies from one satellite to another, is an indicator of the relationship between the effect of a pseudorange bias in the test statistic and in the positioning error. A pseudorange bias leading to a given noncentrality parameter λ will have the highest impact on the positioning error when it appears in the satellite with the highest slope.

The statistic components of the test statistic and the navigation state estimation errors, caused by nominal errors, are uncorrelated [START_REF] Ober | Ways to Improve RAIM/AAIM Availability Using Position Domain Performance Computations[END_REF], i.e. cov(t,e)=0. Therefore, the relationship between t and |e H | at a given epoch can be described as a 2D random variable with the following PDF:

      H H e PDF t PDF e t PDF   , (15)
Once the test statistic and its relationship with the position error have been defined, the remaining RAIM parameters can be derived. These are the fault detection threshold (Th), the minimum detectable non-centrality parameter (λ det ) and the Horizontal Protection Level (HPL). Fig. 1 depicts the different RAIM design process steps in the t 1/2 against |e H | plane, in a similar way as in [START_REF] Brown | GPS RAIM: Calculation of Thresholds and Protection Radius Using Chi-Square Methods-A Geometric Approach[END_REF]. The bidimensional PDF has been represented by an equiprobable line for clarity reasons.

Design parameters (P MD , P FA )

The WLSR RAIM is designed to meet a maximum allowed probability of missed detection (P MD ) and of false detection (P FD ). If the RAIM only has fault detection and not exclusion functions, any missed or false detection results in a missed or false alarm, and the maximum allowed probability of missed alarm (P MA ) and false alarm (P FA ) are equal to P MD and P FD respectively. A RAIM algorithm with only a fault detection function is considered, so the design parameters used throughout this work are P MD and P FA .

Failure Detection Threshold (Th)

The WLSR RAIM detects a failure whenever the test statistic exceeds a threshold (Th). The threshold is chosen in order to assure the fault detection probability in fault-free conditions, i.e. one minus the cumulated density function of a chi-squared function evaluated at the threshold value:

    Th CDF t Th t p P k FA k 2 1 ~2       (16)
Therefore, Th is a function of P FA and k, which in turn depends on the number of pseudoranges N s .

Minimum Detectable Non-Centrality Parameter (λ det )

In the faulty case, the test statistic λ increases with the bias size as in [START_REF] Van Graas | Baseline Fault Detection and Exclusion Algorithm[END_REF]. The minimum detectable non-centrality parameter (λ det ) is the λ that results in a missed detection rate equal to P MD for the threshold calculated in [START_REF] Brown | Self-Contained GPS Integrity Check Using Maximum Solution Separation[END_REF]:

    Th CDF t Th t p P k k MD 2 det det 2 , , ~       (17)
Therefore, λ det is a function of P MD , k (which depends on N s ) and Th (which also depends on P FA ).

Horizontal Protection Level (HPL)

The HPL is calculated as the projection in the position domain of the pseudorange bias that would generate a noncentrality parameter equal to λ det in the satellite with the maximum slope (slope MAX ):

det    MAX slope HPL ( 18
)
The rationale of the HPL calculation of ( 18) is the following. The positioning error |e H | is distributed approximately centered around |b H |, if the bias is sufficiently large. Let us consider a pseudorange bias in the maximumslope satellite with a magnitude such that the test statistic's non-centrality is equal to λ det . The probability that the RAIM algorithm does not detect this pseudorange bias and that the positioning error is larger than the HPL is approximately P MD /2. The probability of missed detection decreases if the biased pseudorange is in other satellite with a lower slope. Larger biases lead to higher λ det , so they are always detected with a probability below P MD . Smaller bias magnitudes have smaller λ det , which sets the probability of not detection over P MD . Fortunately, they also lead to lower positioning errors that offset the higher non-detection probability, resulting in a probability of missed detection of errors exceeding the HPL of less than P MD . Nevertheless, in some cases, especially with low slopes, this may not hold [START_REF] Brown | GPS RAIM: Calculation of Thresholds and Protection Radius Using Chi-Square Methods-A Geometric Approach[END_REF].

C. Algorithm Implementation at the GNSS Receiver

The algorithm run within the receiver consists of two modules, i.e. the RAIM availability check and the Fault Detection (FD) (Fig. 2). The FD could be replaced by a Fault Detection and Exclusion (FDE) module. First, at each epoch, the slope of each pseudorange measurement is calculated thanks to the observation matrix and the nominal error covariance matrix. The HPL is computed afterwards with the maximum slope and the corresponding chi-squared non-centrality parameter. If the HPL exceeds the HAL, RAIM is not available because it cannot monitor integrity with the required HAL, P MD and P FA . In this case, the integrity cannot be monitored, so the estimated position is not valid for its use in ETC.

RAIM Availability Module

Maximum Slope               ii i E i N i N i MAX B I A A slope S 2 , 2 , .. 1 max  Horizontal Protection Level   k slope HPL MAX det    Unavailable RAIM Fault Detection Module Test Statistic   Y B I Y t      1  ?
If the HPL is equal to or lower than the HAL, the RAIM is available and proceeds to check whether the estimated position is faulty or not. The test statistic is computed with the linearized pseudorange measurements, the observation matrix and the nominal error covariance matrix. If the test is higher than the corresponding detection threshold, a fault is detected and the position cannot be used in ETC. When the test is lower than the threshold, the position is valid for ETC.

The values of λ det and Th depend on P MD , P FA and the number of redundant range measurements k. They do not depend on current measurements, so they can be computed offline and stored in the receiver as look-up tables.

The WLSR RAIM can optionally perform FDE in order to reduce service interruptions. This module tries to eliminate the biased pseudorange measurement whenever a fault is detected. If after the fault exclusion HPL ≤ HAL and t ≤ Th, the position estimated without the biased pseudorange is valid for ETC. A possible fault exclusion technique creates N subgroups of N-1 range measurements each; assuming that there is only one faulty pseudorange, the FD module will detect a fault in each subgroup except in the one excluding the faulty measurement. The FDE module needs at least two redundant range measurements.

IV. MODIFIED WLSR RAIM FOR ELECTRONIC TOLL COLLECTION

A. Motivation and Rationale of the Modified WLSR RAIM User/satellite geometry in reduced satellite visibility scenarios like urban environments is likely to be much worse than in the open-air scenarios commonly found in civil aviation. This fact generally increases the Dilution Of Precision (DOP), which degrades the positioning accuracy. Another consequence of bad user/satellite geometries is the augmentation of the maximum slope, which in turn increases the HPL calculated as in [START_REF] Lee | Analysis of range and position comparison methods as a means to provide GPS integrity in the user receiver[END_REF], and consequently degrades the WLSR RAIM availability (which also depends on the HAL). Therefore, a GNSS-based ETC system that monitors integrity with the WLSR RAIM in challenging environments with reduced visibility is likely to have a low number of valid positions per road segment, and consequently a high missed geo-object recognition rate. The aim of this section is to present a modified WLSR RAIM suitable for ETC applications that improves the availability rate in environments with reduced satellite visibility without increasing the effective missed detection rate and therefore the toll liability risk.

According to (1), a road segment is charged to the user when the number of independent positions declared valid by the RAIM inside the geo-object is at least equal to the recognition threshold. The WLSR RAIM may not declare valid a position because it is not available, or because it has detected a failure, regardless of whether it is a correct or a false detection (see Fig. 2). The aim of the modified WLSR RAIM described in this section is to maximize the number of valid positions in the fault-free scenario.

The modified RAIM is designed to assure a constant P MD in order to set a known maximum probability that a faulty position inside the geo-object is declared valid when the user is actually outside it. As opposed to civil aviation, ETC systems do not require continuity, so their RAIM algorithms do not necessarily need to assure a maximum allowed P FA .

