Anabella Mocanu

Rózsa Szűcs

Elsa Caytan

Thierry Roisnel

Vincent Dorcet

Pierre-Antoine Bouit

László Nyulászi

Muriel Hissler

Synthesis, optical and redox properties of regioisomeric benzoheterocycles-fused pyrene

The tuning of the optical and electronic properties of pyrene derivatives is a key issue to diversify the applications of these materials. This led to a creative molecular engineering involving the development of new synthetic approaches for the functionalization of pyrene, the tailoring of substituents and/or the use of heteroatoms 3 (molecules A -B, Figure 1), or extending the π-system with fused heterocycles yielding different electronic properties (molecules C -D, Figure 1). For example, regioisomeric sulfur and sulfonyl bridged phenyl-pyrene (molecules C and D with Y = S or SO2, Figure 1) have been synthesized by Liu, Li et al. 4 They showed that the physical properties are highly dependent on the position of the substitution on the pyrene skeleton. In this context, the synthesis and the study of optical and redox properties of pyrene-heterocycle analogues (C -D with Y = PPh or SiMe2, Figure 1) are of high interest since phosphole and silole rings have strongly different electronic behavior compared to their S-analogs, due to their lowlying LUMO energy levels and the corresponding low aromaticity. 5 In this communication, we present the synthesis based on metalcatalysed C-H bond activation of four regioisomeric pyrenebenzo [b]phosphole and -benzo [b]silole derivatives (C and D with Y = P(=O)Ph and SiMe2, Figure 1). We detail also the impact of the nature of the heterocycle and the position of the pyrene substitution on the physical properties by experimental (UV/Vis absorption, fluorescence, cyclic voltammetry) and theoretical studies.

Most of the pyrene derivatives described in the literature are synthesized through Friedel and Craft reactions. 4 However, this strategy appeared unsuccessful for the incorporation of P and Si atoms in these systems. We thus turned to transition metal-catalyzed P-C/Si-C bond-formation through C-H activation which recently appeared an innovative and powerful synthetic tool to prepare benzoheterocycles. 6 We decided to apply these methods to synthesize the benzo [b]heterocycles based-pyrene derivatives. Starting from pyrene-1-boronic acid 1 (Scheme 1), the phosphine moiety was introduced by means of a Suzuki-Miyaura coupling with (2-bromophenyl)diphenylphosphine (BDP) directly followed by Pd-catalysed cyclization using Chatani's reaction conditions (catalytic amount of Pd(OAc)2, toluene, 160°C, 12h). 6a The first pyrene-fused benzo [b]phosphole 3 was thus prepared in 2 steps (Scheme 1) in moderated yield (45%). The same synthetic strategy was applied for the preparation of pyrene-fused benzosilole 5. The silane was introduced in two steps. First a Suzuki Miyaura coupling between pyrene-1-boronic and bromoiodobenzene (BID) was performed followed by lithiation and quenching with Me2SiHCl of the 1-(2iodophenyl)pyrene to afford 4 (Scheme 1). Finally, the cyclization was conducted with catalytic amount of RhCl(PPh3)3 applying Takai's conditions to afford 5 in moderate yield (23%). 6c Similar synthetic strategy was successfully applied for the synthesis of two other regioisomers 6 and 7 (Scheme S1) indicating that the C-H activation is a method of choice for P-C/Si-C bond-formation on pyrene. Effectively, these reactions can be performed both on activated and also on less activated positions of pyrene. 7

Scheme 1: Synthesis of 3-5 and molecular structures of 6-7.

All the novel pyrene derivatives were fully characterized by multinuclear NMR and HRMS. Furthermore, the structures of 3, 6 and 5 were unambiguously confirmed by X-ray diffraction studies performed on single crystals (see Fig. 2). In all three cases, the bond distances in the heterocycles are classical for benzo [b]phosphole/benzo [b]siloles analogues (see Table S2). 5a Benzo [b]phospholes 3 and 6, in which the P-atom is stereogenic, crystallize as racemic mixtures (see Fig. S6). In 3 and 5, where the heteroatom is linked to the 2-position of the pyrene, some distortion is observed in the polycyclic backbone due to H-H repulsion in the cove region (maximal deviations from the mean plane are respectively: 0.34 Å and 0.47 Å). This feature is not observed for 6 (maximal deviation from the mean plane: 0.05 Å), where the distance between the hydrogens is increased reducing the repulsive interaction. At the intermolecular level, strong differences are observed between the derivatives. The compound 3 crystallizes as face-to-face -stacked pyrene dimers with an interplanar distance of 3.47 Å (see Fig. 2). No long-range interactions are observed. In the case of 6, -stacked dimers are formed (d1 = 3.51 Å, Fig. 2) through interactions of the pyrenic backbone. Those dimers are also involved in -stacking interactions (d2 = 3.58 Å, Fig. 2) through partial overlapping of the whole polycyclic framework thus forming infinite -columns (see Fig. 2). Even if some other factors linked to the molecular structure and packing might play a role, we believe that the higher planarity of the -system might be the driving force for these long-range interactions. Finally, in the crystal structure of 5, an infinite network of CH- interactions (d = 2.46 Å) between the pyrene proton at the 5-position and the pyrenic framework of another molecule is observed. The substitution pattern and the nature of the heteroatom thus strongly influences the molecular packing.

In order to establish structure/properties relationships with benzoheterocycles-fused pyrenes, the optical and electrochemical properties of 3,5-7 were examined in CH2Cl2 (c = 10 -5 M). Benzoheterocycles -fused pyrenes 3,5-7 exhibit structured absorption in the visible (with a better resolution for 5 and 7) (Fig. 3) which are quite similar to those of pyrene, however showing some red shift. At low energy, benzo [b]phosphole-fused pyrenes 3/6 exhibit well resolved S1 ← S0 absorption bands, which are mainly attributed to the short-axis-polarized [START_REF] Wu | Graphenes as potential material for electronics[END_REF] Lb transition present in the pyrene unit. 3b The intensity of these weak bands increases with respect to pyrene (Fig. 3), as a consequence of the reduced symmetry. 4 The intense S2 ← S0 transition corresponds to the long-axis-polarized 1 La transition of pyrene, which is basically a HOMO-LUMO transition (vide infra) as previously described on substituted pyrene derivatives. 3b In the case of 3, there is a slight red shift of these transitions going from hexane to DCM (Fig S2 ); the red shift is somewhat larger for the 1 Lb than for the 1 La band.

