Cui Kaixuan

Wenyan Zhang

Jia Liu

X U Cong

Zhao Yicong

Chen Si

Xiao Tian

W U Long-Fei

Caroline Seamount

Characterization and diversity of magnetotactic bacteria from sediments of Caroline Seamount in the western Pacific Ocean *

Keywords: magnetotactic bacteria, Caroline Seamount, abundance, diversity, magnetosome

Magnetotactic bacteria (MTB) are a group of microorganisms capable of orientating and swimming along magnetic fields because they contain intracellular biomineralized magnetosomes composed of magnetite (Fe 3 O 4 ) or/and greigite (Fe 3 S 4 ). They are ubiquitous in freshwater, brackish, and marine habitats, and are cosmopolitan in distribution. However, knowledge of their occurrence and distribution in seamount ecosystems is limited. In this study we investigated the diversity and distribution of MTB in the Caroline Seamount (CM4). The abundance of living MTB at 12 stations varying in depth from 90 to 1 545 m was 1.143.7 × 10 3 ind./dm 3 . Despite diverse shapes of MTB observed, magnetotactic cocci were the dominant morphotype and could be categorized into two types: (i) typical cocci that appeared to have peritrichous flagella; and (ii) those characterized by having a drop-shaped form and one bundle of flagella located at the thin/narrow end of the cell. Transmission electron microscopy (TEM) analysis revealed that the magnetosomes formed by those magnetotactic cocci are magnetite (Fe 3 O 4 ) with octahedral crystal habit. A total of 41 operational taxonomic units (OTUs) of putative MTB (2 702 reads) were acquired from nine stations, based on high-throughput sequencing. Of these, 40 OTUs belonged to the Proteobacteria phylum and one belonged to the Nitrospirae phylum. We found apparent connectivity between the MTB populations on the Caroline and Kexue seamounts, although the diversity of MTB on Caroline was much richer than on the Kexue Seamount. Our results imply that the unique topography of seamounts and other as-yet unclear environmental factors could lead to evolution of different flagella arrangements in magnetotactic cocci, and the occurrence of octahedral magnetite magnetosomes.

INTRODUCTION

Magnetotactic bacteria (MTB) are a group of Gram-negative bacteria that biomineralize unique membrane-enveloped, single magnetic domain, iron oxide (Fe 3 O 4 , magnetite) or/and iron sulfide (Fe 3 S 4 , greigite) nanoparticles termed magnetosomes. Within MTB, magnetosomes act as a compass needle, and the flagellar apparatus enables it to swim along magnetic field lines in a behavior termed magnetotaxis [START_REF] Bazylinski | Magnetosome formation in prokaryotes[END_REF]. MTB are a morphologically, phylogenetically, and metabolically diverse group of prokaryotes [START_REF] Lefèvre | Evolution of the bacterial organelle responsible for magnetotaxis[END_REF]. Diverse morphologies of MTB have been described, including coccus, ovoid, vibrio, rod, spirillum, and multicellular aggregates [START_REF] Farina | Ultrastructure of a magnetotactic microorganism[END_REF][START_REF] Abreu | Candidatus Magnetoglobus multicellularis', a multicellular, magnetotactic prokaryote from a hypersaline environment[END_REF][START_REF] Isambert | Transmission electron microscopy study of magnetites in a freshwater population of magnetotactic bacteria[END_REF][START_REF] Lefèvre | Characterization of Mediterranean magnetotactic bacteria[END_REF]Lin et al. 2009;Lefèvre et al. 2011a). Based on NCBI taxonomy, the MTB are phylogenetically affiliated with diverse phyla of the domain Bacteria, including the Proteobacteria, Nitrospirae, and Planctomycetes phyla, and the candidate Omnitrophica (previously named as candidate division OP3) and Latescibacteria (previously named as candidate division WS3) phyla [START_REF] Lefèvre | Ecology, diversity, and evolution of magnetotactic bacteria[END_REF][START_REF] Lin | A putative greigite-type magnetosome gene cluster from the candidate phylum Latescibacteria[END_REF][START_REF] Kolinko | Single-cell genomics of uncultivated deep-branching magnetotactic bacteria reveals a conserved set of magnetosome genes[END_REF][START_REF] Lin | Diversity and ecology of and biomineralization by magnetotactic bacteria[END_REF]. Recent studies of reconstructed metagenome-assembled MTB genomes have expanded knowledge of the taxonomy of MTB. For example, 168 genomes were retrieved and classified as belonging to 13 bacterial phyla, based on GTDB (Genome Taxonomy Database) taxonomy, and 7 phyla have been classified based on NCBI taxonomy [START_REF] Lin | Expanding magnetic organelle biogenesis in the domain Bacteria[END_REF]. In another study, 38 novel MTB draft genomes were reconstructed, several of which were related to the phyla Elusimicrobia, Candidatus Hydrogenedentes, and Nitrospinae [START_REF] Uzun | Unravelling the diversity of magnetotactic bacteria through analysis of open genomic databases[END_REF]).

MTB are model organisms for investigating biomineralization processes because of their capacity for intracellular production of magnetite or greigite crystals in a process controlled by the magnetosome gene cluster (MGC) [START_REF] Lin | Diversity and ecology of and biomineralization by magnetotactic bacteria[END_REF]. MTB biomineralize diverse shapes of magnetosomes, including octahedral, cubo-octahedral, elongated-prismatic or parallelepipedal, bullet-shaped and pleomorphic forms (Bazylinski et al. 2013a;[START_REF] Amor | Iron-biomineralizing organelle in magnetotactic bacteria: function, synthesis and preservation in ancient rock samples[END_REF]Li et al. 2020a).

Intriguingly, it has been reported that the morphological diversity of magnetosomes is strongly correlated with specific phylogenetic taxa of MTB [START_REF] Pósfai | Phylogenetic significance of composition and crystal morphology of magnetosome minerals[END_REF]Li et al. 2020a;[START_REF] Liu | Diverse phylogeny and morphology of magnetite biomineralized by magnetotactic cocci[END_REF]. For example, cuboctahedral or elongated-prismatic magnetite magnetosomes are synthesized in the groups of the Alpha-, Eta-, and Gamma-proteobacteria of MTB, while bullet-shaped magnetite magnetosomes are produced by the Deltaproteobacteria class, and the phyla of Nitrospirae and Omnitrophica [START_REF] Pósfai | Properties of intracellular magnetite crystals produced by Desulfovibrio magneticus strain RS-1[END_REF]Li et al. 2010a;Lefèvre et al. 2011c;[START_REF] Lin | Metagenomic analysis reveals unexpected subgenomic diversity of magnetotactic bacteria within the phylum Nitrospirae[END_REF][START_REF] Kolinko | Single-cell analysis reveals a novel uncultivated magnetotactic bacterium within the candidate division OP3[END_REF][START_REF] Lefèvre | Novel magnetite-producing magnetotactic bacteria belonging to the Gammaproteobacteria[END_REF][START_REF] Zhou | A novel genus of multicellular magnetotactic prokaryotes from the Yellow Sea[END_REF][START_REF] Lefèvre | Ecology, diversity, and evolution of magnetotactic bacteria[END_REF][START_REF] Zhang | Novel rod-shaped magnetotactic bacteria belonging to the class Alphaproteobacteria[END_REF][START_REF] Li | Crystal growth of bullet-shaped magnetite in magnetotactic bacteria of the Nitrospirae phylum[END_REF][START_REF] Li | Single-cell resolution of uncultured magnetotactic bacteria via fluorescence-coupled electron microscopy[END_REF][START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF][START_REF] Li | Phylogenetic and structural identification of a novel magnetotactic Deltaproteobacteria strain, WYHR-1, from a freshwater lake[END_REF][START_REF] Amor | Iron-biomineralizing organelle in magnetotactic bacteria: function, synthesis and preservation in ancient rock samples[END_REF]Li et al. 2020a;Li et al. 2020b). However, diverse morphologies of greigite crystals, including bullet-shaped, cubo-octahedral, elongated-prismatic, and pleomorphic, only can be synthesized in Deltaproteobacteria MTB [START_REF] Lefèvre | Ecology, diversity, and evolution of magnetotactic bacteria[END_REF].