Given constant values of P MD , slope MAX and k, the HPL can be decreased by increasing the P FA (Fig. 3): The main idea behind the modified WLSR RAIM algorithm is to adapt the P FA to the maximum slope variations to provide a tradeoff between RAIM availability and false alarms, without any restriction on the maximum allowed P FA .

a b HPL HPL P P a FA b FA    , , (19)

B. Algorithm Design

The objective is to design a RAIM algorithm with the WLSR test statistic described in [START_REF] Pfitzinger | Analysis and Evaluation of the German Toll System Using a Holistic Executable Specification[END_REF], that maximizes the probability that a fault-free position (affected only by nominal errors) is declared valid, i.e. the RAIM is available and does not detect a fault. Since the WLSR test statistic is used, the formulas (2-18) also apply for the modified WLSR RAIM. Moreover, the algorithm must assure that the probability of not detecting, in the faulty scenario, a positioning error larger than the HAL is always equal to or lower than a fixed value P MD .

The first design objective is equivalent to finding the detection threshold (Th) that maximizes the probability of not detecting a failure in the fault-free scenario, subject to the condition that the RAIM is available: Given fixed values of P MD and k, the HPL expression of ( 17) is a monotonically increasing function of Th. Hence, the detection threshold that maximizes [START_REF] Walter | Weighted RAIM for Precision Approach[END_REF] is the one that results in an HPL equal to the HAL.

  
Therefore, the proposed RAIM procedure is designed to provide a constant HPL equal to the HAL. The minimum detectable chi-squared non-centrality parameter that corresponds to an HPL equal to HAL is derived from [START_REF] Lee | Analysis of range and position comparison methods as a means to provide GPS integrity in the user receiver[END_REF]:

  2 det MAX slope HAL   (21)
The detection threshold that maximizes [START_REF] Walter | Weighted RAIM for Precision Approach[END_REF] is derived from equation [START_REF] Sturza | Navigation System Integrity Monitoring using Redundant Measurements[END_REF] with the λ det calculated in [START_REF] Ober | Ways to Improve RAIM/AAIM Availability Using Position Domain Performance Computations[END_REF]:

  MD P CDF Th k 1 2 det ,     (22)
The fault detection algorithm can already be run once the detection threshold has been calculated. For performance analysis purposes, the P FA provided at each instant can be derived from equation ( 16) with the Th calculated in [START_REF] Brown | GPS RAIM: Calculation of Thresholds and Protection Radius Using Chi-Square Methods-A Geometric Approach[END_REF]:

  Th CDF P k FA 2 1    (23)
The resulting algorithm is a Constant-Probability-of-Detection (CPOD) RAIM [START_REF] Sturza | Comparison of Fixed and Variable Threshold RAIM Algorithms[END_REF] with the particularity of not having a maximum allowed P FA . This modified WLSR RAIM is always available (HPL=HAL), but very high slopes lead to high false alarm probabilities. A fault-free estimated position is declared valid by the RAIM with a probability of:

  Th CDF P P k FA valid 2 1     (24)

C. Algorithm Implementation at the GNSS Receiver

The algorithm run at the receiver can be either the Fault Detection (FD) module (Fig. 4), or the Fault Detection and Exclusion (FDE) module. There is no RAIM availability check module because the HPL is set to be always equal to the HAL.

First, at each epoch, the slope of each pseudorange measurement is computed as in the standard WLSR RAIM. Afterwards, the minimum detectable chi-squared noncentrality parameter is calculated with the HAL and the maximum slope.

The detection threshold is then calculated with [START_REF] Brown | GPS RAIM: Calculation of Thresholds and Protection Radius Using Chi-Square Methods-A Geometric Approach[END_REF] as the value for which the Cumulative Density Function (CDF) of a non-central chi-squared distribution with k degrees of freedom and non-centrality λ det is equal to P MD .

Since Th depends on current measurements, its exact value cannot be computed offline and stored like in the WLSR RAIM used in civil aviation. Nevertheless, it is possible to create a look-up table of Th as a function of k and discrete values of λ det (for a given P MD ).

Finally, the test statistic is computed as in [START_REF] Pfitzinger | Analysis and Evaluation of the German Toll System Using a Holistic Executable Specification[END_REF] with the linearized pseudorange measurements, the observation matrix and the nominal error covariance matrix.

The estimated position is declared valid for its use in ETC if the test statistic does not exceed the threshold, and it is rejected if a fault is detected.

V. COMPARISON BETWEEN THE WLSR RAIM USED IN CIVIL AVIATION AND THE MODIFIED ALGORITHM FOR ETC

Both WLSR RAIM algorithms monitor the integrity of the position estimated applying the WLSE to the linearized GNSS pseudorange measurements, assuming a known nominal pseudorange error model and a single biased pseudorange in the faulty scenario (equations (2-6)). The two algorithms use the same test statistic described in [START_REF] Pfitzinger | Analysis and Evaluation of the German Toll System Using a Holistic Executable Specification[END_REF][START_REF] Vargic | On self-similarity in service triggering in NGN networks using satellite based tolling systems[END_REF][START_REF] Velaga | Map-Aided Integrity Monitoring of a Land Vehicle Navigation System[END_REF][START_REF] Toledo-Moreo | Lane-Level Integrity Provision for Navigation and Map Matching With GNSS, Dead Reckoning, and Enhanced Maps[END_REF][START_REF] Toledo-Moreo | High-Integrity IMM-EKF-Based Road Vehicle Navigation With Low-Cost GPS/SBAS/INS[END_REF][START_REF] Van Graas | Baseline Fault Detection and Exclusion Algorithm[END_REF], related with the positioning error as given in [START_REF]Electronic fee collection -Charging performance -Part 1: Metrics[END_REF][START_REF] Salós | Integrity monitoring applied to the reception of GNSS signals in urban environments[END_REF]. Consequently, the relationships [START_REF] Parkinson | Autonomous GPS Integrity Monitoring using the Pseudorange Residual[END_REF][START_REF] Brown | Self-Contained GPS Integrity Check Using Maximum Solution Separation[END_REF][START_REF] Sturza | Navigation System Integrity Monitoring using Redundant Measurements[END_REF][START_REF] Lee | Analysis of range and position comparison methods as a means to provide GPS integrity in the user receiver[END_REF] depicted in Fig. 1 between P MD , P FA , Th, λ det and HPL apply to both algorithms. The computational cost of the proposed algorithm is similar to the civil aviation one if it is implemented with a look-up table of discrete values of Th.

Both WLSR RAIM algorithms assure a detection rate equal to P FA in the fault-free scenario. Note that, assuming that nominal errors do not cause positioning failures, any detection in fault-free scenario is a false detection. Both algorithms also assure that, in the faulty scenario with one biased pseudorange, the missed detection rate of positioning errors exceeding the HPL is equal to or lower than P MD .

The main difference between both algorithms resides in the fact that the WLSR RAIM used in civil aviation provides a time-variant HPL and constant P MD and P FA , while the modified algorithm provides a time-variant P FA and constant P MD and HPL (equal to the HAL).

Fault Detection Module

Maximum Slope 5 illustrates the false detection probability in the faultfree scenario, and the probability that a positioning error larger than HAL, i.e. a positioning failure, is not detected in the faulty scenario with a biased pseudorange such that the noncentrality parameter is λ det (the shaded area). It is important to note that the actual probability of undetected positioning failures in the faulty scenario depends on the slope of the biased pseudorange, and on the bias magnitude that moves the bidimensional PDF along the slope. Fig. 5. Graphical example of the undetected failure probability in the faulty case with a biased pseudorange such that λ=λdet, and of the false alarm probability in the fault-free scenario.

              ii i E i N i N i MAX B I A A slope S 2 , 2 , .. 1 max  Minimum Detectable Non-Centrality Parameter   2 det MAX slope HAL   Detection Threshold   MD P CDF Th k 1 2 det ,     Test Statistic   Y B I Y t      1 Fault Detected No Fault Detected (Valid Position) ✔ x ? Th t  Fig.
The WLSR RAIM for civil aviation is designed to provide at each epoch the lowest HPL that meets the required P MD and P FA . The integrity is monitored only if HPL ≤ HAL. The RAIM detects positioning errors exceeding the HPL with a probability higher than 1-P MD , so the lower the HPL, the lower the actual missed detection probability of positioning failures larger than the HAL (the shaded area in Fig. 5). Positioning errors between HPL and HAL are treated as positioning failures and are detected with a missed detection probability below P MD . In the fault-free case, the algorithm constantly provides the maximum allowed false detection rate P FA . Therefore, the standard WLSR RAIM minimizes the probability of undetected positioning failures at the expense of the false detection rate.