Si-containing pyrenes (Fig. 3) show also red-shifted absorption bands compared to pyrene and the low energy absorptions are very weak, with a somewhat larger optical gap than for the P-analogues, as usually observed for silole/oxophospholes. 5 If we study the effect of the substitution pattern, absorption bands of 3/5, and in particular the S2 ← S0 transition, are red-shifted compared to those of 6/7 indicating a higher extended -conjugation for the bent compounds. These data show the high impact of the heteroatom nature and the substitution pattern on the absorption properties. All compounds display structured emission at lower energy compared to pyrene (Fig. 3 and Fig S3). All photoluminescence quantum yields are rather high (Table 1), unless for 7. This low value remain unexplained. The emission spectrum of 3 exhibits sharp, well-resolved emission in hexane with an average vibrational spacing between the most prominent bands of ca. 1250 cm -1 . These vibrational modes are characteristic for pure π-π* states in emission. 3j As observed for the absorption spectrum, the emission spectrum recorded in DCM for 3 is shifted up to 840 cm -1 compared to the absorption band in hexane showing that the excited state is more polar than the ground state. In solution, no excimeric emission was observed, even in saturated hexane solution (c = 10 -4 M), the corresponding spectra remain identical with increasing concentrations. This is rather surprising as pyrene has tendency to form excimers in nonpolar solvents even in diluted solutions. 8 The presence of the tetrahedral heteroatoms probably induced enough steric hindrance to prevent the formation of excimers even in apolar solvent. The optical properties of 3 were also studied in the solid-state. The UV-Vis absorption in thin film (Fig. S2) showed a broadening of the bands accompanied by a red-shift of the edge of absorption. This indicates some interactions between the compounds in the ground state (as observed in the crystal packing, Fig. 2). Interestingly, the emission of 3 in thin film (Fig. 3) showed a broad red-shifted emission (em = 2700 cm -1 ). Similar effect was observed for some amino and cyano substituted pyrenes. 3h This broad emission is likely to be assigned to aggregates that are formed exclusively in the solid-state due to the packing. Regarding the redox properties (Table 1), in the whole series, benzoheterocycle-fused pyrenes are easier to oxidize and reduce compared to pyrene measured in the same conditions, 9 thus confirming the lower gap measured by optical method, in particular in case of 3 and 5. Furthermore, P=O-containing pyrenes display reversible reduction at relatively low potential (Table 1). This underlines that these compounds possess high electron affinity, especially compared to thiophene-fused pyrenes. 4a The observed electrochemical behaviour is in accordance with the calculated orbital energies. The π-orbitals resemble to the pyrene MOs (Fig. 4), but the geometry of the molecule strongly influences the orbitals' delocalization toward the heterocyclic unit. In case of linear molecules 6 and 7, both the HOMO and LUMO are localized mostly on the pyrene skeleton with a nodal surface at 2,7-position of pyrene. In case of 3 and 5, the geometry allows further delocalization of these orbitals, resulting in the reduction of the HOMO-LUMO gap (causing a red shift on the 1 La band), in accordance with the results obtained from the optical end electrochemical measurements. Interestingly, the H-H repulsion induced non-planarity in case of the bent 3 and 5 has only a small effect on the shift of the HOMO and LUMO energies. While the FMO-s are more influenced by the substitution in case of 3 than in case of the linear 6, both geometric shapes allow the delocalization of the HOMO-1 and LUMO+1 orbitals. The changes in the orbital energies explain that the high intensity [START_REF] Wu | Graphenes as potential material for electronics[END_REF] La band (HOMO-LUMO transition) shows a larger red shift than the Lb band in case of the bent 3. Using both CC2 and TD DFT calculations, and appropriate corrections based on the measured data of the parent pyrene (for details see the SI) the band maxima of the absorption spectra can be well assigned (Fig. 3) as vertical excitation energies, with the exception of the low intensity [START_REF] Wu | Graphenes as potential material for electronics[END_REF] Lb bands in the TD DFT calculation of the linear systems 6.

The NICS(1) aromaticity investigation (Fig. 5) of the molecules revealed that the heteroles keep their usual aromatic properties (slightly antiaromatic for phosphole-oxide and non-aromatic for silole), as previously observed in P-containing PAHs 5e The substitution doesn't have a strong effect on the aromaticity of the pyrene part, in accordance with the conclusion drawn from the investigation of the MO-s. We described the synthesis of novel pyrene-fused benzo [b]heterocyles containing P and Si using transition metal-catalysed C-H bond activation. The compounds were fully characterized including X-ray diffraction. The effect of the heteroatom and the substitution pattern on the optical and redox properties was studied experimentally and theoretically. This study opens the way toward the preparation of novel heteroatom containing PAH structures with potential applications in optoelectronic devices. 10