Magnetotactic cocci were the dominant morphotype of MTB in natural freshwater and marine habitats [START_REF] Spring | Phylogenetic affiliation and ultrastructure of uncultured magnetic bacteria with unusually large magnetosomes[END_REF]Flies et al. 2005a;Lin et al. 2009;[START_REF] Du | Characterization of uncultivated magnetotactic bacteria from the sediments of Yuehu Lake, China[END_REF] including sediments in lakes (Lin et al. 2009), rivers [START_REF] Kozyaeva | Diversity of magnetotactic bacteria of the Moskva River[END_REF], estuaries [START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF], intertidal zones [START_REF] Pan | Characterization of a homogeneous taxonomic group of marine magnetotactic cocci within a low tide zone in the China Sea[END_REF][START_REF] Chen | Unexpected diversity of magnetococci in intertidal sediments of Xiaoshi Island in the North Yellow Sea[END_REF], lagoons [START_REF] Du | Characterization of uncultivated magnetotactic bacteria from the sediments of Yuehu Lake, China[END_REF], continental shelves [START_REF] Xu | Distribution and diversity of magnetotactic bacteria in sediments of the Yellow Sea continental shelf[END_REF], and seamounts [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]. Magnetotactic cocci belonged to the order Magnetococcales have recently been transferred from the Alphaproteobacteria to "Candidatus Etaproteobacteria", based on ribosomal proteins, MTB core genes, whole genome analysis of the MO-1 and MC-1 strains, and a large-scaled identification and phylogenetic analysis on twenty novel magnetotactic cocci [START_REF] Ji | The chimeric nature of the genomes of marine magnetotactic coccoid-ovoid bacteria defines a novel group of Proteobacteria[END_REF][START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF][START_REF] Lin | Genomic expansion of magnetotactic bacteria reveals an early common origin of magnetotaxis with lineage-specific evolution[END_REF][START_REF] Liu | Diverse phylogeny and morphology of magnetite biomineralized by magnetotactic cocci[END_REF]. Many novel magnetotactic cocci species have been described as having differences in magnetosome chain configurations, and the number, crystal size, and morphology of magnetosomes [START_REF] Meldrum | Electron microscopy study of magnetosomes in a cultured coccoid magnetotactic bacterium[END_REF][START_REF] Lefèvre | Isolation and characterization of a magnetotactic bacterial culture from the Mediterranean Sea[END_REF][START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF][START_REF] Liu | Diverse phylogeny and morphology of magnetite biomineralized by magnetotactic cocci[END_REF]. For instance, various models of MTB chain configuration have been reported among the cocci, including single chain, double separated chains, double parallel chains, double bundles containing two parallel chains in each bundle, particle aggregates, and other irregular forms [START_REF] Liu | Diverse phylogeny and morphology of magnetite biomineralized by magnetotactic cocci[END_REF]. Elongated prismatic and (elongated) cuboctahedral magnetite crystals have commonly been reported to occur in the order Magnetococcales and had a relatively consistent morphology [START_REF] Pósfai | Phylogenetic significance of composition and crystal morphology of magnetosome minerals[END_REF]). However, a unique form of (elongated) octahedral magnetosomes have been described in the uncultured freshwater magnetotactic coccus strains SHHC-1 and MYC-5, the former having the crystals arranged in two double chains and the latter in two chains [START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF]Liu et al. 2020).

Similar crystals arranged in a chain have also been observed in the cultured MTB strain Magnetofaba australis IT-1, which was isolated from sediments of a brackishmarine coastal lagoon [START_REF] Araujo | Combined genomic and structural analyses of a cultured magnetotactic bacterium reveals its niche adaptation to a dynamic environment[END_REF].

Magnetotactic bacteria are ubiquitous in natural environments, and peak in abundance at the oxicanoxic transition zone (OATZ) in sediments or chemically stratified water columns in freshwater, brackish, marine, and hypersaline habitats [START_REF] Bazylinski | Magnetosome formation in prokaryotes[END_REF][START_REF] Moskowitz | Magnetic properties of marine magnetotactic bacteria in a seasonally stratified coastal pond (Salt Pond, MA, USA)[END_REF]Bazylinski et al. 2013a). Recent investigations of MTB diversity at the Kexue Seamount have extended our knowledge of the adaptability of MTB to this tropical oligotrophic marine habitat [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]. Seamounts have numerous unique topographic characteristics including acceleration and recirculation of currents [START_REF] Dower | A strong biological response to oceanic flow past Cobb Seamount[END_REF], Taylor columns [START_REF] Hogg | On the stratified Taylor column[END_REF][START_REF] Genin | Dynamics of temperature and chlorophyll structures above a seamount: An oceanic experiment[END_REF], and internal waves [START_REF] Kunze | Abyssal mixing: Where it is not[END_REF] that potentially support diversity hotpots in oligotrophic oceans [START_REF] Mendonça | Is there a seamount effect on microbial community structure and biomass? The case study of Seine and Sedlo seamounts (Northeast Atlantic)[END_REF]. The Kexue Seamount (also designated M2) is situated at the junction of the Yap and Mariana trenches, where complex dynamic hydrological variations can occur dramatically. Intriguingly, 16 novel MTB species specific to this seamount were identified, and phylogenetic analysis showed endemic adaptation of the MTB to the seamount. Some of the magnetotactic cocci from this seamount have the most sophisticated flagellar apparatus known, involving 19 flagella organized in a 3:4:5:4:3 array enveloped in a flagellar bundle [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]. However, studies of the distribution, diversity, and characterization of MTB from seamount ecosystems remain limited. In this study, sediments were collected from the Caroline Seamount (CM4) in the western Pacific Ocean. Various shapes of MTB were identified using transmission electron microscope (TEM) investigations. The dominate MTB population was magnetotactic cocci that formed magnetite-type magnetosomes with octahedral morphology. Analysis using high-throughput 16S rRNA sequencing indicated the occurrence at this seamount of 41 putative MTB operational taxonomic units (OTUs) affiliated to the phyla Proteobacteria and Nitrospirae. We further compared the diversity and characteristics of MTB between the Caroline and Kexue seamounts, and discussed possible explanations for the specificity of MTB and their magnetosomal biomineralization in these seamount habitats.

MATERIAL AND METHOD

Optical and electron microscopy

MTB in the sediments were enriched magnetically for observation on aboard immediately after sampling. Each plastic bottle was shaken to mix the sediment and seawater, then two magnets with opposite sides were attached to the outside of the bottle adjacent to the interface of the seawater and sediment. After 40 min the MTB that concentrated at the interface adjacent to the magnets were removed using a Pasteur pipette and transferred into a clean 1.5 ml tube. The MTB were inspected and counted using the hanging drop technique [START_REF] Schüler | The biomineralization of magnetosomes in Magnetospirillum gryphiswaldense[END_REF]) and an Olympus CX31 microscope. The abundance of MTB was calculated according to the formula A = N/V (A: abundance; N: number of MTB; V: volume of sediment), as previously described [START_REF] Xu | Distribution and diversity of magnetotactic bacteria in sediments of the Yellow Sea continental shelf[END_REF].

Subsequently, the enriched MTB were purified using the modified race-track method with a 1 ml pipette tip to collect MTB cells [START_REF] Wolfe R S | A 'capillary racetrack' method for isolation of magnetotactic bacteria[END_REF]Li et al. 2010b) and examined with TEM observations. Approximately 5 μl purified cells from the bottom of tube was deposited on a carbon-coated copper TEM grid and the grid was washed with Milli-Q water, then dried in air. The morphology of cells and the magnetosomes was investigated using a Hitachi HT7700 TEM operating at 100 kV. Cell size and cell diameter, and the length and width of magnetosome particles were measured from the TEM images of MTB. The detailed morphology, and the composition and crystal structure of magnetosomes were examined using high-resolution transmission electron microscopy (HRTEM; JEM-2100, JEOL) in a system equipped with energy dispersive X-ray spectroscopy (EDXS) operating at 200 kV.

DNA extraction, 16S rRNA gene sequencing, and dataset analysis

Genomic DNA was extracted from 5 g of sediments following the modified methods described by [START_REF] Kvist | Specific single-cell isolation and genomic amplification of uncultured microorganisms[END_REF]). The genomic DNA was purified using the Wizard @ DNA Clean-up System (Promega), following the manufacturer's protocol. The hypervariable region V3V4 of the bacterial 16S rRNA gene was amplified using the bar-coded universal primers 338F (5′-ACTCCTACGGGAGGCAGCA-3′) and 806R (5′-GGACTACHVGGGTWTCTAAT-3′).

Paired-end reads were generated using the Illumina MiSeq platform, and were overlapped using FLASH (Fast Length Adjustment of Short reads, version 1.2.11) [START_REF] Magoč | FLASH: fast length adjustment of short reads to improve genome assemblies[END_REF]. High quality reads were clustered into OTUs (operational taxonomic units) using UPARSE [START_REF] Edgar | UPARSE: highly accurate OTU sequences from microbial amplicon reads[END_REF] with a 97% threshold, and UCHIME (version 4.2.40) was used to filter and remove chimeras [START_REF] Edgar | UCHIME improves sensitivity and speed of chimera detection[END_REF]. MTB were identified using BLAST and the NCBI nt database. The alignment of MTB sequences was performed using CLUSTAL X (version 2.0) with manual correction [START_REF] Larkin | Clustal W and Clustal X version 2.0[END_REF]. A phylogenetic tree was constructed using MEGA (version 7.0.26) software via the neighbor-joining method [START_REF] Saitou | The neighbor-joining method: A new method for reconstructing phylogenetic trees[END_REF]. Bootstrap values were calculated based on 1000 replicates.

RESULT

Sampling stations and the distribution of MTB in sediments of the Caroline Seamount

The Caroline Seamount (CM4) is located approximately 129 km to the southeast of the Kexue Seamount, and they are separated by the Mariana Trench (Fig. 1). Optical microscopy observations were performed immediately following magnetic enrichment of MTB. Living MTB cells were observed in samples from 12 of the 13 stations, and were present at an average abundance of 1.5 × 10 4 ind./dm 3 (1.143.7 × 10 3 ind./dm 3 ), with magnetotactic cocci being the dominant morphotype. However, no live MTB were observed in samples from the deepest station CM4-00, which was far from the summit area of the Caroline Seamount at a depth of 2 805 m (Fig. 2a).