The WLSR RAIM for ETC is designed to provide at each epoch, in the fault-free case, the lowest probability of false P FA that meets the required P MD and HAL. The algorithm constantly provides an HPL equal to the HAL. For this reason, the actual probability of detection probability of positioning failures larger than the HAL (the shaded area in Fig. 5) is less conservative than in the original algorithm. Therefore, the modified WLSR RAIM minimizes the probability of false detection, at the expense of a less conservative probability of undetected positioning failures.

High maximum slopes due to bad user/satellite geometries result in high HPL in the civil aviation RAIM procedure and in high P FA in the modified algorithm. This means that positions rejected by the civil aviation algorithm due to RAIM unavailability can be monitored with the new algorithm at the cost of increasing the P FA . Fig. 6 shows the probability of rejecting a fault free position for both RAIM procedures with one redundant pseudorange measurement (k=1), as a function of the ratio HAL/slope MAX . Let us remember that a position is declared valid when the RAIM is available and does not detect a failure. The availability condition for the RAIM used in civil aviation can be rewritten using [START_REF] Lee | Analysis of range and position comparison methods as a means to provide GPS integrity in the user receiver[END_REF] as:

MAX slope HAL  det  (25)
Following the example of Fig. 6, equations ( 16) and [START_REF] Sturza | Navigation System Integrity Monitoring using Redundant Measurements[END_REF] give a value of λ det 1/2 =7.5 with P MD =10 -3 , P FA =10 -5 and k=1. In that case, the RAIM is available if HAL/slope MAX is larger than 7.5, and unavailable if it is not. When the RAIM is available, the false detection is constantly P FA =10 -5 , while when it is unavailable integrity cannot be monitored and the position is always rejected.

On the other hand, the modified WLSR RAIM presents a decreasing false alarm probability as HAL/slope MAX increases. For instance, continuing with the case depicted in Fig. 6, a ratio HAL/slope MAX equal to 7 would cause the original RAIM to be unavailable and to reject the position, but the modified algorithm is able to monitor integrity and validate the position with a probability of 1-10 -4 . Fig. 6. Probability of not declaring valid a fault-free position. Configuration: k=1, P MD =10 -3 , RAIM for civil aviation P FA =10 -5 . The modified WLSR RAIM is suitable for applications like ETC that need the maximum number of positions assured to be within a given HAL with a given P MD , rather than a continuity requirement. Other studies have addressed the use of RAIM algorithms with flexible P FA in applications with continuity constraints like civil aviation [START_REF] Feng | A measurement domain receiver autonomous integrity monitoring algorithm[END_REF].

VI. SIMULATION RESULTS

This section presents the navigation system performance; the final toll charging performance should include other possible failures like geo-object database errors. The WLSR RAIM performance depends on the design parameters (HAL, P MD , and, in the classic algorithm, P FA ) and on the maximum slope, which in turn depends on the environment, i.e. the user/satellite geometry. The RAIM performance in rural and urban environments has been obtained via simulations.

The simulated scenario consists of a user moving at a constant velocity of 50 km/h along the axis of a 20-metre wide straight street. Buildings are generated statistically at both sides of the street as in Table I, separated by a gap with a probability of 10 -1 . The nominal 24-satellite GPS and 27satellite Galileo constellations are simulated, and only line-ofsight satellites with an elevation angle over 5° are assumed to be received by the user. The simulation length is set to 72-hour to cover approximately all possible GPS & Galileo satellite ground track combinations. Data is sampled every second.

Three GNSS receivers are studied. A single frequency GPS L1 C/A with a wideband front-end of 16 MHz augmented with SBAS corrections, a single frequency dual constellation GPS & Galileo L1/E1 BOC(1,1) with a 4-MHz frontend filter augmented with SBAS corrections, and a dual frequency GPS & Galileo L1/E1MBOC & L5/E5a BPSK [START_REF] Toledo-Moreo | Lane-Level Integrity Provision for Navigation and Map Matching With GNSS, Dead Reckoning, and Enhanced Maps[END_REF] with a 14-MHz and a 20-MHz frontend filter respectively. The first configuration will give the performance of current high performance receivers, and the GPS & Galileo configurations with modernized signals represent the performance attainable in a near future. In the dual constellation case, a modernized SBAS capable to correct Galileo signals is assumed.

Various charging metrics can be used to define the ETC required performance [START_REF]Electronic fee collection -Charging performance -Part 1: Metrics[END_REF], but numerical values of these metrics are not standardized. This section considers, as in [START_REF] Salós | Integrity monitoring applied to the reception of GNSS signals in urban environments[END_REF], a fault-detection WLSR RAIM configuration with P MD = 5•10 -5 and two possible values of P FA , 5•10 -3 and 5•10 -5 . The HAL depends on the road topology; in this paper numerical examples are given for HAL of 25 and 50 meters [START_REF] Salós | Integrity monitoring applied to the reception of GNSS signals in urban environments[END_REF].

A pseudorange nominal measurement model suitable for integrity applications in urban environments is used. Following a similar approach as in [START_REF]International Standards and Recommended Practices, Annex 10 to the Convention on International Civil Aviation, Aeronautical Telecommunications, Volume I, Radio Navigation Aids[END_REF][2], the pseudorange error is calculated as the result of various independent error sources: ionosphere and troposphere delays, tracking loops errors, multipath and ephemeris and satellite clock errors. The model is summarized as follows. The ionospheric residual error model is that of the civil aviation standards for single frequency GPS and SBAS [START_REF] Rtca | Minimum Operational Performance Standards for Global Positioning System / Wide Area Augmentation System Airborne Equipment[END_REF], and zero for dual frequency users. The troposphere residual error model standardized for civil aviation is used [START_REF] Rtca | Minimum Operational Performance Standards for Global Positioning System / Wide Area Augmentation System Airborne Equipment[END_REF]. The tracking loop errors are modeled as in [START_REF] Julien | Design of Galileo L1F tracking loops[END_REF], considering a 1-Hz DLL, a 20-ms integration time, a dot-product discriminator and a carrier to noise ratio C/N 0 of 30 dB. The multipath error model is detailed in [START_REF] Salós | Nominal GNSS Pseudorange Measurement Model for Vehicular Urban Applications[END_REF]. Finally, the GNSS are assumed to be sufficiently modernized to assure ephemeris and satellite clock nominal errors with a standard deviation of 85 cm. The total pseudorange error model is a zero-mean Gaussian distribution with the standard deviation (σ PSR ) of Fig. 7. It is important to note that σ PSR is expected to decrease with higher C/N 0 , especially in dual frequency receivers that eliminate the ionospheric delay at the cost of amplifying the thermal noise error. The number of visible satellites and the HPL distribution obtained with the classic WLSR RAIM remarks the relevance of the environment and of the number of constellations (Fig. 8 and Fig. 9). Both dual constellation receivers show similar performances. For instance, in the dual constellation case and a HAL of 50 m, the percentage of epochs in which a RAIM configured with P MD =5•10 -5 and P FA =5•10 -3 is available decreases from almost 100% in the rural environment to approximately 55% in the urban one. In the GPS case, it decreases from 50% to around 7%. Lower P MD or P FA would decrease the availability rate. Fig. 10 shows the CDF of the number of valid positions for a dual constellation user during a 30-s trajectory trough a road segment. The modified WLSR RAIM provides the highest number of valid positions. Let us consider an ETC system that charges a road segment when there is at least one valid position inside the geo-object, that is, N Th =1 in (1). This threshold has been proved to meet the overcharging requirement providing the lowest probability of missed geo-object [START_REF] Salós | Integrity monitoring applied to the reception of GNSS signals in urban environments[END_REF]. Fig. 11 shows the probability of not charging a user that has driven through a road segment as a function of the trajectory duration, a time between independent positions (T c ) of 5 s, and various receiver and RAIM configurations. Both GPS & Galileo receivers have similar performance, so for the sake of clarity only the dual frequency results are plotted. The novel algorithm always provides the best results, reaching a difference of more than one order of magnitude with respect to the classic WLSR RAIM in the dual constellation case for durations longer than 20 s. The classic WLSR RAIM has better performance with a P FA of 5•10 -3 than of 5•10 -5 , which means that in this case the gain in the availability rate compensates the loss in the false alarm rate. The reduced visibility penalizes the single constellation performance: while the probability of not charging the road segment with a HAL of 50 m and after 25 s of trajectory is 10 -5 for GPS & Galileo users, it is still over 0.1 for GPS-only users.