EXPERIMENTAL SECTION

All experiments were performed under an atmosphere of dry argon using standard Schlenk techniques. Commercially available reagents were used as received without further purification. Solvents were freshly purified using MBRAUN SPS-800 drying columns. Separations were performed by gravity column chromatography on basic alumina (Aldrich, Type 5016A, 150 mesh, 58 Å) or silica gel (Merck Geduran 60, 0.063-0.200 mm). 1 H, 13 C, and 31 P NMR spectra were recorded on Bruker AV III 300 and 400 MHz NMR spectrometers equiped with BBO or BBFO probeheads. Assignment of proton and carbon atoms is based on COSY, NOESY, edited-HSQC and HMBC experiments. For products 3 and 6, special 31 P decoupled experiments ({ 31 P} 1 H, { 31 P-1 H} 13 C, { 31 P}-HSQC or HMBC) were performed on a Bruker Av III HD 500 MHz fitted with a triple inverse probehead ( 1 H-31 P-X). These 31 P decoupled experiments have been performed using the PRISM core facility (Biogenouest©, UMS Biosit, Université de Rennes 1-Campus de Villejean-35043 RENNES Cedex, FRANCE). 1 H and 13 C NMR chemical shifts were reported in parts per million (ppm) using residual solvent signal as reference. In the NMR description, Cq corresponds to quaternary carbon; ipso, ortho, meta, para correspond to the respective positions on the exocyclic P-Ph;  and  to the position 2 and 3 of the heterole ring. High-resolution mass spectra were obtained on a Varian MAT 311 or ZabSpec TOF Micromass instrument at Scanmat (UMS 2001). UV-Visible spectra were recorded at room temperature on a VARIAN Cary 5000 spectrophotometer. The UV-Vis emission and excitation spectra measurements were recorded on a FL 920 Edimburgh Instrument equipped with a Hamamatsu R5509-73 photomultiplier for the NIR domain (300-1700 nm) and corrected for the response of the photomultiplier. Quantum yields were calculated relative to quinine sulfate (H2SO4, 0.1 M), ref= 0.55). The electrochemical studies were carried out under argon using an Eco Chemie Autolab PGSTAT 30 potentiostat for cyclic voltammetry with the threeelectrode configuration: the working electrode was a platinum disk, the reference electrode was a saturated calomel electrode and the counter-electrode a platinum wire. All potential were internally referenced to the ferrocene/ ferrocenium couple. For the measurements, concentrations of 10 -3 M of the electroactive species were used in freshly distilled and degassed dichloromethane and 0.2 M tetrabutylammonium hexafluorophosphate. (2-bromophenyl)diphenylphosphine BDP, 1-(2-bromophenyl)pyrene, pyrene-2-boronic acid, 2-(2-bromophenyl)pyrene were prepared according to the literature. 11 7-Phenylbenzo [b]phenaleno [1,9-ef]phosphindole 7-oxide (3). pyrene-1-boronic acid (0.05 g, 0.20 mmol), (2-bromophenyl) diphenylphosphine BDP (0.08 g, 0.22 mmol) and potassium phosphate (0.13 g, 0.60 mmol) were dissolved in DMF (4 mL). The solution was degassed and 1,1′-Bis (diphenylphosphino)ferrocene]dichloropalladium(II) (0.05 eq.) was added to the reaction mixture and was heated four days at 135 °C. The product dissolved in DCM and extracted with water. The organic layer was dried on MgSO4, filtrated and then the solvent was evaporated. The crude mixture was filtrated on dry Celite pad with dry DCM to give the  3 , 3 P intermediate 2 ( 31 P NMR (161.99 MHz, CD2Cl2):  (ppm) -14.4 (s), HR-MS (MS (ESI, CH3OH/CH2Cl2: 95/5, m/z): [M] + calc for C34H24P: 463.1616; found: 463.1617) as a yellow solid (0.04 g, 41 % yield). The compound was dissolved in toluene (0.60 mL) and the mixture was degassed before adding palladium acetate (0.05 eq.). The reaction was stirred 12h at 160 °C and then after cooling to room temperature, a H2O2 30 % solution (1 mL) was added. The product was extraction with DCM, the organic layer was washed with water and then dried over MgSO4, filtrated and the solvent evaporated. The crude mixture was purified by silica gel chromatography using ethyl acetate/heptane 9/1 as eluent to afford 3 as a yellow solid (0.05 g, 45% yield). 1 H NMR (500.15 MHz, CD2Cl2):  (ddt, 3 J(H-H) = 7.5 Hz, 3 J(H-H) = 4.7, 4 J(H-H) = 2.3 Hz, 2H, CHortho); 1H);1H,CHpara);2H,CHmeta);1H);3 J(H-H) = 10.5 Hz, J(H-P) = 7.2 Hz, 5 J(H-H) = 0.6 Hz, 1H); 7.98 (d, 3 J(H-H) = 8.8 Hz, 1H); 8.02 (t, 3 J(H-H) = 7.6 Hz, 1H); 8.04 (d, 3 J(H-H) = 8.8 Hz, 1H); 8.17 (d, 3 J(H-H) = 7.6 Hz, 1H); 8.18 (d, 3 J(H-H) = 7.3 Hz, 1H); 8.19 (d, 3 J(H-H) = 9.4 Hz, 1H); 8.43 (d, 3 J(H-H) = 10.8 Hz, 1H); 8.63 (dd, 3 J(H-H) = 8.1 Hz, 4 J = 3.5 Hz, 1H); 8.93 (d, 3 J(H-H) = 9.4 Hz, 1H). 13 1-(2-bromophenyl)pyrene (0.10 g, 0.28 mmol) was dissolved in 6 mL of distilled THF and cooled down at -78 °C before adding nBuLi (0.15 mL, 0.36 mmol, M = 2.4 mol/L). After 1 h of stirring at -78°C, the temperature was cooled down to -110 °C and chlorodimethylsilane (0.09 mL, 0.84 mmol) was added. The reaction mixture was stirred overnight at room temperature followed by dissolution in DCM and extraction with water. The organic layer was dried on MgSO4, filtrated and then the solvent evaporated. The crude mixture was purified by silica gel chromatography using pentane as eluent to afford 4 as colourless solid (0.09 g, 88 % yield). 1 H NMR (400.16 MHz, CD2Cl2):  -0.07 (d, 3 J(H-H) = 3.8 Hz, 6H, SiMe2); 4.05 (hept, 3 J(H-H) = 3.8 Hz, 1H, Si-H); 7.48-7.50 (m, 1H); 7.58 (td, 3 J(H-H) = 7.5 Hz, 4 J(H-H) = 1.9 Hz, 1H); 7.61 (td, 3 J(H-H) = 7.4 Hz, 4 J(H-H) = 2.0 Hz, 1H); 7.82 (d, 3 J(H-H) = 9.2 Hz, 1H); 7.85-7.88 (m, 1H); 8.01 (d, 3 J(H-H) = 7.8 Hz, 1H); 8.05 (d, 3 J(H-H) = 9.0 Hz, 1H); 8.08 (d, J(H-H) = 8 Hz, 1H); 8.18 (d, 3 J(H-H) = 9.1 Hz, 1H); 8.20 (d, 3 J(H-H) = 9.1, 1H); 8.22-8.25 (m, 1H); 8.28 (d, 3 J(H-H) = 7.6 Hz, 1H); 8.29 (d, 3 J(H-H) = 7.8 Hz, 1H). 13 359.1232; found: 359.1226. 7,7-Dimethyl-7H-benzo[b]pyreno [1,2-d]silole (5). A mixture of 4 (0.53 g, 1.57 mmol) and 1,4-dioxane (2 mL) was degassed, then tris(triphenylphosphine)rhodium(I) chloride (0.07 g, 0.08 mmol) was added and stirred at 135 °C overnight. The resulting dark brown mixture was dissolved in DCM and the organic phase washed with water. The organic layer was dried on MgSO4, then the solvent evaporated and the crude mixture was purified by silica gel chromatography (pentane/ethyl acetate, 98/2), by neutral alumina chromatography (pentane) and by preparative TLC (pentane/ethyl acetate, 98/2) to afford 5 as a yellowish solid (0.12 g, 23% yield). 1 H NMR (400.16 MHz,CD2Cl2):  0.60 (s, 6H, SiMe2); 7.40-7.44 (m, 1H); 7.60-7.65 (m, 1H); 7.86 (ddd, 3 J(H-H)= 7.0 Hz, 4 J(H-H) = 1.5 Hz, 5 J(H-H) = 0.7 Hz, 1H); 8.06 (dd, 3 J(H-H) = 7.2 Hz, 4 J(H-H) = 4.0 Hz, 1H); 8. 10-8.16 (m, 2H); 8.20-8.25 (m, 3H); 8.49 (s, 1H); 8.63 (dd, 3 J(H-H) = 8.1 Hz, 5 J(H-H) = 0.8 Hz, 1H); 9.12 (d, 3 J(H-H) = 9.5 Hz, 1H). 13 357.1076; found: 357.1070. 11-Phenylbenzo[b]phenaleno [1,9-fg]phosphindole 11-oxide (6). Pyrene-2-boronic acid (0.05 g, 0.20 mmol), (2-bromophenyl) diphenylphosphine (0.08 g, 0.22 mmol) and potassium phosphate (0.13 g, 0.60 mmol) were dissolved in DMF (4 mL). The solution was degassed and [1,1′-Bis(diphenylphosphino) ferrocene] dichloropalladium (II) (0.05 eq.) was added to the reaction mixture and heated three days at 135 °C. The solution was then extracted with DCM. The organic layer was dried on MgSO4, filtrated and then the solvent was evaporated. The crude mixture was filtrated on Celite® with dry DCM to give to give the  3 , 3 P intermediate ( 31 P NMR (161.99 MHz, CD2Cl2):  (ppm) = -13.5 (s)) as a yellow solid (0.03 g, 33 % yield). The crude was dissolved in toluene (0.6 mL) and the mixture was degassed before adding palladium acetate (0.05 eq.). The reaction was stirred 12h at 160 °C, then after cooling, a 30 % aqueous H2O2 solution (1mL) was added for oxidation followed by dissolution in DCM and extraction with water. The organic layer was dried on MgSO4, filtrated and then the solvent was evaporated. The crude mixture was purified by silica gel chromatography using ethyl acetate/heptane, 9/1 as eluent to afford 6 as a yellow solid (0.03 g, 25% yield). [START_REF] Wu | Graphenes as potential material for electronics[END_REF] H NMR (500.15 MHz, CD2Cl2):  7.37 (t, 3 J(H-H) = 7.6 Hz, 2H, Hmetha); 7.47 (t, J(H-H) = 7.3 Hz, 2H ); 7.65-7.71 (m, 1H); 7.72 (m, 2H, Hortho); 7.77-7.79 (m, 1H); 8.02 (t, 3 J(H-H) = 7.6 Hz, 1H); 8.12 (d, 3 J(H-H) = 9.0 Hz, 1H); 8.16 (dd, 3 J(H-H) = 5.2 Hz, 4 J(H-H) = 2.7 Hz, 1H); 8.19 (d, 3 J(H-H) = 5.9 Hz, 2H); 8.21 (d, J(H-H) 11,11-Dimethyl-11H-benzo[b]pyreno [2,1-d]silole (7). 2-(2-bromophenyl)pyrene (0.19 g, 0.55 mmol) was dissolved in distilled THF (10 mL), then the mixture was cooled down at -78 °C before to add nBuLi (0.28 mL, 0.71 mmol, M = 2.45 mol/L). After one hour at -78 °C, chlorodimethylsilane (0.18 mL, 1.65 mmol) was added. The reaction mixture was stirred overnight at room temperature, dissolved in DCM and extracted with water. The organic layer was dried on MgSO4, filtrated and then the solvent was evaporated. The crude mixture was purified by silica gel chromatography using pentane as eluent to afford 4b (see SI) as yellow oil (0.06 g, 35% yield). Intermediate 4b (HR-MS (ESI, CH3OH/CH2Cl2: 70/30, m/z): [M+Na] + calcd for C24H20NaSi: 359.1232; found: 359.1227) has been engaged without further purification in the next step. 4b (0.18 g, 0.53 mmol) and 1,4-dioxane (1 mL) was degassed, then tris(triphenylphosphine)rhodium(I) chloride (0.03 g, 0.03 mmol) was added and the reaction mixture stirred at 135 °C overnight. The resulting dark brown mixture was extracted with DCM and the organic phase washed with water. The organic layer was dried on MgSO4, filtrated and then the solvent evaporated. The crude mixture was purified by silica gel chromatography (pentane/ethyl acetate, 98/2), then by neutral alumina chromatography (pentane) and finally by preparative TLC (pentane/ethyl acetate, 98/2) to afford 7 as a clear yellowish solid (0.02 g, 11 % yield). 1 H NMR (400.16 MHz,CD2Cl2):  0.74 (s, 6H, Si-(CH3)2); 7.42 (td, 3 J(H-H) = 7.2 Hz; 4 J(H-H) = 1.0 Hz, 1H); 7.60 (td, 3 J(H-H) = 7.4 Hz, 4 J(H-H) = 1.3 Hz, 1H); 7.82 (ddd, 3 J(H-H) = 7.0 Hz, 4 J(H-H) = 1.4 Hz, 5 J(H-H) = 0.8 Hz, 1H); 8.04 (t, 3 J(H-H) = 7.6 Hz, 1H); 8. 14 -8.20 (m, 4H); 8.20-82.26 (m, 3H)