MTB were mainly detected on the north, south, and east slopes of the Caroline Seamount (Fig. 2a). The average abundance of MTB in the northern region (including stations CM4-7, CM4-6, CM4-6-1, and CM4-5) was 2.4 × 10 4 ind./dm 3 , and was greater than in the southern (1.6 × 10 4 ind./dm 3 ; stations CM4-9-1, CM4-9, and CM4-11), western (7.7 × 10 3 ind./dm 3 ; station CM4-8 only), and eastern (7.3 × 10 3 ind./dm 3 ; stations CM4-2-1, CM4-10, CM4-2, and CM4-4) regions. The vertical distribution of MTB abundance was illustrated by three groups defined according to the water depth and the dissolved oxygen in the seawater (Fig. 2b). Above the 200 m layer (near the euphotic layer), sediments were sampled at station CM4-9-1 only (90 m depth), which had a MTB abundance of 1.4 × 10 4 ind./dm 3 . In the 2001 000 m layer (twilight zone) there were seven stations that had an average MTB abundance of 1.5 × 10 4 ind./dm 3 . In this layer the number of MTB at the various stations decreased slightly with increasing water depth. Below 1 000 m (the bathypelagic layer) there were four stations that had an average MTB abundance of 1.5 × 10 4 ind./dm 3 . In this layer, the abundance tended to increase with increasing water depth, and the abundance was particularly high at 1 545 m depth (station CM4-7). Nevertheless, the highest and lowest abundances of MTB both occurred at depths beyond 1000 m: 4.4 × 10 4 ind./dm 3 at station CM4-7 (1 545 m depth) and 1.1 × 10 3 ind./dm 3 at station CM4-11 (1 423 m depth). The most abundant station CM4-7 is located in an oxic-anoxic transition region with a dissolved oxygen content of 3 mg/L (Fig. 2b).

Diverse morphologies of MTB and characterization of magnetosomes

Using TEM, diverse morphologies of MTB (coccus, vibrio, and spirillum) were observed (Fig. 3) in the sediments of merely six stations of the Caroline Seamount in situ (Table S1), but magnetotactic cocci were the dominant morphology. Four types of MTB were categorized based on characteristics including the morphology of cells, the flagellar apparatus, and the magnetosome shapes. The first and most abundant type was typical cocci (Fig. 3a1) having an average diameter of 1.5 ± 0.4 μm (n = 38); one of these appeared to have peritrichous flagella (approximately 35) that were distributed over the cell (Fig. 3a1). The second type was drop-shaped cocci that had numerous flagella in a tuft at one end of the cell (Fig. 3b1). They had an average cell size of 2.1 ± 0.3 × 1.7 ± 0.3 μm (n = 11), and the flagella length varied from 5.3 to 26.2 μm, which exceeded the cell length by a factor of 5.7 in average (the longest flagellum is 9.8 times larger than the corresponding length of the cell). Magnetotactic spirillum (Fig. 3c) and vibrio (Fig. 3d) cells comprised the other two MTB categories, having cell sizes of 4.2 × 0.4 μm (n = 1) and 2.0 × 0.4 μm (n = 1), respectively. of the orange framed area of e1. The corresponding indexed Fast Fourier transform (FFT) pattern of the octahedral magnetosome particle (e3). EDXS analysis of magnetosomes (f). Scale bars are 2 μm in a1 and b1; 1 μm in c1; 0.5 μm in d1; 200 nm in a2, b2, and c2; 100 nm in d2; 10 nm in e1; and 5 nm in e2.

The magnetosomes within the MTB cells were all organized in chains having diverse arrangements. Most magnetotactic cocci biomineralized a single magnetosome chain in each cell (Fig. 4a), while others biosynthesized two parallel (Fig. 4b) or intertwining (Fig. 4c) magnetosome chains. Three chain forms were observed in some cocci (Fig. 4d). In the spirillum and vibrio, the magnetosome particles were arranged as a single chain along the long axis (Fig. 3c1 and3d1).

Two main morphologies of magnetosome were observed including the octahedral and prismatic shapes (Fig. 3a2d2). The average sizes of the octahedral magnetosomes in these three types of MTB were 57.3 ± 11.4 × 53.9 ± 10.4 nm (n = 554), 60.3 ± 12.9 × 56.6 ± 12.4 nm (n = 204) and 48. 1 ± 4.8 × 45.3 ± 4.3 nm (n = 22), respectively, and the average width/length ratio of these MTB types was 0.94 ± 0.04 (n = 780). The magnetosome crystals in the vibrio cells were predominantly elongated prismatic, and were 66.9 ± 3.9 × 53.0 ± 3.2 nm in size and had a width/length ratio of 0.79 ± 0.01 (n = 5). HRTEM and EDXS analysis indicated that all magnetosomes types analyzed were composed of magnetite (Fe 3 O 4 ).

Phylogenetic diversity of MTB in sediments of the Caroline Seamount

Sufficient DNA for analysis was extracted from sediments from nine stations (CM4-2, CM4-5, CM4-6, CM4-7, CM4-8, CM4-9, CM4-10, CM4-11, and CM4-00; depth range: 6122 805 m). High-quality 16S rRNA gene sequences for each station ranging from 35 523 to 46 743 were retrieved from the raw data. The rarefaction curves indicated that the sequencing depths were sufficient, and the sequencing results were reliable. These reads were classified into 2 1843 301 OTUs, based on a threshold of 97% sequence similarity (Tindall et al. 2010). In total, 41 OTUs (2 702 reads) were affiliated with MTB, based on a BLAST search of the NCBI nt database (Table 1 and Fig. 5). Among these putative MTB sequences, 1732 OTUs of putative MTB were detected at each station (Fig. 6a). The largest number of putative MTB OTUs (32) occurred at 1 376 m depth at station CM4-8, while the lowest value (17) occurred at 680 m depth at station CM4-5. The maximum number of MTB reads (557) was found at station CM4-8 (1 376 m depth), and the next greatest number of reads (541) was found at station CM4-9 (612 m depth). The lowest number of reads ( 165) was found at station CM4-6 (944 m depth), and the second lowest number (172) was found at station CM4-00 (2 805 m depth) (Fig. 6b).

Table 1 MTB OTUs, reads, and abundances at nine stations on the Caroline Seamount

MTB OTUs and reads were determined using next generation sequencing. The MTB abundance (× 10 3 ind./dm 3 ) was calculated based on microscopy observations of live MTB. All the putative MTB OTUs were related to the Alphaproteobacteria, except for OTU4156 and OTU1871 (Fig. 5). Based on the most up-to-date NCBI taxonomic database, OTU4156 (four reads) and OTU1871 (seven reads) were the closest to uncultured Magnetococcus clone OTU9 (MF099880) belonging to "Candidatus Etaproteobacteria", and "Candidatus" Magnetoovum mohavensis strain LO-1 (GU979422) belonging to the phylum Nitrospirae, respectively. Among Remarkably, the most common five OTUs, including OTU102 (718 reads), OTU154 (432 reads), OTU356 (190 reads), OTU94 (155 reads), and OTU594 (139 reads), accounted for 60.5%

(1 623 reads) of the total MTB reads. They all belonged to the genus Magnetospira, and were distributed among almost all the nine stations on the Caroline Seamount; the exception was OTU594, which was not detected at station CM4-7 (Fig. 6c). The MTB reads data were transformed logarithmically.

DISCUSSION

Based on direct microscope counts of MTB, their abundance in sediments of the Caroline

Seamount averaged approximately 1.5 × 10 4 ind./dm 3 , which is higher than the average abundance in sediments of the continental shelf of the Yellow Sea (290 ind./dm 3 in summer; 130 ind./dm 3 in winter) [START_REF] Xu | Distribution and diversity of magnetotactic bacteria in sediments of the Yellow Sea continental shelf[END_REF], but is orders of magnitude lower than the abundance of MTB at a seamount station (4 × 10 5 ind./dm 3 at site 1 726) in the South Atlantic Ocean [START_REF] Petermann | Detection of live magnetotactic bacteria in South Atlantic deep-sea sediments[END_REF], in the Mediterranean Sea (10 5 10 6 ind./dm 3 in summer) [START_REF] Lefèvre | Characterization of Mediterranean magnetotactic bacteria[END_REF], and in intertidal sediments of the Yellow Sea including at Lake Yuehu (10 6 10 7 ind./dm 3 ) [START_REF] Du | Characterization of uncultivated magnetotactic bacteria from the sediments of Yuehu Lake, China[END_REF] and Xiaoshi Island (10 7 10 8 ind./dm 3 ) [START_REF] Chen | Unexpected diversity of magnetococci in intertidal sediments of Xiaoshi Island in the North Yellow Sea[END_REF]. Notably, the MTB abundance at the Caroline Seamount was much higher than that at the Kexue Seamount (54.6 ind./dm 3 ); these seamounts are adjacent to each other but separated by the Mariana Trench [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF].

Previous studies have suggested that many MTB populations have the ability to fix nitrogen, as they contain the full suite of nif genes in their genomes [START_REF] Bazylinski | Nitrogen fixation (acetylene reduction) in Aquaspirillum magnetotacticum[END_REF][START_REF] Bazylinski | N 2 -dependent growth and nitrogenase activity in the metal-metabolizing bacteria, Geobacter and Magnetospirillum species[END_REF][START_REF] Schübbe | Complete genome sequence of the chemolithoautotrophic marine magnetotactic coccus strain MC-1[END_REF]Bazylinski et al. 2013b). Recently, the nap, nar, and nir genes were found in Mcas genome (strain MYR-1, Nitrospirae phylum), which also implied that the magnetotactic Mcas strain has the potential ability to transform nitrate to N 2 /NH 4 + [START_REF] Lin | Genomic insights into the uncultured genus 'Candidatus Magnetobacterium' in the phylum Nitrospirae[END_REF]Li et al. 2020c). Investigation of the distribution of nutrients in the euphotic zone (0200 m) at the Kexue (also designated M2) and Caroline (also designated C4) seamounts has recently indicated that nitrogen limitation at the Caroline Seamount (N:P = 13.5:1) was less than at the Kexue Seamount (N:P = 3.7:1) [START_REF] Ma | Environmental characteristics in three seamount areas of the Tropical Western Pacific Ocean: Focusing on nutrients[END_REF]). Thus, it is possible that the greater abundance of MTB at the Caroline Seamount contributes to this phenomenon, although further investigation of this is required.