VII. CONCLUSION

GNSS-based ETC systems need to monitor the positioning integrity in order to control the effects of undercharging and overcharging due to positioning failures. With this purpose, two RAIM algorithms have been studied: the WLSR RAIM used in civil aviation and a modified algorithm that, maintaining the P MD , maximizes the number of valid positions (that is, available RAIM and no fault detected).

The aim of the proposed algorithm is to decrease the rate of undercharging in reduced visibility scenarios like urban environments, assuring the same maximum allowed overcharging risk as the civil aviation RAIM procedure. This objective has been demonstrated by simulations. It has also been shown the improvement of dual constellation receivers in urban environments, which provide undercharging rates several orders of magnitude lower than GPS-only ones.

The proposed design with a variable P FA and a fixed HPL can be extended to other existing RAIM algorithms.

Fig. 1 .

 1 Fig. 1. WLSR RAIM design process: a) Fault detection threshold (Th). b) Minimum detectable non-centrality parameter (λdet). c) Horizontal Protection Level (HPL = slope MAX • λdet 1/2 ).

Fig. 2 .

 2 Fig. 2. WLSR RAIM algorithm with Fault Detection capabilities run within the GNSS receiver.

Fig. 3 .

 3 Fig. 3. Effect of the PFA in the WLSR RAIM with a fixed PMD and a number of chi-squared degrees of freedom k.

Fig. 4 .

 4 Fig. 4. Modified WLSR RAIM algorithm run within the GNSS receiver.

Fig. 7 .

 7 Fig. 7. Pseudorange nominal error model.

Fig. 8 .Fig. 9 .Fig. 10 .

 8910 Fig. 8. Distribution of visible satellites.

Fig. 11 .

 11 Fig. 11. Probability that any of the positions estimated during the user trajectory through a geo-object is not validated by the RAIM (P MD =5•10 -5 ).

  /E1 MBOC & L5/E5a BPSK(10) users, HPL = 25 meters. b) L1/E1 MBOC & L5/E5a BPSK(10) users, HPL = 50 meters. a) Wideband L1 C/A + SBAS users, HPL = 50 meters. WLSR RAIM (P FA =5•10 -5 ) Grey: rural environment WLSR RAIM (P FA =5•10 -3 ) Black: urban environment WLSR RAIM modified for ETC rural environment WLSR RAIM (P FA =5•10 -3 ) Black: urban environment WLSR RAIM modified for ETC p


1 phu: upper part of the valley, pasture. Rebecca Norman writes to me : "The small structures ares pu-lu, unaspirated, and not the same word as phu, high valley. I spell it pu-lu.. 'brok is pronounced brok in western Sham, ḍok in eastern Sham, and in Sham it doesn"t mean the structure, but only an area. In Sham it is not always or even usually at higher altitude than the main house, in fact I think it might be the Sham word for Leh yarsa, just whatever fields or workplace are far away from the main house. I think in Zangskar the ḍok is as you describe. Some people in Leh say ḍok for the grazing area with pulu structures, but most people in Leh don"t have the word ḍok at all.

Patrick Kaplanian THE LADAKHI HOUSE I -Definition

The word khangpa (spelling: khang-pa) as distinct from khangu or khangbu (spelling: khangchung), refers both to a place of residence and to a social unit, in particular an electoral unit (for example for the election of a goba (sp. 'go-ba or mgo-ba; the village head) and his assistants. The word trongpa (sp. grong-pa) denotes the residence complex as a whole including a winter floor, a summer floor, ground floor stables, a chotkhang (sp. mchod-khang) on the upper storey, etc. However, it also denotes a social unit (reference to the undivided family as opposed to the khangpa/khangchung fission) with a well defined position in the social hierarchy (opposition tronchen/troncung, sp. grong-chen/grong-chung)). Thus there is no term, at least not one commonly used, to designate the house as a building. The terms used always refer to social or familial groupings, to the segmentations in village society, each with a defined function and place in the social hierarchy. The word yarsa or yartsa (sp. dbyar-sa) denotes a summer residence. In fact it has two meanings: 1) either it refers to the summer floor, the second storey and in particular the kitchen (the words can-sa (byan-sa) and thap-sa (sp. thab-sa) are normally used for the winter kitchen). In such case yarkhang (dbyar-khang) is also used.

2) or a small dwelling near the fields where it is possible to stay for some time during the summer when the pressure of work requires of one to be on the spot continuously for the harvest or ploughing. We have seen that urban expansion is manifested by the construction of the main house near the fields, displacing the yarsa or yarkhang (sp. dbyar-sa, dbyar-khang) altogether. So the main house becomes a yarsa or yarkhang in its entirety. So, theoretically at least, there is a summer house and a winter house but the latter is commonly abandoned or sublet to migrant workers and the summer house is therefore reorganized into summer and winter floors. The words pulu (pu-lu) and brok ('brog) 1 denote stone shelters up in the high pastures, where those who look after the herds during transhumance reside (mostly women).

II -Construction

The first problem is a choice of site; this should not be a lhu-sa (klu-sa), that is a place sacred to a lhu (klu) or sadag (sa-bdag), from which stems the necessity to consult the onpo (dbon-po) in the first place. If the chosen spot is a lhusa it should either be given up, or a lama called in to do pujas. Whoever fails to take these precautions exposes himself to worse troubles. He will witness the loss of his wealth and illness befall his family. If a lhu is hurt by the builders' pick axes the result will be particularly serious. Most often a plan is not made. The owner discussed the number of rooms he needs, their approximate size and orientation, with the (r)tsikspon (architect). The (r)tsikspon (rtsig-dpon) is left to trace the plan on the ground according to these demands. The onpo (dbon-po) fixes the date for the work to begin. Once the plan is made on the ground, the foundations are sunk. The entire space to be occupied by the house is not dug up, only ditches corresponding to the course of walls. Thus the floor of the ground floor, is the ground itself. There is no cellar.