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website. Photophysical data, computational procedures, X-ray crystallographic data, NMR spectra.

Figure 1 .

 1 Figure 1. Functionalized pyrenes A -B and pyrene-fused heteroles C -D.

Figure 2 .Figure 3 .

 23 Figure 2. Crystallographic structure of 3 (left), 6 (middle), 5 (right) in top (up) and side view (middle) and view of the packing (down)

a

  4.06), 395 (4.32), 383 (4.91), 361 (4.76) 434 54 0.93 d -2.13 d 5 404 (2.89), 385 (4.26) 364 (3.91), 348 (3.90) 408 47 0.72 d -2.41 d 6 414 (3.33), 403 (3.00), 390 (3.29), 369 (4In CH2Cl2 (10 -5 M). b Measured relative to quinine sulfate (H2SO4, 0.1 M), ref= 0.55 c In CH2Cl2 with Bu4N + PF6 -(0.2 M) at a scan rate of 100 mVs -1 . E ox (E red ) = 1/2(Epc Epa) for reversible or quasi-reversible process, otherwise E ox (E red ) = (Epa). Potentials vs ferrocene/ferrocenium. d reversible process.

Figure 4 .

 4 Figure 4. Molecular Orbitals (HOMO-1, HOMO, LUMO, LUMO+1) of pyrene, 3, 6, 5 and 7 at the B3LYP/6-31+G* level.

Figure 5 .