Based on high-throughput 16S rRNA sequencing analyses, the dominant group of MTB at the Caroline Seamount was related to the Magnetospira, while magnetotactic cocci were the most abundant group in the intertidal sediments of Yuehu Lake [START_REF] Zhang | Diversity of magnetotactic bacteria in intertidal sediments of Lake Yuehu, Rongcheng[END_REF], and Nitrospirae MTB dominated in sediments of the Yellow Sea continental shelf [START_REF] Xu | Distribution and diversity of magnetotactic bacteria in sediments of the Yellow Sea continental shelf[END_REF]. Although MTB OTUs affiliated to Magnetospira were the dominant groups at both the Kexue and Caroline seamounts, the communities of MTB in the sediments of the Caroline Seamount were more complex and diverse (Fig. 7a). At the Kexue Seamount, [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF] S2.

The data suggest that the diversity of MTB at the Caroline Seamount was richer than at the Kexue Seamount, but lower than in the Yellow Sea and Yuehu Lake. Discrepancies in the community compositions of MTB may be influenced by the environmental characteristics in the various habitats. Biogeographic studies have suggested that environments heterogeneous for factors including salinity, temperature, nitrate, or sulfur compounds may be responsible for differences in the abundance or community composition of MTB [START_REF] Martins | Salinity dependence of the distribution of multicellular magnetotactic prokaryotes in a hypersaline lagoon[END_REF][START_REF] Postec | Magnetotactic bacteria in microcosms originating from the French Mediterranean Coast subjected to oil industry activities[END_REF]Lin et al. 2012b;[START_REF] Martins | Spatiotemporal distribution of the magnetotactic multicellular prokaryote Candidatus Magnetoglobus multicellularis in a Brazilian hypersaline lagoon and in microcosms[END_REF][START_REF] Lin | Integrating niche-based process and spatial process in biogeography of magnetotactic bacteria[END_REF][START_REF] Silva | Genome-wide identification of essential and auxiliary gene sets for magnetosome biosynthesis in Magnetospirillum gryphiswaldense[END_REF].

Although the diversity of MTB at the Caroline Seamount was richer than at the Kexue Seamount, 11 MTB OTUs were shared between the two seamounts (Fig. 7b), accounting for 26.8% and 52.4% of the total MTB OTUs at these two seamounts, respectively. The reads of shared MTB OTUs accounted for 63.6% (1 719 reads) and 54.8% (619 reads) at the Caroline and Kexue seamounts, respectively. More interestingly, among 11 shared MTB OTUs, four OTUs are the most common for Caroline Seamount (OTU102, 154, 356 and 594) which correspond to OTU1697 (third most common), 2037 (most common), 684 (thirteenth most common) and 675

(fifth most common) for Kexue Seamount, respectively. This finding suggests that the dominant MTB populations were consistent between the two seamounts. In addition, the phylogenetic analyses showed that most of the shared MTB OTUs were clustered into a single large branch in the Alphaproteobacteria. Notably, these two seamounts are both shallow [START_REF] Genin | Bio-physical coupling in the formation of zooplankton and fish aggregations over abrupt topographies[END_REF], with the distance from summit to the sea surface being < 200 m, and the sediment at both is mainly composed of coral and foraminiferan sands (Fig. S1; [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]. The similar geological properties and hydrological conditions of the seamounts may be significant in determining the occurrence of MTB. Therefore, it is reasonable to infer that there is population connectivity between these two seamounts, at least for the MTB community. TEM observations showed that diverse morphotypes of MTB, including cocci, vibrio, and spirillum forms, were present in enrichments of the samples collected from the Caroline Seamount.

Magnetotactic cocci were the dominant morphology, which was a finding consistent with previous reports [START_REF] Spring | Phylogenetic affiliation and ultrastructure of uncultured magnetic bacteria with unusually large magnetosomes[END_REF]Flies et al. 2005b;Lin et al. 2009;[START_REF] Lin | Uncultivated magnetotactic cocci from Yuandadu Park in Beijing, China[END_REF][START_REF] Du | Characterization of uncultivated magnetotactic bacteria from the sediments of Yuehu Lake, China[END_REF][START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF][START_REF] Xu | Distribution and diversity of magnetotactic bacteria in sediments of the Yellow Sea continental shelf[END_REF]. Based on previous studies, most magnetotactic cocci affiliated to the Proteobacteria phylum have two tufts of flagella. For example, both Magnetococcus marinus MC-1 (Bazylinski et al. 2013b) and magnetotactic ovoid strain MO-1 [START_REF] Zhang | Complex spatial organization and flagellin composition of flagellar propeller from marine magnetotactic ovoid strain MO-1[END_REF] have two sheathed bundles of flagella, while magnetotactic cocci strains IT-1 [START_REF] Araujo | Combined genomic and structural analyses of a cultured magnetotactic bacterium reveals its niche adaptation to a dynamic environment[END_REF], SHHC-1 [START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF], and QHL [START_REF] Pan | Characterization of a homogeneous taxonomic group of marine magnetotactic cocci within a low tide zone in the China Sea[END_REF] have two bundles of lophotrichous flagella lacking a sheath. At the Kexue Seamount, one type of magnetotactic cocci having two bundles of flagella was found, with the 19 flagella in each bundle arranged in a 3:4:5:4:3 array [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]; this is unlike MO-1, which has only seven flagella [START_REF] Ruan | Architecture of a flagellar apparatus in the fast-swimming magnetotactic bacterium MO-1[END_REF]. It has been speculated that the more complex flagellar assembly is the result of adaptation to the seamount environment [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]). In the present study we observed magnetotactic cocci having putative peritrichous flagella (It remains possible that the spread of a single bundle of flagella may have given the appearance of peritrichous flagella) (Fig. 3a1), and drop-shaped cocci having a single bundle of flagella (Fig. 3b1). MTB affiliated to the Nitrospirae phylum, including the large rod "Candidatus Magnetobacterium casensis" [START_REF] Lin | Genomic insights into the uncultured genus 'Candidatus Magnetobacterium' in the phylum Nitrospirae[END_REF], the watermelon-shaped MWB-1 (Lin et al. 2012a), and the large ovoid LO-1 (Lefèvre et al. 2011a) have been reported to have single bundles of flagella. Magnetotactic cocci having two bundles of flagella have been reported

as one of the fastest natural micro-swimmers [START_REF] Bente | High-speed motility originates from cooperatively pushing and pulling flagella bundles in bilophotrichous bacteria[END_REF]). These findings imply that having a single bundle of flagella is sufficient to enable motility of MTB at the Caroline Seamount.

During sampling of sediments from this seamount using the ROV "Faxian", the occurrence of strong ocean bottom currents was evident, and these may cause the surface sediment to drift. In addition, seamount slope topography is known to affect the spatial distribution of sediments. Thus, it is likely that the MTB inhabiting the Caroline Seamount surface sediment can move easily because of ocean currents and the seamount slope, which could result in the evolution of single bundle of flagella.

Although the properties of magnetosomes are controlled by genes in the MTB, there are some evidences that they can be influenced by environmental conditions (see the recent review by [START_REF] Moisescu | The effect and role of environmental conditions on magnetosome synthesis[END_REF]. For example, Fe uptake rates and pH seem to affect the size and morphology of magnetite crystals in the type strain of Magnetospirillum gryphiswaldense MSR-1 [START_REF] Faivre | Environmental parameters affect the physical properties of fast-growing magnetosomes[END_REF][START_REF] Moisescu | Iron uptake kinetics and magnetosome formation by Magnetospirillum gryphiswaldense as a function of pH, temperature and dissolved iron availability[END_REF], and the size of magnetosomes in M. magneticum strain AMB-1 varies with variations in the oxygen concentration or magnetic field intensity [START_REF] Wang | Effects of hypomagnetic field on magnetosome formation of Magnetospirillum magneticum AMB-1[END_REF][START_REF] Popa | Effect of oxidative stress on the growth of magnetic particles in Magnetospirillum magneticum[END_REF][START_REF] Li | Environmental factors affect magnetite magnetosome synthesis in Magnetospirillum magneticum AMB-1: Implications for biologically controlled mineralization[END_REF][START_REF] Moisescu | The effect and role of environmental conditions on magnetosome synthesis[END_REF]. In culture, Desulfamplus magnetovallimortis strain BW-1 synthesizes bullet-shaped magnetite magnetosomes in the presence of < 0.3 mM sulfide, and roughly rectangular greigite magnetosomes when the sulfide concentration is > 0.3 mM (Lefèvre et al. 2011b). In the present study, octahedral magnetite magnetosomes were found to occur in magnetotactic cocci and the magnetotactic spirillum (Fig. 3).