The depth of the foundation ditches depends on the nature of the terrain: two feet when the ground is hard, up to five feet if it is boggy. The width is usually three feet. The bottom of the ditches is covered with large stones packed together and leveled. Then 1/2 foot is left on either side and a small wall is built to ground level. The space between the sides of the ditch

(1)
Foundations of the wall of a house. a -layer of stones, b -bank of earth in three layers, c -the rest of the ditch filled with earth, d -stone foundations flanked by two earthfilled ditches. The foundations are narrower than the bank of earth. e -wall of the building. This system of reduction also existed for walls far wider at the base, and can still be seen today. The insloping walls give the houses their elegant and gracious appearance. and the wall is then filled. Then the main outside wall is raised on this small wall. This operation is sometimes performed twice. For example, in a 3 foot wide, 2 foot deep ditch, a small wall 1 foot high is erected -leaving 1/2 foot on either side. Then a second wall, also 1 foot high is built, reaching ground level, again leaving foot on either side. The main wall is built on the second wall, again allowing 1\2 foot on either side, which makes it 1 foot thick. These measurements are by no means a rule, only a possible example. The door is raised before the wall (but after the threshold) as the rough and irregular stones must be arranged exactly for the two steps and the lintel. Once the wall is begun, they have to start anew for the windows, also inserted prior to the walls around them for the same reason. Whilst the wall is being built, the door and window frames are blocked up with loose stones so as not to warp under the pressure of the walls under construction. (Fig. 2) A beam, or to be more precise, several beams, connect the lintels of the doors and windows, and are eventually covered with cement. (Fig. 3) The window has only recently been introduced. Before the introduction of glass there were only some small skylights, stopped up with rags or paper. These openings are always present on the ground floor. (Numerous houses in the Zanskar valley still retain this feature.) At any rate windows were always confined to the houses of the king and the nobility. They were closed with decorated wooden latticework.

A particular feature called rapsal (rab-gsal) should be mentioned here. This is a kind of balcony made of wooden latticework reminiscent of the mouharabiehs of Ottoman architecture. Amongst other things the rapsal is an observation post for the household members; in numerous tales the hero sees the enemy or his loved one from the rapsal. The introduction of glass will make the rapsal increasingly obsolete. The main door, which theoretically faces east, is called gyazgo (rgya-sgo). Though thought of as the main door because of its orientation, it is not necessarily the largest or most used one. Many houses are built on a slope, as a result a second door on the mountain side leads directly to the first floor. (Fig 4)

(2)
Building the base of a wall. The two vertical jambs (c), and the horizontal traverse lintel (d), are constructed first, so that the stones of the wall (a), can be as level with the jambs as possible. As the wall is being built, the space between the jambs is filled with stones (b), so that the former do not lean inwards under the pressure of the wall. These stones are removed later.

(3)

The wall is built up to the level of the lintel. The stones have been removed. A chain moulding runs along the length of the wall joining the beams of the doors and windows. The joists rest on this chain moulding. The whole ensemble is then rough cast, and the chain moulding will no longer be visible except above the doors and windows. At the same time the spaces between the stones and the wood are filled in with mortar which is made of fine sieved earth to which some sand has been added. This same mixture is used as plaster, pisé (for enclosure walls), for the floor and the parapet, for balconies and roofs. The door frame is not masked. In the sketch given here, the surround is very simple indeed. There could be a second horizontal beam at the bottom of the door. This may be complicated further by another larger beam as a threshold under the door frame (Tib. mathem) and a lintel above the frame (ya-them).

(4)

A house built against a slope. One can either go downstairs directly or by some stairs from the first floor (called the second floor by Ladakhis). Likewise one can go onto the roof directly (the Ladakhis call the roof third floor, when a house has one of our floors).

Clay, the hardness of which leaves much to be desired, is used as cement. However, houses are frequently rebuilt; 30 -40 years is an average lifespan for a house. The top floor (the second floor if the house is two-storey) is constructed with mud bricks (paku; sp. pag-gu or pa'u2 ), much less expensive than stone, but also much less solid. However, the walls have no more floors to support. When the stone walls of the ground and first floor are finished, the ka (ka), central pillar of the kitchen, is erected. In general there is only one ka in the kitchen and none in the other rooms. However, some kitchens have two, and some larger houses may have a ka in other rooms. Often there may be one or two ka in the chotkhang, but here their sole function is decorative. If the kitchen ka is a tradition which rarely suffers exception, its presence can also be explained in functional terms. The kitchen is the largest room and the central beam (mardung-ma, sp. ma-gdung) is supported by the ka. Sometimes the ka enables two beams to be joined in a capital. When the external walls and ka axe finished, a feast with chang (chang) may be held. Less important transverse beams called burdung (bu-gdung3 ) join the walls, or the walls and the mardung. The spaces between the mardung are filled with small sticks (tralu, sp. gral-bu) and the ceiling is covered with a species of dried grass called yagdzes (sp. yag-rdzas or g.yag-rdzas)4 , which is then covered with earth. This also constitutes the floor of the next storey (fig 5).

(5) The arrangement of beams in a kitchen: (a) the central pillar (ka). (b) capital (kazhu, sp. ka-gzhu). (c) main beam (mardung, sp. ma-gdung). (d) cross beams (rdungma, sp. gdung-ma) (e) wooden beading (tralu, lath work, sp. gral-bu) in the spaces between the cross beams. The sticks are covered with a plant called yagdzes (sp. yag-rdzas or g.yag-rdzas) and earth, which forms the floor of the next storey. The cross beams rest on the chain moulding (fig 3) and more rarely on the stones or the bricks of the wall. The main beam rests on the stones of the wall. The terminology used for beams seems to be a fairly imprecise.

The plan of the second storey is the same as that of the first. The ceilings/floors are not strong enough to support walls above them; thus walls are built on walls. In the case of a three-storey house, one rarely finds that the second floor is built up entirely. Only certain rooms of the first floor can be found again on the third, leaving an empty space in the middle, either facing the open or (6) A simplified plan of a modern house at Chanspa. Above the rooms to the right of the corridor, an extension of the walls of the two rooms is built, thus forming another two rooms on the second storey. The summer kitchen is right above the winter kitchen, but being smaller, one of its walls is erected above the main beam (A), of the winter kitchen. The one hearth is above the other, which means that the ventholes are also aligned in this way. On the other hand the opening (thokskar) above the secondary hearth (mera; me-ra) (B), gives out onto the unbuilt terrace.

sometimes closed off into a patio. Nevertheless there is one exception; it is possible to build a wall above the central rdung-ma in the kitchen. Anyway it is almost a rule that the main vent hole (thokskar; sp. thog-skar or thog-dkar, cf thog, roof and dkar-khung or skar-khung, pronounced (s)karkhung, window) of the kitchen, above the mera (me-ra, see below) leads to an open space on the second floor. For example it is possible to do this by reducing the summer kitchen by half in relation to the winter kitchen, and it is thanks to this device that the thokskar of the mera opens up into the sky. Often it is also protected by a wind break closed off on three sides and on top. On the other hand the two hearths are one above the other and the outlets for the smoke (where there are no chimneys), also called thokskar, are also aligned in this way (Fig 6). This is only one possibility. The summer kitchen may not be above the winter kitchen at all, but above another room. We can see how important wood is in the Ladakhi house. It is the most taxing element of the budget. The wood (willow or poplar) is rare and precious in Ladakh, or else 5 it must be brought by truck from Srinagar. Until the first truck reached Tungri in September 1977 wood had to be transported on horseback in the Zanskar valley.