 5 Figure 5. NICS(1) aromaticity patterns of pyrene, 3, 5-7 at the B3LYP/6-31+G* level.

  C{ 1 H} NMR (125.78 MHz, CD2Cl2):  123.7 (s, CH); 125.2 (s, Cq); 126.1 (d, 3 J(C-P) = 9.8 Hz, CH); 126.4 (s, CH); 126.5 (d, 3 J(C-P) = 10.4 Hz, CH); 127.0 (s, CH); 127.6 (s, CH); 128.0 (d, 3 J(C-P) = 10.4 Hz, Cq); 128.1 (s, CH); 128.5 (d, 5 J(C-P) = 1.8 Hz, Cq); 129.1 (s, CH); 129.3 (d, 2 J(C-P) = 12.5 Hz, CHmeta); 129.4 (d, 2 J(C-P) = 11.1 Hz, CH); 130.0 (s, CH); 130.8 (d, 3 J(C-P) = 9.2 Hz, CH); 131.4 (s, Cq); 131.7 (d, 2 J(C-P) = 10.8 Hz, CHortho); 132.2 (d, 1 J(C-P) = 103.4 Hz, Cipso); 132.4 (d, 2 J = 11.9 Hz, Cq); 132.6 (d, 4 J(C-P) = 2.9 Hz, CHpara); 132.7 (d, 1 J(C-P) = 104.5 Hz, Cα); 134.1 (d, 4 J(C-P) = 2.1 Hz, CH); 134.5 (d, 2 J(C-P) = 21.6 Hz, Cβ); 135.4 (d, 1 J(C-P) = 104.1 Hz, Cα); 144.4 (d, 2 J(C-P) = 21.2 Hz, Cβ). 1 Cq is not observed. 31 P NMR{ 1 H} (161.99 MHz, CD2Cl2):  +  (s). HR-MS (ESI, CH3OH/CH2Cl2: 70/30: m/z): [M+Na] + calcd for C28H17ONaP: 423.0915; found 423.0909. Dimethyl(2-(pyren-1-yl)phenyl)silane (4).

  C NMR { 1 H} (100.62 MHz,CD2Cl2):  -3.4 (d, 1 J(C-Si) = 10.0 Hz, CH3); 124.0 (s, CH); 124.5 (s, Cq); 124.7 (s, Cq); 125.0 (s, CH); 125.2 (s, CH); 125.8 (s, CH); 126.1 (s, CH); 126.8 (s, CH); 127.2 (s, CH); 127.4 (s, CH); 127.5 (s, CH); 128.0 (s, CH); 128.9 (s, CH); 129.6 (s, Cq); 130.5 (s, CH); 130.8 (s, Cq); 131.0 (s, Cq); 131.5 (s, Cq); 135.0 (s, CH); 137.7 (s, Cq); 138.7 (s, Cq); 147.5 (s, Cq). HR-MS (ESI, CH3OH/CH2Cl2: 70/30, m/z): [M+Na] + calcd for C24H20NaSi:

  = 7.4 Hz, 1H); 8.24(d, J(H-H) = 8.0 Hz, 1H); 8.35(d, 3 J(H-H) = 9.0 Hz, 1H); 8.60 (s, 1H).13 C { 1 H} NMR (125.78 MHz, CD2Cl2):  117.6 (d, 3 J(C-P) = 10.6 Hz, CH); 122.4 (d, 3 J(C-P) = 10.1 Hz, CH); 124.9 (d, 4 J(C-P) = 5.9 Hz, CH); 125.2 (d, J(C-P) = 83.0 Hz, Cq); 126.0 (d, 1 J(C-P) = 97.1 Hz, Cα); 127.1 (s, CH); 127.2 (s, CH); 127.4 (s, CH); 128.0 (s, CH); 129.0 (d, 3 J = 12.0 Hz, Cq); 129.3 (d, 2 J(C-P) = 12.4 Hz, CHmeta); 130.1 (d, 3 J(C-P) = 9.8 Hz, CH); 130.3 (d, 3 J(C-P) = 11.1 Hz, CHpara); 130.6 (s, CH); 130.8 (s, CH); 131.2 (d, J(C-P) = 49.1 Hz, Cq); 131.6 (d, 3 J(C-P) = 10.8 Hz, CHortho); 132.5 (d, 3 J = 9.8 Hz, Cq); 132.6 (d, 1 J(C-P) = 102.3 Hz, Cipso); 132.6 (d, 4 J(C-P)= 2.8 Hz, CH); 133.2 (d, 3 J(C-P) = 8.9 Hz, Cq); 134.0 (d, 4 J(C-P) = 2.1 Hz, CH); 135.0 (d, 1 J(C-P) = 106.9 Hz, C); 136.1 (d, 4 J(C-P)= 2.0 Hz, Cq); 140.1 (d, 2 J(C-P) = 21.4 Hz, Cβ); 142.8 (d, 2 J(C-P) = 21.5 Hz, Cβ). 31 P { 1 H} NMR (161.99 MHz, CD2Cl2):  (s). HR-MS (ESI, CH3OH/CH2Cl2: 80/20, m/z) [M+Na] + calcd for C28H17ONaP: 423.0915; found 423.0909.

Table 1 :

 1 Optical and electrochemical data

	abs (logε a

  CH); 138.8 (s, Cα); 141.3 (s, Cα); 141.7 (s, Cβ); 149.7 (s, Cβ). 1 Cq is missing due to overlapping. HR-MS (ESI, CH3OH/CH2Cl2: 70/30, m/z): [M+Na] + calcd for C24H18NaSi:

	133.3 (s,
	C NMR { 1 H} (100.62
	MHz, CD2Cl2):  -3.3 (s, CH3); 124.3 (s, CH); 124.7 (s, CH); 125.3
	(s, CH); 126.1 (s, CH); 126.4 (s, CH); 126.5 (s, Cq); 126.6 (s, Cq);
	126.9 (s, CH); 127.2 (s, CH); 127.5 (s, CH); 127.7 (s, CH); 129.1
	(s, CH); 130.1 (s, CH); 130.3 (s, Cq); 130.9 (s, Cq); 131.8 (s, Cq);

  ; 8.68 (s, 1H). 13 C NMR { 1 H} (100.62 MHz, CD2Cl2):  -2.8 (s, CH3); 117.3 (s, CH); 121.4 (s, CH); 124.2 (s, Cq); 125.0 (s, Cq); 125.3 (s, CH); 125.4 (s, CH); 125.8 (s, CH); 127.8 (s, CH); 127.9 (s, CH); 128.0 (s, CH); 128.1 (s, CH); 128.2 (s, CH); 130.4 (s, CH); 130.9 (s, Cq); 131.2 (s, Cq); 132.9 (s, CH); 133.4 (s, Cq); 135.3 (s, Cα); 135.6 (s, Cq); 139.6 (s, Cα); 145.9 (s, Cβ); 148.2 (s, Cβ). HR-MS (ASAP, 150 °C): M +. calcd for C24H18Si: 334.1178; found: 334.1172.