And among living MTB reported elsewhere, only few appear to be able to synthesize octahedral magnetite magnetosomes, including Magnetofaba australis IT-1, magnetotactic coccus strains SHHC-1 and MYC-5, and an unclassified magnetotactic spirillum from a pond [START_REF] Vali | Magnetotactic bacteria and their magnetofossils in sediments[END_REF][START_REF] Araujo | Combined genomic and structural analyses of a cultured magnetotactic bacterium reveals its niche adaptation to a dynamic environment[END_REF][START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF]Liu et al. 2020) Intriguingly, the dominant magnetotactic cocci at the Kexue Seamount without growing in the bottles also synthesized octahedral magnetite crystals [START_REF] Liu | Bacterial community structure and novel species of magnetotactic bacteria in sediments from a seamount in the Mariana volcanic arc[END_REF]. It is notable that both the IT-1 and SHHC-1 strains appear to have a greater adaptability to changing environments, based on genomic data for IT-1 and the co-occurrence of various magnetosome forms in individual SHHC-1 cells [START_REF] Araujo | Combined genomic and structural analyses of a cultured magnetotactic bacterium reveals its niche adaptation to a dynamic environment[END_REF][START_REF] Zhang | Magnetotactic coccus strain SHHC-1 affiliated to Alphaproteobacteria forms octahedral magnetite magnetosomes[END_REF]). As noted above, the sediments at both seamounts are mainly composed of unconsolidated coral and foraminiferan sands (Fig. S1), which can easily drift in ocean currents.

Thus, it is possible that unstable habitats result in an increase in the biomineralization of octahedral magnetosomes by MTB. Further research should be undertaken to test this hypothesis.

In contrast, octahedral magnetofossils seem to be common and the main magnetosome type in deep sea sediments [START_REF] Vali | Magnetotactic bacteria and their magnetofossils in sediments[END_REF][START_REF] Yamazaki | Organic carbon flux controls the morphology of magnetofossils in marine sediments[END_REF][START_REF] Dong | The detection of magnetotactic bacteria in deep sea sediments from the east Pacific Manganese Nodule Province[END_REF][START_REF] Yamazaki | Dependence of bacterial magnetosome morphology on chemical conditions in deep-sea sediments[END_REF][START_REF] He | Magnetofossil abundance and diversity as paleoenvironmental proxies: A case study from southwest Iberian margin sediments[END_REF]Li et al. 2020d) and especially red clay [START_REF] Yamazaki | Abundant bacterial magnetite occurrence in oxic red clay[END_REF][START_REF] Usui | Changing abundance of magnetofossil morphologies in pelagic red clay around Minamitorishima, western North Pacific[END_REF]. In red clay, octahedral magnetofossils were found to be associated with high oxygen concentrations, inferring that some MTB species that synthesize octahedral magnetosomes may be oxygen tolerant [START_REF] Yamazaki | Dependence of bacterial magnetosome morphology on chemical conditions in deep-sea sediments[END_REF]. Therefore, the MTB living in unstable seamount sediments may be subject to high oxygen concentrations, leading to the domination of octahedral magnetosomes in some MTB species.

CONCLUSION

In this study we described the diversity, characteristics, and distribution of MTB from the Caroline Seamount (CM4). Based on TEM observations, magnetotactic cocci were the dominant morphotype. Among the typical MTB cocci, one type appeared to have peritrichous flagella (approximately 35); the other type of coccoid cells showed drop-shaped, and had a single bundle of flagella approximately a factor of 5.7 longer than the cell diameter in average. The dominant magnetosome morphology biomineralized in most MTB individuals with octahedral crystal habit;

this study is the first to report the occurrence of octahedral magnetite particles among the diverse species of MTB living in the same seamount habitat. It was inferred that the biomineralization of magnetosome magnetite was related to both the species and environmental parameters.

High-throughput 16S rRNA sequencing identified 41 putative MTB OTUs belonging to two phyla, Proteobacteria and Nitrospirae. Comparison of MTB diversity between the Caroline and Kexue seamounts suggested that there is both commonality (indicating connectivity) and specificity in terms of the MTB populations on these two seamounts.

DATA AVAILABILITY STATEMENT

All data generated and/or analyzed during the study are available from the corresponding author on reasonable request.

2. 1

 1 Sediment sampling Sediment samples were collected in the tropical western Pacific Ocean from the Caroline Seamount (CM4, 10.310.9°N, 139.9140.4°E) during cruise WPOS-M4 conducted by the Chinese research vessel Kexue from 7 August to 5 September, 2017. The peak of the seamount is 57 m below the sea surface and it has a height of 5 950 m. Samples were collected from 13 stations at various depths (902 805 m) in the seamount area (Figs.1 and 2a) using the remotely operated vehicle (ROV) Faxian (Fugro Geosolutions, Shenzhen, China). On return to the main vessel the sediments and seawater (ratio 1:1) were immediately transferred into 500-ml plastic bottles and incubated in dim light at ambient temperature (~ 20C) for subsequence research. In parallel, approximately 50 g sediment samples from each station were transferred to sterile sealed bags and stored at 80C for later DNA extraction.

Fig. 1

 1 Fig.1 Location of the sampling area and the Caroline Seamount

Fig. 2

 2 Fig.2 Distribution of MTB at the Caroline Seamount

Fig. 3

 3 Fig.3 Morphology of the magnetotactic bacteria and characteristics of magnetosomes

Fig. 4

 4 Fig.4 Magnetosome chain configurations and the features of magnetosomes in magnetotactic cocci

2 (

 2 the 39 OTUs affiliated to the Alphaproteobacteria, 24 were closest to Magnetospira sp. QH-EU675666), with seven of these closest to Magnetospira thiophila MMS-1 (EU861390), four closest to uncultured Magnetospira clone (KP183009), two closest to uncultured Magnetospirillum clones (HQ222269 and HQ154657), and two closest to Magnetovibrio blakemorei MV-1 (L06455).

Fig. 5

 5 Fig.5 Neighbor-joining phylogenetic tree showing the relationship of the putative 41 MTB OTUs from the

Fig. 6

 6 Fig.6 Vertical distribution of MTB OTUs (a) and MTB reads (b), and a heatmap of the various compositions

  detected 21 putative MTB OTUs (1 130 reads), while 41 MTB OTUs (2 702 reads) were found at the Caroline Seamount. The numbers of both MTB OTUs and reads at the Caroline Seamount were approximately twice that at the Kexue Seamount. In addition, the MTB OTUs affiliated with Etaproteobacteria and Nitrospirae were only detected at the Caroline Seamount. Up to now, Nitrospirae MTB biomineralize bullet-shaped magnetosomes, but those characteristic particles were not examined within MTB individuals by TEM analyses unfortunately. It might result from the low number of Nitrospirae MTB cells dwelled in the seamount habitat, which made it difficult to detect them though they were present at the Caroline Seamount actually. Comparison of the mean Chao, Shannon, and Simpson diversity indices for MTB from different habitats is shown in Table

Fig. 7

 7 Fig.7 Comparison of MTB communities from the Caroline (CM4) and Kexue (M2) seamounts

ACKNOWLEDGEMENT

This study was financially supported by the National Natural Science Foundation of China (Nos. 41776130 & 41776131), the National Natural Science Foundation of China-Shandong Joint Fund (U1706208), the Youth Talent Support Program of the Laboratory for Marine Ecology and Environmental Science, Pilot National Laboratory for Marine Science and Technology (Qingdao) (LMEES-YTSP-2018-01-07), and the Science & Technology Basic Resources Investigation Program of China (2017FY100803). We thank the crew and captain of vessel Kexue, the ROV team for sediments sampling. We thank Liu Wei, Sun Yuanyuan at the IOCAS (Institute of Oceanology, Chinese Academy of Sciences) for assistance in TEM observations. We thank the engineer Mr. Tang Xu at the IGGCAS (Institute of Geology and Geophysics, Chinese Academy of Sciences) for assistance in TEM experiments.

* Supported by the National Natural Science Foundation of China (Nos. 41776130 & 41776131), the National Natural Science Foundation of China-Shandong Joint Fund (U1706208), the Youth Talent Support Program of the Laboratory for Marine Ecology and Environmental Science, Pilot National Laboratory for Marine Science and Technology (Qingdao) (LMEES-YTSP-2018-01-07), and the Science & Technology Basic Resources Investigation Program of China (2017FY100803).


domain: spi phys math info

text:
Enzo Iglésis
email: iglesise@coventry.ac.uk

Nadjim Horri
email: nadjim.horri@coventry.ac.uk

James Brusey
email: james.brusey@coventry.ac.uk

Karim Dahia
email: karim.dahia@onera.fr

Hélène Piet-Lahanier
email: helene.piet-lahanier@onera.fr

Simultaneous Actuator and Sensor Faults Estimation for Aircraft Using a Jump-Markov Regularized Particle Filter

The advances in aircraft autonomy have led to an increased demand for robust sensor and actuator fault detection and estimation methods in challenging situations including the onset of ambiguous faults. In this paper, we consider potential simultaneous fault on sensors and actuators of an Unmanned Aerial Vehicle. The faults are estimated using a Jump-Markov Regularized Particle Filter. The jump Markov decision process is used within a regularized particle filter structure to drive a small subset of particles to test the likelihood of the alternate hypothesis to the current fault mode. A prior distribution of the fault is updated using innovations based on predicted control and measurements. Fault scenarios were focused on cases when the impacts of the actuator and sensor faults are similar. Monte Carlo simulations illustrate the ability of the approach to discriminate between the two types of faults and to accurately and rapidly estimate them. The states are also accurately estimated.

I. INTRODUCTION

A major issue in small Unmanned Aerial Vehicles (UAVs) is to maintain a safe flight in the event of faults in either actuators or embedded sensors. As these faults may deeply impact control system performance and cause catastrophic accidents, it is essential to detect and estimate them in order to limit their adverse effect on the flight. An efficient approach for state and fault estimation relies on the use of mode switching between faulty and non-faulty models, governed by a Markovian process. In recent years, many approaches have been reported to detect and estimate faults using a jump Markov representation [START_REF] Blackmore | Active estimation for jump markov linear systems[END_REF]- [START_REF] Wang | Fault estimation for continuoustime markovian jump systems by a mode-dependent intermediate estimator[END_REF].