Perhaps this explains the rarity of wooden staircases. More frequently they are made of stone, filled in underneath and reinforced with beams. The stairs leading to the first floor are sometimes outside. A ladder is frequently placed against the wall and leads directly to the roof. This may also explain the rarity of skorlam (skor-lam) which is a wooden balcony encircling the chotkhang used for ritual circumambulations (skor). This leaves the parapet (charlen; char-len) which surrounds the roof, or, if the second floor is not built up completely, then a parapet is built around all the open sections. It is supported by small beams (tralu; gral-bu) and protrudes about 10 cm from the outside wall. It is surmounted by a stone which is slightly projecting. This stone is painted red or black (Fig 7). Burnt ochre earth is used for the red, the bottoms of kitchen pots are scoured, or the interior of batteries used to obtain the substance used for black (similarly for blackening the hearth or window surrounds). The black band is called nakchu (nakpo: black, chu; water; sp. nag-chu, nag-po, chu), in other words black ink, and the red is called spenma (spen-bad or span-bad 6 ) . In principle the rules are the following: a) nakchu for houses of the laity b) nakchu or spenma for monks' houses (trashak, gra-shag) c) spenma for monasteries, labrang (bla-brang, a kind of hostel belonging to the monastery), and the chotkhang of kings, the kalhon (bka'-blon) and lhonpo (blon-po). d) Black is associated with the laity. The laity may be called mi-nak-pa (mi-nag-pa; black people) but these rules have almost completely fallen into disuse. Certain informants told me that at one period black was reserved for the royal families and the nobility. e) The spenma/nakchu is frequently situated just below the parapet. Sometimes rather than a painted line, it may be composed of fine twigs packed together and embedded in the wall, then painted over. f) This black/red opposition seems to possess a certain importance in Ladakhi civilization. In the archery festivals the target is called bennak (ben, target, here we come across nakpo, nag-po, black, again) and the central part tsaga (sp. tsha-kha) of ochre, the yellow earth which turns red when burnt and is used to colour the tsandos (btsan-mdos)). 5 Willow and poplar are local, but other wood is available from lumberyards that bring wood from Kashmir. 6 According to Hubert Feiglstorfer, "Revealing Traditions in Earthen Architecture : Analysis of Earthen Building Material and traditional constructions in the western Himalaya", in Art and Architecture of Ladakh, edited by J. Bray and E. Lo Bue, Brill, Leiden, 2014, page 383. Rebecca Norman : "What I was told is that spedma/spezma is if you make it out of sticks with the chopped ends; nakchu is black paint anywhere it belongs on a building, along the parapet or around windows; and charlen is the parapet. spen-ma is in Tib dictionaries as tamarisk, including compounds that refer to the red parapet on monasteries, so may be the same word. But Ladakhis make the spedma out of any available sticks, such as leftover tralu, and not just tamarisk."

(7) The end part of a wall at Hemis monastery. The part between the beams is packed with sticks, and the beading is painted red in a monastery, and black in the houses of the wealthy and the nobility.

All that now remains is to apply a coat of fine clay smoothly around the windows, and to paint it black. The remaining walls are whitewashed with lime using a rag attached to the end of a stick. The description of the house as a whole will be complete when I have recalled the elements which are added according to taste and circumstance: tarchen (dar-chen), tarcok (dar-lcog), trashitaling (bkra-shis-khra-ling), sago-namgo (sa-mgo gnam-mgo), sangspor (bsangs-phor), sangskung (sangskhung), described in my article 'The constituent elements of architecture and urbanism in Ladakh' 7 There are also tsandos (btsan-mdos) and the red decorations on the wall; triangles, lines of dots and sometimes swastikas. The head of an ibex (skin, skyin), a goat or any other animal favored by the owner, is used as a decoration above the door.

When the house is finished, religious ceremonies follow. There are three kinds: a) ceremony to displace the pha(z)lha (pha-lha) from the old to the new lhatho (lha-tho) b) Rabnes (rab-gnas), a ceremony. It is concerned with obtaining lha and installing them in the house. c) Zingsek (sbyin-sreg), this ceremony can take place at the inauguration of the house. The purification procedure is the same for a house as for a monastery, when these are overrun by malignant spirits. It is dedicated to a Darmapala (choskyong, chos-skyong). In the case of the Gelukpas the darmapala is Vajrabhairava. 77 Out of print but, it will be soon on HAL.

III -Organisation

An example will enable us to appreciate more fully the arrangement of rooms inside the house. Fig. 8 is the plan of the ground floor of a bourgeois house in Leh. By this I mean a non-peasant house where the ground floor is inhabited and not used as a stable. Leading from the main entrance (gyazgo) is a long corridor (Fig 8), from which a staircase takes us to the floor above. The room (nang) no. 7 is extended into a verandah (no. 9). Nos. 9 and 9a could very well form a separate verandah.

In many Ladakhi houses there is a shelkhang (shel-khang), most frequently on the upper storey. The shelkhang (shel, sp. shel: glass) is a room in a corner of the house with panes of glass on both sides looking out onto the open. It is a gathering place used mostly during the winter months. If the door faces east, conforming to the theoretical rule, then it will be placed in the corner to the left of the main entrance, that is S.E. which ensures maximum sunlight. The actual form of the shelkhang only dates back to the introduction of glass. Previously it was constructed with wooden latticework like the windows and rapsal and was called congsa8 . Our contemporary Western architects have rediscovered the shelkhang which they call 'window in the style of Frank Lloyd Wright' after its inventor, (information Paul Miremont). In our plan we can also have: in 9 a verandah in 9 a shelkhang in 9 a verandah and the room above it a shelkhang in 9 a verandah, there is nothing above 9 and the room above 7 is a shelkhang a final hypothesis which is not excluded is that a room is built above 9 and that above 7 there is a 'semi-shelkhang', that is with one side of glass instead of two. 1 and 4 are simple rooms (nang, sp. nang) and 7 is readily used as a living room (dronkhang, the room khang where one receives the guests dron-po (sp. mgron; this room is also called zabkhang, maybe from gzab9 ). Note that the shelkhang is itself a living room and therefore a particular form of dronkhang or zabkhang. It is one of the rare rooms where there are a few pieces of furniture; low tables (coktse, lcog-rtse), with large square cushions behind them called boldan ('bol-gdan; 'bol-mo means soft), measuring about 1 x 1 m. Frequently they are covered with rugs. But in the poorer houses there will be no boldan, merely some mats. Boldan and choktse are practically the only furniture, for there are no beds (one sleeps on mats or boldan) or cupboards, only niches with crude shelves called staksha10 (the cupboard is replaced by the dzot (mdzod) which we shall return to later). Whether the zabkhang/dronkhang is a shelkhang or an ordinary room, it should always be kept impeccably clean as guests could come in at any time. It is a more formal meeting place than the kitchen, where close friends, relatives and neighbors are received without much ceremony. Sitting in the zabkhang implies a certain effort in dressing up. Access to the washroom (thruskhang, khrus-khang) no 3 is by way of a small alcove, no 2. This is not a general rule. The thruskhang is a small, plain, square room into which pitchers and buckets are brought. Many houses do not have one in which case one washes in the kitchen, or, in the summer, outside.

In our example the latrines (chakra, honorific, decot -n o 10) 11 are not really a part of the house. There is a small room added to the exterior of the building which therefore lacks foundations. The list of rooms given in this example is far from exhaustive, in the more important residences one may find the following: Outside the food dzot (mdzod), another dzot, where balls of wool, tools, pieces of cloth garments and coats are stored. The main agricultural tools such as the plough, are kept on the ground floor. The second dzot is frequently on the second floor.