ACKNOWLEDGMENT

Financial Support from OTKA NN 113772 and BME-Nanonotechnology FIKP grant of EMMI (BME FIKP-NAT) for LN are gratefully acknowledged. ANR-16-CE05-0003-01, Heterographene, China-French AIL in "Functional Organophosphorus Materials", PICS SmartPAH (08062), PHC Balaton (38522ZH), EU-COST network CM1302 "Smart Inorganic Polymers" (SIPs) are also thanked.

AUTHOR INFORMATION

Corresponding Authors * E-mail: muriel.hissler@univ-rennes1.fr * E-mail: nyulaszi@mail.bme.hu * E-mail: pierre-antoine.bouit@univ-rennes1.fr ORCID Pierre-antoine Bouit: 0000-0002-0538-9276 Muriel Hissler: 0000-0003-1992-1814

Notes

All authors have given approval to the final version of the manuscript.


Gabriel Frisch

Philippe Xu

Emmanuel Stawiarski

High integrity lane level localization using multiple lane markings detection and horizontal protection levels

For autonomous driving, lane level accurate localization is a necessity for complex driving maneuvers. Classical GNSS based methods are usually not accurate enough to have an unambiguous lane level localization. Having camera measurements such as lane marking detections along with high definition maps can enhance localization performance. In this paper, we are interested in high integrity localization, meaning being robust with low risk level. We propose a novel geometrical approach using horizontal protection levels on localization to propagate uncertainties and use lane markings to have an unambiguous map-matching. We demonstrate on real data that the algorithm can cope with high levels of noise on both localization and detection.

I. INTRODUCTION

Having a precise and reliable pose estimation is critical for autonomous vehicles. GNSS only solutions are most of the time not precise enough to realize complex maneuvers with low risk. Many other sensors may be combined to improve this localization. High definition maps can also be used to improve accuracy. Maps contain a lot of information such as positions of traffic signs, intersections, lane markings or driving lanes [START_REF] Ph | Lanelets: Efficient map representation for autonomous driving[END_REF], [START_REF] Bétaille | Creating enhanced maps for lanelevel vehicle navigation[END_REF]. In order to use information from maps, it is necessary to realize a map-matching procedure, which means making a link between the objects detected by the sensors and the features in the map. There exists many techniques for map-matching, with their advantages and complexity. The most simplistic ones rely on geometrical analyses, such as point-to-point or point-to-curve matching [START_REF] Ch | Some map matching algorithms for personal navigation assistants[END_REF]. The most advanced ones use more refined concepts such as the theory of belief functions [START_REF] El Najjar | Road selection using multicriteria fusion for the road-matching problem[END_REF], Extended Kalman Filter [START_REF] Tao | Lane marking aided vehicle localization[END_REF] or Particle Filtering [START_REF] Li | Using High Definition Maps to Estimate GNSS Positioning Uncertainty[END_REF].

Apart from having good pose estimation, guaranteeing the reliability of the estimation is even more important and challenging in safety-critical applications such as autonomous driving. The concepts of integrity and protection levels initial defined in aviation have been extended to road vehicles in the recent years [START_REF] Dbouk | Comparison of different bounding methods for providing gps integrity information[END_REF], [START_REF] Navarro Madrid | New approach for integrity bounds computation applied to advanced precise positioning applicationsg[END_REF].

The motivation of this paper is not to improve the localization but to present a method that realizes a lane level mapmatching with a high integrity. This approach uses horizontal protection levels on localization to propagate uncertainties and uses multiple lane marking detections to have a unique unambiguous map-matching. Section II states the general problem, the map representation, the camera model and the working frames. Pose integrity concepts and over-bounding uncertainties on sensors are introduced in Section III. Section IV provides a description of the new map-matching algorithm and the multiple hypothesis disambiguation process. Finally, experimental results of this algorithm are presented in Section V.

II. PROBLEM STATEMENT

The aim of this work is to position a vehicle in its actual driving lane. If the vehicle is represented by its pose, i.e., position and heading, we want to guarantee with a high degree of confidence that the coordinates of the position are within the bounds of its corresponding lane, which are assumed to be given within a map. In order to guarantee a low risk of wrong lane selection, our approach will provide a decision in case of non-ambiguous hypothesis. The uncertainty of the pose is modeled by protection levels representing a space domain in which the vehicle is certain to be with a given risk.

A. Working frames

In general, GNSS and map data are expressed in geographic coordinates [START_REF]Department of defense world geodetic system 1984: its definition and relationships with local geodetic systems[END_REF]. However, Cartesian coordinates are usually preferred as the computation of geometric transformation becomes easier. We choose to work in a local Cartesian ENU (East, North, Up) [START_REF] Tao | Sequential data fusion of GNSS pseudoranges and Dopplers with map-based vision systems[END_REF] reference frame R O ; its origin can be any position close to the navigation area.

Several working frames are defined and illustrated in Fig. 1. The first one denoted R M is attached to the vehicle at point M , representing the middle of the rear wheels. The vehicle pose is defined at point M as [x, y, θ] T in R O which includes the position [x, y] T and the heading θ. The second frame R C represents the camera frame in which the measurements will be represented. Its origin C is virtually situated at the center of the front bumper. Both x M and x C are longitudinal axes pointing forward while y M and y C are lateral axes pointing to the left side of the vehicle.

B. Map representation

The map used in this research has a scale between the macro-scale (e.g., road guidance maps) and micro-scale (e.g., point cloud from perception sensors) [START_REF] El Najjar | Road selection using multicriteria fusion for the road-matching problem[END_REF]. In our map, the lanes are discretized as polylines, i.e., a sequence of line segments representing the center of the lanes. The border of a lane corresponds either to a lane marking, or the limit of the drivable road space defined by sidewalks, for example. The lane borders are also represented by polylines but with an additional associated type: solid, dashed, double, etc.

C. Camera model

The aim of the camera module is to return measurements of detected lane markings. The image processing step is out of the scope of this paper. In our case, we used an off-theshelf intelligent camera: Mobileye. The camera is able to detect up to four markings at a time; two on each side of the vehicle. For each detected lane marking, the coefficients of a third degree polynomial are returned. In the camera frame R C , the equation can be expressed as

y = C 3 x 3 + C 2 x 2 + C 1 x + C 0 . (1)
In this paper, only the coefficient C 0 is used in the mapmatching process. The value of C 0 corresponds to the lateral distance to an observed lane marking along the y C axis. In the example pictured in Fig. 1, the coordinates of the point L, which belongs to an observed lane marking [AB], are equal to [0, C 0 ] T in the camera frame R C . In the rest of the paper, a detected lane marking will be represented by its corresponding point L in the camera frame. In addition to the lateral distance, the camera is able to give the type (dashed, continuous, double, etc.) and also a quality indicator (with value in {0,1,2,3}) associated with each lane marking detection. Our approach can be used with any other lane marking detection algorithm from the literature as long as they provide similar information.