It should be pointed out that most of the methods mentioned above are only tackling one type of fault, i. e., either sensor fault or actuator fault, when both should be considered simultaneously in a multimode fault tolerant system. Kalman Filters have for example been adapted to a variety of joint state and fault estimation problems. In [START_REF] Zhang | Adaptive kalman filter for actuator fault diagnosis[END_REF], an adaptive Kalman filter was designed to estimate actuator faults by modelling the aircraft dynamics as a Linear Parameter Varying (LPV) system. In [START_REF] Zhang | Detection and diagnosis of sensor and actuator failures using imm estimator[END_REF], sensor and actuator faults were estimated using an Interacting Multiple Model Kalman Filters (IMM-KF) architecture, where interacting filters are associated with nominal or faulty models. However, the IMM-KF has the limitations associated with Kalman filters and can diverge in highly nonlinear or multimodal cases [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF].

In [START_REF] Li | Robust fault estimation and fault-tolerant control for markovian jump systems with general uncertain transition rates[END_REF], [START_REF] Li | Robust simultaneous fault estimation and nonfragile output feedback fault-tolerant control for markovian jump systems[END_REF] fault estimation and fault tolerant control for Markov Jump Systems (MJS) are considered in the presence of actuator faults and sensor faults. State and fault observers have been proposed in [START_REF] Yang | Descriptor observers design for markov jump systems with simultaneous sensor and actuator faults[END_REF], [START_REF] Song | Descriptor statebounding observer design for positive markov jump linear systems with sensor faults: Simultaneous state and faults estimation[END_REF], but it is difficult to guarantee that their speed of convergence to the fault state will be high enough to allow reconfiguration of the vehicle. Moreover, an issue that is seldom tackled in the presented approach is the need to discriminate between sensor or actuator faults when both have the same impacts on the system behaviour, at least on a given time horizon, creating a variation of the same level of magnitude on the impacted state components. It is thus necessary to develop estimation methods that efficiently handle ambiguity and/or multimodality.

Particle filters were successfully used for estimation problems including non-linearities or ambiguous measurements [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF], [START_REF] Merlinge | A box regularized particle filter for state estimation with severely ambiguous and non-linear measurements[END_REF]. In multimode systems involving sensor and actuator faults, one possible approach is the extension of the multiple model concept to particle filters, as in [START_REF] Yu | An improved multiple model particle filtering approach for manoeuvring target tracking using airborne gmti with geographic information[END_REF] where the emphasis was on target tracking. However, the computational demand of such an approach would not be suitable to real time implementation in small and medium endurance UAVs. MJS models are therefore often used to transition between faulty and nominal operation modes in such systems. MJS models were combined with a sequential importance sampling based particle filters by Doucet et al. in [START_REF] Doucet | Particle filters for state estimation of jump markov linear systems[END_REF]. Tafazoli and Sun [START_REF] Tafazoli | Hybrid system state tracking and fault detection using particle filters[END_REF] also developed a particle filter for a hybrid MJS model with improvements in fault detection compared to conventional particle filtering, but the mode selection was performed by testing all modes with the same number of particles and selecting the most likely one, which is computationally demanding for real time applications. In [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF], a regularization step (see [START_REF] Musso | Improving Regularised Particle Filters[END_REF] from Musso et al.) was added to a jump-Markov particle filter approach to deal with ambiguities due to sensor redundancies, with Markov jumps between nominal and faulty sensing. Particle filters were also applied to incipient faults in [START_REF] Balchanos | Incipient failure detection: A particle filtering approach with application to actuator systems[END_REF].

In this paper, the focus is on the estimation of intermittent and abrupt sensor and actuator additive faults for ambiguous and multimodal fault scenarios. The approach is applied to a fixed-wing UAV. A Jump-Markov Regularized Particle Filter (JMRPF) approach is proposed to estimate sensor and actuator faults even in cases when both occur simultaneously.

The main contributions of the paper are as follows:

• A jump strategy for both sensors and actuators is presented, where the a priori distribution of the fault is computed using sensor and actuator innovation terms. Then it makes possible to keep testing the alternate mode using a small subset of sentinel particles, allowing them to transition to the correct fault mode. This enhances real time operation prospects compared to previous Jump-Markov Particle Filter approaches. • A Kalman correction step is introduced in the JMRPF to place the particles in the most likely areas of the state space.

The paper is organized as follows. Section II describes the problem formulation and a jump Markov linear system model, adapted to fault estimation, is presented. Section III details the JMRPF approach for actuator and sensor fault estimation. In Section IV, the fault detection and estimation algorithms are evaluated on a scenario involving ambiguous faults in the elevator and in pitch rate. The JMRPF is compared to a Regularized Particle Filter (RPF) (see [START_REF] Musso | Improving Regularised Particle Filters[END_REF]). Section V concludes the paper.

II. PROBLEM STATEMENT

A. Ambiguous fault

A fault from an actuator or sensor with an impact on the same measurement is hereby referred to as an ambiguous fault. It is common in feedback control systems when a sensor is used to measure a state variable and an actuator is used to control the same variable to a setpoint. If an actuator is faulty, the associated state variable and measurement will be affected. Likewise, a sensor fault will have a direct impact on the same output measurement. Therefore, if measurements are detected as being faulty, it is not trivial to determine if the fault originated from the sensor or the actuator 1 .

This ambiguous fault case may lead to a multimodality in the likelihood and conditional density. Indeed, let us consider a discrete system with a state vector denoted z k at time step k. This system has one actuator and one sensor that provides a measurement at each time step k denoted y k . A fault on the actuator or on the sensor induces a similar effect on the measurements.

To jointly estimate the state, actuator fault and sensor fault, an extended state vector is defined and given by:

x k = z k f a k f s k (1)
where f a and f s respectively denote the actuator and sensor faults. When a faulty measurement occurs, the likelihood p (y k |x k ) has two peaks corresponding to two possible modes (solutions) that are: z k f ak 0 and z k 0 f sk . In other words, several states x k may be associated with the same measurement.

This results in the multimodality of conditional density p (x k |Y 1:k ) as illustrated in Fig. 1. In this case, the Extended Kalman Filter (EKF) is not suitable.

B. Jump Markov linear system model

The problem considered in this paper is the joint state and fault estimation in the case of sensor and actuator faults that can occur simultaneously. The occurrences of faults can be modelled using a MJS, by associating a fault-free and faulty mode to the system. The discrete state space model system based on [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF], [START_REF] Svensson | Identification of jump markov linear models using particle filters[END_REF] is represented as follows:

z k f ak 0 z k 0 f sk Conditional density States space p (x k |Y 1:k-1 ) p (y k |x k ) p (x k |Y 1:k ) z k f ak 0 z k 0 f sk
     m k+1 ∼ p (m k+1 |m k ) x k+1 = A mk x k + B mk u k + η k y k = C mk x k + D mk u k + ν k (2a) (2b) (2c)
where m k is a discrete mode vector of the system at time step k. A mode of this vector can either be faulty m (1) or fault-free m (0) . The vector x k ∈ R nx represents the system state, u k ∈ R nu is the control input, y k ∈ R ny is the vector of measurements. For jointly state, actuator fault and sensor fault estimation the state vector x k is an extended state vector that contain the regular states of the system denoted here z k ∈ R nz , the actuator and sensor fault states estimate denoted here respectively f ak ∈ R na and f sk ∈ R ns . Then, the state vector x k is given by

x k = z k f a k f s k .
The process and sensors noises are η k ∈ R nx and ν k ∈ R ny . They are assumed to be of zero mean and the covariance matrices are respectively defined as

E η k η k = Q k and E ν k ν k = R k .
They are assumed to be independent E η k ν k = 0. The matrices A mk , B mk , C mk and D mk denotes the usual discrete state space matrices terms and depend on the modes m k at time step k. They are given by:

A mk =   A z G azm a k 0 nz× ns 0 na× nz G am ak 0 na× ns 0 ns× nz 0 ns× na G sm s k   (3a) B mk = B z 0 na+ns× nu (3b) C mk = C z 0 ny×ns G sy ms k (3c) D mk = D z 0 na+ns× nu (3d)
Where A z , B z , C z and D z denotes the usual discrete state space matrices terms applied to state vector z k . The matrices G am ak and G sm s k respectively represent the actuator and sensor fault dynamics, applied respectively to state vectors f ak and f sk , and depend on the mode vectors m a and m s at time step k. The mode vectors m a and m s are respectively the mode vector associated to the actuator and sensor fault sate vector f a and f s that compose the mode vector m k which is given by m k = m a k m a k . The matrices G az and G sy respectively represent the coupling matrices of the actuator and sensor faults on the state and measurements at time step k, and they depend respectively on the mode vectors m a and m s According to (2), the system switches between as many dynamical models as there are elements of m k . However, if a dynamical model is associated to a mode m (0) , then the fault state is in a fault-free mode and its value is equal to 0. In this case, irrespective of the state transition matrix, when it is multiplied by the estimated fault state in a fault free mode, then the new fault state is equal to 0. Only a state in a faulty mode m (1) has an influence on the new fault state. The dynamical model is then simplified and only associated to the state transition matrix for mode m (1) . In the following sections, matrices A mk , B mk , C mk and D mk with all the modes of the vector m k set to m (1) are denoted A m (1) , B m (1) , C m (1) and D m (1) . The modes then only affect the f a and f s states. A jump strategy is then defined to switch between the fault-free and faulty states.