(8) Plan of a modern house in Leh. This is the kind of house built by young couples nowadays: l -room (nang). 2 -antichamber. 3 -washing room (thrus-khang). 4 -room (nang). 5kitchen (thap-sa/ cansa). 6 -dzot, storeroom with access to the kitchen. 7 -room (nang) which would readily be used as a living room, or for receiving guests (zabkhang). 8 -main entrance (gyaz-go) and corridor. The shel-khang is above 9, if a larger one is required then it is above a) Changkhang (chang-khang); a room for storing chang in earthenware jars, often adjacent to the food dzot. On the occasion of important festivals (marriage, etc) a person called the changma (chang-ma) stands near the changkhang and distributes chang, similarly the dzotma (mdzod-ma) next to the dzot, and the thapma (thab-ma) next to the hearth. They are mainly chosen from within the phaspun. c) Shakhang (sha-khang) a room in which dried meat is stored (sha, sp. sha: meat), or where yak or goat meat is dried. d) Pangnga (bang-nga): a silo where barley is stored. From here a trap door opens out into the room above called pang-khang (bang-khang). The latter is likely to be the dzot or kitchen. e) tangra 12 : stable or sheep pen, etc. This is on the ground floor. Sometimes this is outside the house and may or may not be adjoined to the ground floor. The word stara (rta-ra) may also be used for horses (sta, sp. rta: horse)• The dog's kennel is called khipul (khyi: dog, pul: pul< pu-lu small simple structure). Dogs are more or less obligatory guardians of Ladakhi houses. f) Markhang (mar-khang): room for storing butter (mar, sp. mar). In view of the large quantities consumed in salt tea (gurgur ca sp. gur-gur ja), butter is extremely important. Besides Ladakh is not self-sufficient in this respect. Butter is valuable. The wealth of a house may be expressed in quantities of butter. g) phograks: room where straw 13 (phoma or phugma; phug-ma) is stored. This room is also called pukrak/pugrak (phug-rags).The fodder chunpo (chun-po) is simply left on the roof and parapet (khathok) referred to as the third level even if this is not built (sumthok, gsum-thog).

12 Rebecca Norman : "I spell it dang-rwa because some people in lower Sham pronounce it dangra or dagra, though Leh and Zangskar pronounce it tangra. There is wide variation between regions in the meaning and words for various animal-related structures, but certainly tangra is a common word." 13 According to Das phug-ma means chaff in Tibetan. According ro Rebecca Norman phoma/phugma means straw in Ladakhi, not chaff, and phokrak /phug-rags is where you keep the straw, not proper fodder, which is chunpo and is kept on the roof. chun-po is a Tib word: bundle.

Therefore apart from the latrines (cakra.), the washroom (thruskhang), and the shelkhang which is used as a living room (zabkhang), most of the rooms with a specific usage are these small rooms for the storing of wood (shingkhang; shing-khang), meat (shakhang; sha-khang), food (dzot), textiles and clothes (dzot), grain (pangnga), etc. However the kitchen deserves special mention.

IV -The kitchen

First let us recall briefly what has already been said about the kitchen (cansa or thapsa14 , sp. thabsa, for the main kitchen which we are mainly concerned with here, yarsa for the summer kitchen). The latter term denotes more generally the summer floor, or summer house, there is no specific word for summer kitchen.

(9) .Plan of a kitchen. The black circle stands for the central pillar (ka). ( 1) is the end of the row of seated guests (traljuk), ( 8) is the end of the row of tables (coktse), and (2) is the beginning of this row (tralgo). The guest of honour or the father sits here. (3) is the furthest point of the row; it is the 'end of the house' (khyim-juk). The daughter-in-law of the father also seated at the tralgo (2), sits in front of him on the other side of the hearth. Her place is called thap-ma. (A) is the position of the big pot of drinking water (dik, sp. dig). ( 5) is the secondary hearth (mera). ( 6) is another container, frequently a metal can, for the fluid and semi-fluid leftovers (trhuchu; khru-chu). ( 7) is the daber (da-ber), a wooden partition next to the hearth. This word is also used for the wooden screens masking the lower parts of the windows. The arrows A -B -C, indicate the direction of sweeping. Sweeping itself also follows a hierarchical order. The thapltak (thab-ltag) is found between (2) and ( 9). It is a container for ashes and glowing embers, and is surrounded by a small wall. The person sitting at (2) tralgo, has the privilege of removing the embers through an opening in the hearth on his side, with a metal spade called lcaks-yok. On the other side, the left hand side of the seated woman (thap-ma), a small stone wall (bustak, sbud-ltag) is used for keeping the bellows (butpa, spud-pa). One end of the bellows is fixed into the hearth.

The kitchen is the usual gathering place for the household members, neighbors and visiting relatives. The focal point of the room is the hearth (thap, sp. thab) which I shall describe in detail below. The thap is built against one of the four walls which is lined with shelves (langs; slangs-(ka)), more or less carved. It is surrounded by a line of choktse (low tables), beginning with the tralgo (go, sp. mgo; beginning, of the line; tral, sp. gral) where the nangdak (nang-bdag) is seated (the household head i.e. the oldest man in the male line) and ending at the door (traljuk, sp. gralmjug; end of the line).

(10)Langs, shelves covering the back wall of the kitchen. The hearth is represented here by a simple rectangle, with the thap-ltak in profile on the right, and the bellows (butpa) and bustak on the other side. In the lower part is an empty wooden section (I), where the seated woman helps herself to wood and dung. Enough fuel for everyday needs is kept here (1). This part is called pangong (in some of the large traditional kitchens, there is a small structure specially for keeping fuel, c.f. Mme Pommaret-Imaeda's thesis where it is described in detail). Behind the thap-ltak is a section with three little doors (6), called cakar, where objects of common use are kept, especially those used in spinning. Above, the two shelves are divided into two sections. The one on the left is used for beverages (or tea in particular), and the one on the right for food. So on the shelves above the shakar 15 we find a thermos flask (16), cups (kore) (15), and saucers. The drawings above are the two kinds of teapot; earthenware (tibril) (17), and brass (thagu) (18). A capskyan (chab-rkyan, chang pot 17) could also have been added.

On the shelves to the right are two kinds of container for food; (dik; dig) (9), and (zambu, zangs-bu) (10). Above are plates (thali, Hindi/Urdu word) (12), large metal dishes (tabak or thabak; tha-pag, also lagin, probably a Urdu word itself borrowed from Persian) (11), and soup bowls for kholak (gormo, sgor-mo) (15). small brush for stirring the thukpa called silkya (sil-skya) and a wooden board (tharo could just spell tha-ro) on which paba is placed, are also found here. The brazier on which the teapot is placed, mezlang (me-slang), is often next to the tralgo. A very large dik in one corner of the kitchen is used for storing drinking water, and the churn is placed next to the ka.

(12) The hearth seen from above and from the side. There are two kinds of brazier; zhong is the main one, (b), and tamik (thab-mig) the secondary ones (a), which serve to keep containers warm. Apart from the thap, a secondary hearth, mera (me-ra), is in the centre of the room. It is not a built oven but simply a square hollowed out in the ground. A fire is lit here in winter (during the winter all the family sleeps in the kitchen). Above the mera a large opening, thokskar opens onto the roof. I noticed that in many kitchens rays of sunlight passing through the thokskar fall first on the thap in the morning, and then shift in a straight line, until, in the evening, they fall on the bottom of the wall opposite the thap. I was unable to ascertain whether this was a rule, I was simply told that this ray of light was used as a sundial. Above the thap there is a small thokskar for smoke to escape. However, since their introduction by missionaries in the 19th century, more ventilation has been installed.

The thap is still mostly made of earth. It takes on the appearance of cast iron when it is blackened and polished. The missionaries introduced the metal stove which has the advantage of taking up less space. They are most likely to be found in the summer kitchen. A small mud wall on the outside edge in relation to the seated woman, is called bustak (sbud-ltag). The bellows (butpa; sbud-pa) are kept here. Thus the woman has the bellows on the one hand, and the store of wood and dung on the other side. She stokes the fire by putting the wood in a large hole in front of her. On top of the thap the main opening above the flame is called zhon. Apart from this main source of heat there are two secondary ones called tamik (thab-mig, eye of the thab), used for keeping cooking pots warm. By the tralgo another small wall, less high than the first, delimits a space in which the ashes and cinders are disposed of. This is the work of the nangdak who removes them with a shovel (mekem, me-khyem) and tongs (melen; me-len). This section is called thapltak (thab-ltag). (Fig. 11)

The thap is decorated on the side facing the room. There is a line of swastikas (yundrung; g.yungdrung) above, and a jewel in the middle (norbu; sp. nor-bu) which is a symbol of wealth. Both sides of the norbu are frequently adorned with a palpi (dpal-be'u), one of the eight auspicious Buddhist symbols. A frieze of inversed lotus petals creates a border on the lower level of the thap. Should one recall that the hearth is the seat of a lha, the thap-lha?