III. UNCERTAINTY AND INTEGRITY

The uncertainty of measurements are usually represented as an additive Gaussian white noise from which probabilistic confidence bounds can be computed given a level of risk α. Assuming that errors are normally distributed is often unrealistic in practice due to outliers [START_REF] Agamennoni | An outlier-robust kalman filter[END_REF]. Robust methods have been proposed using more cautious models such as intervals [START_REF] Abdallah | A multiple-hypothesis map-matching method suitable for weighted and box-shaped state estimation for localization[END_REF], [START_REF] Tran | Interval kalman filter enhanced by positive definite upper bounds[END_REF] or heavy tail distributions [START_REF] Agamennoni | An outlier-robust kalman filter[END_REF], [START_REF] Bin Ahmad | Characterization of GNSS Receiver Position Errors for User Integrity Monitoring in Urban Environments[END_REF]. The aim of these methods is to over-bound the true error distribution resulting in more consistent confidence bounds called protection levels. For a given risk α, also referred to Integrity Risk (IR), the Protection Level (PL) is a statistical bound on the Position Error (PE) such that the probability that the error exceeds the PL should be equal to the Integrity Risk: P r(P E > P L) = IR. Because the true probability density function of the position error is usually not known, we often handle instead a Target Integrity Risk (TIR) which verifies P r(P E > P L) ≤ T IR.

A. Pose uncertainty

We will directly introduce the pose error within the mobile frame R M . In this frame, the true vehicle pose is [0, 0, 0] T , the estimated pose can be written as

xM , ŷM , θM T = [0, 0, 0] T + [e x , e y , e θ ] T , (2)
where XM = xM , ŷM , θM T is the estimated pose and is equal to the estimation error ê = [e x , e y , e θ ] T .

In general, a confidence domain D at risk α, verifies P (ê / ∈ D) = α and is defined as a 3-dimensional ellipsoid. Manipulating such domain may be complex. One solution is to over-bound it by the smallest 3-dimensional parallelepiped D aligned with the frame axis. As D ⊂ D, we have

P (ê / ∈ D) ≤ α.
In the case where the estimation error ê follows a zero mean Gaussian distribution with a diagonal covariance matrix Σ = diag(σ 2

x , σ 2 y , σ 2 θ ), the domain D is defined by intervals over the three coordinates.

D = [-x, +x] × [-y, +y] × -θ, +θ , (3)
with q = z 1-α /2 σ q , q ∈ {x, y, θ}, (4)
where z β is the β-quantile of the standard normal distribution. Within the mobile frame, x represents the along protection level (P L x ), y the across protection level (P L y ) and θ the heading protection level (P L θ ).

B. Map and camera uncertainty

We do not consider the map as being perfect and we decide to take into account the map positional error. As the error distribution is not known, we prefer to over-bound the error. We assume that the true position of any point defining the polylines of the map is located within a circle of radius l [START_REF] Tao | Lane marking aided vehicle localization[END_REF]. We consider that the circle is a guaranteed domain, i.e., with a probability of one. In the same way as we did with the pose uncertainty, we bound a line segment between two consecutive points by the smallest rectangle containing the two circles as illustrated in Fig. 2.

Similarly to map uncertainties, we also over-bound the camera measurement error within a ±∆C 0 bound. If the uncertainties on maps and camera measurements are known, these bounds can also be replaced by confidence domains w.r.t. a given risk. These uncertainties are illustrated in Fig. 2.

IV. MAP MATCHING OF THE CAMERA MEASUREMENTS

A. Principle of the algorithm

The map matching process is to find within the digital map the lane markings that are observed by the camera. The algorithm presented in this paper combines both the vehicle pose, the protection levels associated with a given risk α, the measurements of the camera with their uncertainties and the high definition map with positional uncertainties.

For each camera measurement, and with the use of the protection levels and the camera uncertainty, the method generates a search area centered on the estimated detected marking. This area represents the possible locations of the point L representing the detected marking. Therefore, any marking from the map intersecting this area is considered as a plausible candidate for the map-matching. It is possible to have several markings intersecting this area and so several candidates. However, with the combination of the different camera measurements and the road configuration (one, two or more lanes), it is possible in some cases, to disambiguate the situation and have a final unique matching hypothesis for each detected marking.

B. Search polygon

The first step of the algorithm in defining the search area S T IR for a given TIR (Fig. 3). This area has to take into account uncertainties on both the pose (P L x , P L y , P L θ ) and the camera measurement (∆C 0 ). Computing directly this shape might be tricky so the construction is divided into three steps.

• Step 1: we first ignore P L θ . Due to P L x and P L y , the actual position of point M may be anywhere within a 2 • P L x length and 2 • P L y width rectangle. As a result, the detected lane marking point might be anywhere in this same size rectangle but translated to point L (on Fig. 3-a: plain black rectangle). The camera measurement is also uncertain, therefore the rectangle needs to be augmented by 2 • ∆C 0 along the lateral axis. We obtain a 2•(P L y +∆C 0 )×2•P L x rectangle centered on L (red colored area in Fig. 3-a).

• Step 2: we now introduce P L θ . If the heading of the vehicle belongs to [θ -P L θ ; θ + P L θ ], the origin of R C is moving on an arc and so is the previously defined rectangle. The domain covered by the rectangle when the heading θ goes from θ -P L θ up to θ + P L θ is a shape with two curved sides. There is an outer convex side (between points B and C in Fig. 3-b) and an inner concave side (between points E and F in Fig. 3-b).

• Step 3: having to manipulate the search domain resulted from Step 2 is not convenient because of the curved parts, therefore, we will over-bound it by a convex polygonal hull. Because the inner side in concave, we link the points E and F by a straight line. On the contrary, because the outer side in convex, a straight line between the points B and C will not lead to an over-bounding. Instead, we add an additional point G with corresponds to the intersection of the tangent at point B and the tangent at point C. The final search domain (see Fig. 3-c) is a convex polygon containing the one from the previous step, therefore verifying the integrity constraint.

C. Map-matching hypothesis

A lane marking is also represented by a polygon, therefore a lane marking is considered as a candidate for the mapmatching is its corresponding polygon intersects the search polygon defined previously. To find candidate markings, we can use a clipping algorithm such as Weiler-Atherton [START_REF] Weiler | Hidden surface removal using polygon area sorting[END_REF] or Sutherland-Hodgman [START_REF] Sutherland | Reentrant polygon clipping[END_REF] algorithms. We used the later one as it is optimized for convex polygons. These algorithms return the intersection between two polygons. If the result is not empty then the marking is considered as a plausible hypothesis. Only nearby markings are treated to optimize the algorithm. The map contains a R-tree index to efficiently retrieve markings in a rectangular area.