C. The transition probability based jump strategy

The probability to switch from a mode m (i) to m (j) is denoted by

π ji = P m (j) k+1 |m (i) k
. Hence, π 10 is the probability to switch from nominal mode m (0) to a faulty mode m (1) while the probability π 01 is the probability to switch from a faulty mode m (1) to a nominal mode m (0) . A matrix Π is defined as the transition probability matrix, which represents the probability of switching from one mode to another. It is given by:

Π = π 00 π 10 π 01 π 11 (4)
Each state of the state vector f a and f s is associated with a Π matrix. The diagonal elements of the π jj matrices represent probabilities to remain in the same mode for the given sensor or actuator. The Markov chains can be represented by the transitions diagram shown in Fig. 2:

m (0)
m (1) π 11 π 00 π 10 π 01 Fig. 2. Markov chain of the JMRPF applied to fault estimation

The objective of the method presented here is to simultaneously detect the occurrence of faults and to estimate their amplitude.

Evolution of x k is represented by ( 2) and is conditioned by the probabilities of switching from one mode to another represented by Π.

III. JUMP-MARKOV REGULARIZED PARTICLE FILTER

The transition matrix allows for abrupt changes between non-faulty and faulty modes. Jump Markov based filters have been designed to handle such transitions. Moreover, in the context of simultaneous sensor and actuator faults, the system may present multi-modalities, as in the case where the conditional density p (x k |Y 1:k ) with Y 1:k = [y 1 , . . . , y k ] presents several peaks. This justifies the use of a Jump-Markov Particle Filter. In [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF], a first version of a JMRPF was introduced to handle sensor fault estimation in presence of ambiguous measurements. In this paper, the particles x i k are corrected using a Kalman update to place the particles in the most likely areas of the state space. The particle weights are calculated by taking into account the Kalman update, which makes it possible to reduce the variance of the weights and improve the estimation accuracy of the JMRPF. The JMRPF is fed by the control input, the previous state estimate and the measurement to provide the estimated state vector xk and its associated estimated covariance matrix Pk . The number of particles is denoted N p .

The proposed global JMRPF algorithm [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF] with the Kalman update and the actuator fault estimation is introduced hereafter in Algorithm 1. It is composed of prediction, update, estimation and regularizationresampling steps. The PREDICT and UPDATE functions were modified as described in Algorithms 2 and 4 for combined actuator and sensor fault estimation and using a jump function within the predict function as part of the hypothesis testing.

Algorithm 1 Jump-Markov Regularized Particle Filter k ← 0 . . . Initialization loop k ← k + 1 for each i ∈ [1, N p ] do PREDICT(x i k|k-1 , x i k-1 , m i k , u k , y k ) end for ESTIMATE(x k|k-1 , Pk|k-1 , w 1:Np k-1 , x 1:Np k|k-1 ) S k ← C m (1) Pk|k-1 C m (1) + R k K k ← Pk|k-1 C m (1) S -1 k Kalman gain for each i ∈ [1, N p ] do UPDATE(x i k , w i k , w i k-1 , x i k|k-1 , K k , S k , u k , y k ) end for ESTIMATE(x k , Pk , w 1:Np k , x 1:Np k ) N eff ← 1 Np i=1 w i k 2 if N eff ≤ N p Γ then if true then resample MULTINOMIAL(x 1:Np k , x 1:Np k , w 1:Np k ) for each i ∈ [1, N p ] do w i k ← 1 Np Reset the weights REGULARIZE(x i k , xi k ) end for end if end loop

A. Prediction step

In the particle filter, the i th state variable is propagated using the following probability transition density for the state x k|k-1 :

x i k|k-1 ∼ p x k|k-1 |x i k-1 , m i k (5)
Then, one obtains a predicted cloud of particles

(x 1 k|k-1 , x 2 k|k-1 , • • • , x Np k|k-1
). The mode of each state and particles of f a and f s are updated in the prediction step. This update is performed here using a uniform draw and compared to user defined probabilities π ji to switch from one mode to another as described in Fig. 2.

To simplify notations in this section, it is assumed that the number of possible actuator faults n a is equal to the number of actuators n u and the possible number of sensor faults n s is equal to the number of sensors n y . The same index j is also used to denote the j th state of vectors f a and f s , respectively representing fault estimates of the j th actuator of u and of the j th sensor of y.

A new jump strategy for sensors and actuators fault modes is proposed. It uses the a priori distribution of the fault, which is computed using sensor and actuator innovation terms from ( 9) and [START_REF] Li | Robust fault estimation and fault-tolerant control for markovian jump systems with general uncertain transition rates[END_REF]. When a sensor or actuator is in a fault free or faulty mode, the alternate mode of the device will continue to be tested using a small number of fault particles that will be named sentinel particles. Those particles will be selected from a uniform distribution and their number will depend on the transition probability matrix. Indeed, the number of sentinel particles can be decreased by reducing the transition probabilities π 01 and π 10 . Those probabilities will be set based on expected device false alarm and missed detection rates. This small number of sentinel particles will continuously test the probability of transition of jump to the alternate fault modes. The fact that the number of sentinel particles is small reduces computational demand compared to previous particle filter jump strategies, such as the one of reference [START_REF] Tafazoli | Hybrid system state tracking and fault detection using particle filters[END_REF] where both modes are tested using the total number of particles at all times before selecting the mode with the higher probability.

The jump amplitudes of the i th particle of the j th state of f a at time step k are computed as follows:

f a i,j k|k-1 =        λ i,j k if U ≤ π j 10 and m a i,j k = m (0) f a i,j k|k-1 if U < π j
11 and m a i,j k = m (1) 0 else [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF] where U ∼ U (0, 1) and λ i k is given by:

λ i k = u k -r z i k|k-1 (7)
where r is a stabilizing control law used to compute

u k = r (ẑ k ).
The jump amplitudes of the i th particle of the j th state of f s at time step k are computed as follows:

f s i,j k|k-1 =        β i,j k if U ≤ π j 10 and m s i,j k = m (0) f s i,j k|k-1 if U < π j 11 and m s i,j k = m (1) 0 else (8)
where U ∼ U (0, 1) and β i k is given by:

β i k = y k -C m (1) x i k|k-1 + D m (1) u k (9)
The prediction step is described in Algorithm 2.

The JUMP function used in Algorithm 2 is described in Algorithm 3.

Algorithm 2 Detail of the function PREDICT from Algorithm 1 function PREDICT(x i k|k-1 , x i k-1 , m i k , u k , y k ) η i k ∼ N (0, Q k ) x i k|k-1 ← A m (1) x i k-1 + B m (1) u k + η i k λ i k ← u k -r z i k|k-1
See ( 7)

for each j ∈ [1, n a ] do Jump step of f a JUMP(f a i,j k|k-1 , m a i,j k , λ i,j k ) See Algorithm 3 end for β i k ← y k -C m (1) x i k|k-1 + D m (1) u k See (9) for each j ∈ [1, n s ] do Jump step of f s JUMP(f s i,j k|k-1 , m s i,j k , β i,j k ) See Algorithm 3 end for end function Algorithm 3 Detail of the function JUMP from Algo- rithm 2 function JUMP(f i,j k|k-1 , m i,j k , Υ i,j k ) U ∼ U (0, 1) if m i,j k = m (0) then f i,j k|k-1 in mode m (0) if U ≤ π 10 then Transition m (0) → m (1) f i,j k|k-1 ← Υ i,j k m i,j k ← m (1) else Transition m (0) → m (0) f i,j k|k-1 ← 0 end if else if m i,j k = m (1) then f i,j k|k-1 in mode m (1) if U ≤ π 01 then Transition m (1) → m (0) f i,j k|k-1 ← 0 m i,j k ← m (0) end if end if end function

B. Update step

In the particle filter, each i th particle x i k are assigned to a weight w i k that is proportional to its likelihood:

wi k ∝ w i k-1 p y k |x i k|k-1 , m i k ( 10a
)
w i k = wi k Np i=1 wi k (10b)
In (10b) a normalization is applied to ensure that Np i=1 w i k = 1. Compared to the update step described in [START_REF] Iglésis | A jump-markov regularized particle filter for the estimation of ambiguous sensor faults[END_REF], an additional feature was introduced. Indeed, a Kalman update on the particles x i k|k-1 is applied to better place the particles. The Kalman update is given by:

x i k = x i k|k-1 + K k ỹi k ( 11
)
This step is performed by the UPDATE function which is detailed in Algorithm 4 In this algorithm it is assumed that the likelihood is a Gaussian distribution.

Algorithm 4 Detail of the function UPDATE from Algo- rithm 1 function UPDATE(x i k , w i k , w i k-1 , x i k|k-1 , K k , S k , u k , y k ) ỹi k ← y k -C m (1) x i k|k-1 + D m (1) u k Innovation wi k ← w i k-1 N (ỹ i k ; 0, S k ) See 10a w i k ← wi k Np i=1 wi k x i k ← x i k|k-1 + K k ỹi k See (11) end function

C. Estimation

The estimation step aims to perform a global estimate of the state vectors xk and xk|k-1 , with its associated covariance matrices Pk and Pk|k-1 respectively. This step is described in Algorithm 5.