The metal stoves are made by the gara (mgar-ba). The earthen ones are not constructed by any particular specialists. Amongst others the (r)tsiks-spon know how to make them. First the (r)tsiksspon draws the outline on the ground. The workers help and hand him clods of earth mixed with 3 parts sand and 2 parts 'stove earth', thap-sa, clay that is. So he builds a parallelepipedal mass. This takes three days. The (r)tsiks-spon then outlines the holes for the fire, the opening for the wood (on the side of the thapma (sp. thab-ma) and the outlet for the cinders (on the side of the thapltak). Then he hollows these out using a metal pipe. The hollowing out can be avoided with another method. This involves inserting pieces of wood whilst the thap is being built. They are then removed leaving empty spaces. The bellows must be carefully plugged in. A special stone is used for polishing. Polishing is considered an important operation as the earth may crack without this. Then the thap is tried out. The air should not be sucked back. It should be directed into the flames. One can always put this right. The surroundings of the thap should always be kept clean. We have already seen how important the than is with respect to the prohibitions relating to the back and the feet. At the New Year offerings of butter, and salutations are made to the thap or rather the thap-lha.

The description of the house is now complete. A few words should be said about the garden wall. It is either made of loose stones on top of each other (nyagra, not a Tibetan word so could be spelled nyag-ra), like those surrounding orchards (bag, Urdu word borrowed from Persian), or of cemented stones or bricks (kyang spelled gyang) 18 . Like the main entrance of the house, the entrance into the garden is called gyazgo 19 .

Translated from French by Maria Phylactou (London School of Economics) Drawing by Lucy Vallauri (CNRS, Aix en Provence) Patrick Kaplanian 18 Rebecca Norman: "kyang is freestanding wall outside, eg surrounding the courtyard. Nyagra is very simple drystone walling, eg between fields. rtsikpa if it"s the wall of a building" 19 I am grateful to Rebecca Norman who helped me a lot in finding the proper spelling of the Ladakhi words. I am using the Wylie system.

pag-gu or pa'u according to S. C. Das, A Tibetan English dictionary, New Delhi 1985 [Calcutta 1902], p. 777. S. C. Das mentions that it is a Ladakhi word. Rebecca Norman suggests pag-bu and adds "Tibetan is only pha-gu". She writes "Leh, Sham, Nubra pronounce it pagbu or pakbu".

mardung (sp.ma-gdung) for the main beam that holds up smaller beams, which are then called burdung (bu-gdung). All beams are generically dungma (gdung-ma).

Rebecca Norman : "I spell it yag-rdzas though g.yag-rdzas would be just as good; in Upper Ladakh where the pronunciation of yag and g.yag would have different tones, they don"t use this word, they say bi-lap instead, so I can"t use their pronunciation as the clue to its spelling. Its Latin name is Stachys tibetica and it"s not a grass at all, but Ladakhis speaking English tend to say "grass" for any plant smaller than a tree. In Leh, the word bilap means this role in roofing, which nowadays can be done with discarded cardboard boxes, whereas yagdze(s) means the specific plant, Stachys tibetica. In Changthang and Nubra, bilap is the name of the plant itself".

Spelling unknown. The word is not used any longer today. People prefer to say rapsal or shelkhang.

in Tibetan, according to Das: 'well behaved, attentive and polite to guests, careful, cautious and also well dressed".

Spelling unknown, maybe stag-sha. The word is not used any longer today. This article was written in 1979.

According to Das, phyag-ra toilet, but the more recent Podgya Tshigdzot Chenmo doesn"t list phyag-ra or chag-ra. Honorific, decot, maybe bde-spyot, but it"s not Tibetan.

Rebecca Norman : "I"ve never heard thapsa for kitchen. Monks sometimes use the Tib word thap-tshang, which in Zangskari might be pronounced thaptsha, but in Leh area it"s not a common or known word"

My article 'The constituent elements of architecture and urbanism in Ladakh'.

see Kaplanian, Les Ladakhi du Cachemire, Paris 1981, pp. 75-77.

Different utensils are hanging from a board on the right; a copper ladle for tea and water (thumbu or thazu), an aluminum ladle for the soup (camca, 3, Hindi/Urdu words like thali), a wooden spoon for the yoghurt (zho) or whey, called zaru (za-ru) (4). Sometimes this is kept in the yoghurt churn (zobker) often found near the ka_. There is also a board for the bapa, a dough made out of boiled tsampa (taro) (8), a stick for mixing the bapa (skya) ( 14) and a kind of small, stiff brush for mixing the soup (silkya) (5). Below this is a large dik (dig) for drinking water (7).

The woman seated in front of the nangdak is very often his daughter-in-law or wife, or failing these, his eldest daughter or sister. The place where the woman sits, in relation to the tralgo and next to the thap is called thapma (thab-ma). In most cases she has her back turned towards the door, form which she is separated by a partition called daber (da-ber). The daber, which is a simple wooden screen, is sometimes replaced by a unit of shelves. (Fig 9)

The fact that the woman has her back turned to the door, and that the daber separates the two, can be explained in two ways: a) We know that the section near the door is the end of the tral called traljuk. As it is rude to have one's back turned, the woman's back is turned as far as possible to the lower strata, next to the door (note that in Fig. 9 she does not do this openly; the door is not directly behind her). b) This impoliteness is mediated by the presence of the daber, which on the other hand protects her from impurity. I will not describe the arrangement of coktse of decreasing height in the tralgo or traljuk, here 16 . Another item of furniture next to the coktse should be notedkacok (ka-lcog) is the name for a group of shelves around the central pillar (ka: pillar, coktse: table). The kacok is rare and only found in the kitchens of large and wealthy households. More common perhaps is the shelf above the door (goltak , sgo-ltag, this is a general term: the riks-sum-gonpo (rigs-gsum-mgon-po) above the gyazgo, rests on the outside of the goltak as well). But the langs is the item of kitchen furniture invested with the greatest importance. Rows of shelves cover the entire wall against which the thap is built, (Fig 10) the langs house all the kitchen utensils. Three levels can be distinguished: a) the lower level is that of the thap. As the thap itself touches, or almost touches the wall, a section of the langs space on the lower level is unusable. At the level of the thapma (to the right on our example) there is a store of wood and dung which is in easy reach of the seated woman, called pangong or pangongs (spelling unknown). The shakar is found at the level of the tralgo, this shuts with small doors. Objects used in weaving the female spindle (phang, sp. phang), the male spindle (skuru ; sku-ru-a short stick or yokshing, yog-shing), the base of the phang called the phangkor which looks like an incense burner, and various other objects are stored here 17 . b) On the second level above the shakar is the place of the teacups (kore; ko-re), saucers and glasses as well as bottles and thermos flasks. Above the thap are the various casseroles (zambu; zangs-bu), such as the dik and kabukma (kha-bug-ma), large plates (tabak, tha-pag), and lagin which are very large dishes in which the dough is kneaded. c) Above the tralgo on the third level, are the chang pots (chabskyan; chab-rkyan) and teapots thragu (khra-gu) if made of metel, often copper (no real spelling found but should be khra-gu), tibril if made of clay (maybe tib-ril), and above the thap are bowls for eating kolak (tsampa, Ladakhi phe (phye), mixed with tea or whey: tara (dar-ba), until a dough is formed) called gormo (sgor-mo) and plates (thali, Urdu word). To the extreme right ladles (thazu, sp. kra-tsu, Tib. thum-bu) are hung. The copper ladles with cylindrical scoops are used for tea and water (camca, Urdu word), the aluminum ones with semispherical scoops are used for food, especially soup (thukpa, thug-pa). The skya (skya) is also hung here. This is a stick used for making paba (pa-ba), a mixture made by boiling tsampa in water. A