Algorithm 5 Detail of the function ESTIMATE from Algorithm 1

function ESTIMATE(x, P, x 1:Np , w 1:Np ) x ← Np i=1 w i x i P ← Np i=1 w i x i -x x i -x end function

D. Regularization-Resampling step

The regularization-resampling step consists of two stages, the resampling and the regularization of the selected particles. Its purpose is to remove the particles with a low likelihood by duplicating the particles with a high likelihood and regularizing the duplicated particles.

a) Resampling step: The particles are selected according to a multinomial law with w i k as parameter. Then the probability to choose a particle is:

P xj k = x i k = w i k (12)
This corresponds to the MULTINOMIAL function in Algorithm 1. b) Regularization step: The particles are randomly moved according to a regularization kernel K (x). The regularization is given by:

x i k = xi k + hD k ε i k ( 13
)
where h ∈ R + * is the bandwidth factor in the rescaled kernel density K (•) and with

P k = D k D k and ε ∼ K (x).
The kernel density is a symmetric probability density function such that:

xK (x) dx = 0, x 2 K (x) dx < ∞ (14)
The optimal kernel K (•) and bandwidth factor h are those which minimize the Mean Integrated Square Error (MISE) between the theoretical and estimated posterior density, and is defined as:

MISE (p) = E (p (x k |Y 1:k ) -p (x k |Y 1:k )) 2 dx k (15
) where p (x k |Y 1:k ) is the particle filter approximation of the state conditional density. In the case where all particles have the same weight, during the resampling step, a suitable choice of the kernel is the bounded Epanechnikov kernel [START_REF] Silverman | Density estimation for statistics and data analysis[END_REF].

K (x) = nx+2 2cn x 1 -x 2 if x < 1 0 else (16)
where c nx is the volume of the unit hypersphere in R nx . The algorithm of the regularization is described in Algorithm 6.

Algorithm 6 Detail of the function

REGULARIZE from Algorithm 1 function REGULARIZE(x i k , xi k ) ε i k ∼ K x i k see (16) x i k ← xi k + hD k ε i k end function
However, this regularization-resampling step is not performed at each time step. A criterion is defined to know if a resampling step is needed. The criterion that is used in this paper is the efficiency N eff .

N eff = 1 Np i=1 w i k 2 (17)
If Neff Np is lower than user-defined threshold Γ ∈ (0; 1) then the resampling step is performed.

Finally, after performing all above mentioned steps, the approached conditional density is given by:

p (x k , m k |Y 1:k ) ≈ Np i=1 w i k K h x k -x i k δ m i k (m k ) (18)
where:

K h (x k ) = 1 h nx K 1 h x k (19)

IV. SIMULATION MODEL AND RESULTS

A. UAV Dynamical model

The application example is a fixed-wing UAV. We focus on the longitudinal model as ambiguities can occur when we consider faults on the pitch rate sensor or on the elevation actuator. The state vector representing UAV longitudinal dynamics is z = p d u w θ q . The state p d denotes altitude loss, u represents the deviation with respect to the longitudinal velocity trim condition along the i b axis, w represents the vertical velocity along the k b axis (see Fig. 3) and the states θ and q respectively denote the pitch and pitch rate. The control input vector is u = δ e δ t T , where δ e and δ t respectively represent the elevator deflection and throttle input. The full state is observed using an Inertial Navigation System (INS) hybridized with a Global Navigation Satellite System (GNSS) receiver, a magnetometer and a barometer. The trim condition for the UAV model is straight level flight at a velocity of 40 m s -1 and an altitude of 500 m. A linear model of the Aerosonde UAV given by [START_REF] Beard | Small unmanned aircraft: Theory and practice[END_REF] is used for the simulation analysis. The linear model is discretized at 40 ms and the state, control, observation and output matrices associated with the state vector z k are given by:

A z =       1 0 0.
C z = I 5 (20c) D z = 0 7×2 (20d)

B. Control system

The longitudinal autopilot uses a desired flight path angle command γ c and a velocity vector norm command V c . The actuator inputs δ e and δ t are given by:

δek+1 = -L θ ẑk -L θi θik+1 δtk+1 = -L u ẑk -L ui ūik+1 (21a) (21b)
where the bar notation represents a variation around the trim condition. The gains L θ , L u , L ui , L θi are obtained using a Linear Quadratic Regulator (LQR) with integral correction and weighting matrices Q = diag 1 0 4 0 0 , R = I 2×2 . The integral gains are L θi = 1.00 and L ui = -1.00. Integrated state deviations θi and ūi are given by:

     θik+1 = (γ c k + A u ûk + A w ŵk -θ)dt + θik ūik+1 = (( V c k -V w ŵk ) 1 V u -ûk )dt + ūik (22a) (22b)
where the parameters V u = 1.00, V w = 0.05, A u = 0 and A w = 0.03 relate pitch and speed reference guidance commands to γ c and V c .

C. Filter parameters

For the simulations two filters are used: a JMRPF introduced in this paper and a RPF for comparison. The stochastic process model is given by:

             x k+1 =   A z G az 0 5×1 0 1×5 G a 0 0 1×5 0 G s   x k + B z 0 2×2 u k + η k y k = C z 0 5×1 G sy x k + D z 0 2×2 u k + ν k (23a) (23b)
where η k and ν k are independent Gaussian noises with zero mean and covariance matrices denoted by Q k and R k respectively. G az , G a , G s and G sy are given by: G az = 0.01 0.05 -1.04 -0.03 -1.69

(24a) G a = 1 (24b) G s = 1 (24c)
G sy = 0 0 0 0 1 (24d)

The JMRPF and RPF parameters are 2 :

• The standard deviation vector used to compute the covariance matrix P 0 = diag σ 2 0 for the extended state vector x k is given by:

σ 0 = 1 1 1 0.1 0.1 0.1 0.1 (25)
• The standard deviation vectors used to compute the covariance matrices

Q k = diag σ 2 Q and R k = diag σ 2
R are respectively given by: σ Q = 0.01 0.02 0.02 0.3 0.1 0.3 0.3

σ R = 1 1 1 0.3 0.1 (26)
• The number of particles N p is set to 5000.

D. Fault scenario

From the expressions of the B z matrix given by (20b), pitch rate is linked to elevator deflection δ e . An actuator fault on δ e is therefore difficult to discriminate from a sensor fault on q, which represents an ambiguity on the source of the fault. For the simulation analysis, the fault sequence is described in Fig. 4. High fault amplitudes of 10 degrees on the elevator and 10 degrees per second on the pitch rate are assumed to evaluate robustness to severe abrupt faults.

E. Simulation results and analysis

In Fig. 5, the JMRPF initially estimates the actuator fault faster when it occurs at 2 s, although the estimate of the sensor fault is briefly disrupted in the JMRPF. However, this deviation is shown in Fig. 7 to be so brief that altitude estimation is not affected, as hypothesis testing quickly resolves the ambiguity between sensor and actuator faults. Between 6 s and 7 s, both faults are simultaneously active and the JMRPF converges faster to the true fault modes and amplitudes compared to the RPF. Both estimators then accurately track the sensor fault from 7 s to 10 s. When the sensor fault is no longer active, the JMRPF quickly jumps to the fault free state but the RPF response to this change is approximately 2 s slower because the response of the RPF is more heavily restricted by the model dynamics, while the jump strategy of the JMRPF has a more instantaneous effect.

In Fig. 6, except for a brief jump at time 2 s, the JMRPF is shown to have significantly lowered Root-Mean-Square Error (RMSE) than the RPF, for both sensor and actuator faults. The evolution of RMSE on the faulty scenarios illustrates the difference of convergence speed between JMRPF and RPF.

In Fig. 7, pitch rate and altitude deviations with respect to the setpoint are shown and the JMRPF clearly outperforms the RPF in terms of state estimation accuracy. The JMRPF accurately estimates both sensor and actuator faults and also estimates longitudinal states with better robustness to faults.

V. CONCLUSION

In this paper, a new JMRPF was proposed and applied to state and fault estimation in the presence of pitch rate sensor and elevator faults affecting the longitudinal states of a fixed-wing UAV. The proposed filter accurately estimates the states and faults even in the ambiguous case when both faults are active at the same time. The proposed Jump strategy allows a small subset of sentinel particles to explore the alternate mode and quickly detect A Kalman correction places the particles in the most likely regions of the state space. Numerical simulations illustrate that the proposed JMRPF outperforms a RPF, in terms of convergence rate to the correct fault mode and fault estimation accuracy, even when sensor and actuator faults are simultaneously active. State estimation is also more accurate and robust to faults with the JMRPF.

Fig. 1 .

 1 Fig. 1. A representation of the conditional density p (x k |Y 1:k ) in the case of sensor and actuator faults

Fig. 3 .

 3 Fig. 3. Side view of an UAV with references axis and angles

•

  The transition probability matrices for sensor and actuator faults are both equal to: transition Π matrix has been driven by reflecting the ambiguity which required to select identical matrices for sensor and actuator faults and being of the magnitude of potential false alarm probabilities indicated in such device.• The resampling threshold Γ and regularization bandwidth h are: Γ = 0.75, h = 0.27

2Fig. 4 .

 4 Fig. 4. Faults scenario used for the simulation

  Pitch rate sensor fault estimate.

Fig. 5 .

 5 Fig. 5. Actuator (a) and Sensor (b) additive fault estimates. Median results of the 100 simulations.

Fig. 6 .

 6 Fig. 6. (a) RMSE of the actuator additive estimated fault. (b) RMSE of sensor additive estimated fault. RMSE are based on 100 simulations.

Fig. 7 .

 7 Fig. 7. Median result of the 100 simulations of selected state variables: (a) Altitude, (b) Pitch rate

Fault can also come from other sources, but they are not considered in this paper