Depending on the considered target integrity risk, there could be no matching (Fig. 4-a), a unique matching (Fig. 4b) or multiple matching candidates (Fig. 4-c). It is important to note that as we have supposed the map error to be strictly bounded, the bounds on the lane markings do not change w.r.t. the TIR. On the contrary, a high TIR will result in a small search polygon while a low TIR will lead to a large one.

The optimal strategy of the algorithm is to give an integrity risk range in which the map matching is not ambiguous. However, determining this range, even with a dichotomous method has a high computational cost. The solution retained to keep a low computation cost, to the detriment of the algorithm availability, is to execute the algorithm with a preselected TIR scale to roughly constrict the true range.

D. Disambiguation with multiple measurements

Multiple marking hypotheses could result from very large protection levels or large uncertainties. However, it is possible to disambiguate the hypotheses if the road lanes configuration is jointly used with several camera measurements. We remind that lane markings are made up of a sequence of line segments. We introduce the following notations: M ij represents the j-th segment of the i-th marking of the map, (i, j) ∈ N 2 and h (k) i is the k-th map-matched marking hypothesis corresponding to the i-th camera measurement, i ∈ {1, 2, 3, 4}. The marking segments are ordered from left to right (according to R C ) so the index i of M i represents the i-th marking starting from the left. Moreover, only markings nearby the car are considered. We also consider that all connected segments represent the same marking and thus the same hypothesis. The h (k) i hypotheses are merged:

∀i ∈ N, H i = {h (k) i , ∀k ∈ N}. (5)
The disambiguation process is based on the assumption that the car is always driving on a lane and not outside of the road; thus left side detected markings cannot be matched with the most right road marking on the map and vice versa:

(H 4∨3 = M 1 ) ∧ (H 1∨2 = M n ), (6)
with M n the most right markings given the context. The camera also never returns two measurements for the same detected marking:

∀(i, j) ∈ N 2 , i = j ⇒ H i = H j . (7)
The camera measurements are ordered, from left to right, which implies:

(H m = M i ) & (H n = M j ) ⇒ m < n & i < j. (8)
The algorithm generates all valid combinations from the map matched hypotheses. To do so, a depth-first possibility tree exploration is made. First, some hypotheses are united according to [START_REF] Bin Ahmad | Characterization of GNSS Receiver Position Errors for User Integrity Monitoring in Urban Environments[END_REF]. Then, at each node, conditions ( 6), ( 7) and (8) must be verified; if not the exploration of the branch is abandoned. If there is only one hypothesis left, then all ambiguities are removed and the final map-matching is returned.

For instance, let us consider the configuration as pictured in Fig. 5: a three-lane road delimited by four lane markings. Suppose that the camera provides four marking detections and that the map matching algorithm returned the following hypotheses : 5) merges segments of the same marking. If rule ( 6) is applied, then M 4 is removed from H 2 because the most right marking cannot be matched with a left side measurement. If we suppose that H 1 = M 2 then because of rules ( 7) and ( 8), we would get H 2 = M 3 , H 3 = M 4 and H 4 = ∅, which is impossible. If we keep applying rules, we finally obtain one unique M i marking for each hypothesis H j , which means there is no more ambiguities:

• H 1 = {(M 11 ∨ M 12 ) ∨ (M 21 )} = M 1 ∨ M 2 • H 2 = {(M 11 ) ∨ (M 21 ∨ M 22 ) ∨ (M 31 ) ∨ (M 41 )} = M 1 ∨ M 2 ∨ M 3 ∨ M 4 • H 3 = {(M 21 )∨(M 31 )∨(M 41 ∨M 42 )} = M 2 ∨M 3 ∨M 4 • H 4 = {(M 31 ) ∨ (M 41 ∨ M 42 )} = M 3 ∨ M 4 Rule (
(H 1 = M 1 ) ∧ (H 2 = M 2 ) ∧ (H 3 = M 3 ) ∧ (H 4 = M 4 ).

E. Constraints on detected markings

The camera provides additional information about detected markings: the type of marking (dashed, solid, double, etc.) and the quality of the detection (with value in {0,1,2,3}). It is possible to add constraints to the map-matching algorithm and decide to ignore the low quality detected markings (i.e., 0 or 1, which represent about 20% of the measurements) or ignore markings from the map if the detected type does not match. We will measure the impact of these restrictions in the experimental part.

V. EXPERIMENTS

The algorithm has been tested with real data recorded on open road using ROS framework. The vehicle was equipped with a RTK-GNSS receiver to provide the ground truth localization. A Mobileye camera was used to provide a detection of up to four lane markings at a time. The experiment took place in December 2017 in Palaiseau, France (Fig. 6). The map-matching algorithm has been implemented in Python and runs in real time at 30 Hz.

A. System availability

We first set the TIR to 10 -4 and assessed the localization system availability w.r.t. to the level of positioning error. We added artificial noise to the position data to simulate errors in the pose estimation. A Gaussian noise N (0, Σ) was added to the RTK-GNSS measurements, which are considered as the ground truth. The over-bound ∆C 0 of the camera measurement errors and the radius l of the map errors were set to 60 cm. Figure 7 shows the system availability with respect to the noise standard deviation. In the case where only GNSS pose was used, the system was considered as available when the pose and its protection levels remained inside the lane. With the use of the camera, the system was considered as available when the map-matching algorithm returned a nonambiguous hypothesis. The system availability was computed with variants of our algorithm: we decided alternatively to ignore or not the types and the quality level of the detected markings.

Unsurprisingly, the availability of the GNSS only solution decreases very quickly when the noise variance increases. Also, removing lowest quality detections and forcing correspondence of marking type at the same time gave the lowest rates. The version of the algorithm where marking types were handled regardless of the quality gave the best results. Indeed, keeping only highest detection qualities could lead to no measurements at all or to a lack of measurements and realizing disambiguation would be impossible. On the other hand, keeping all quality measurements and not requiring a good correspondence of marking types leads to multiple map-matching hypotheses which are impossible to disambiguate.

B. Integrity risk

Conversely, we then set the variance to fixed value σ 2 = 0.75, and studied the minimum level of integrity risk achievable using either the GNSS only solution or the map-matching one. We used our map-matching algorithm with marking type correspondences as it has been shown previously to have the highest availability. Figure 8 shows the limit integrity risk with respect to the time throughout the experiment. Blue points were computed with the GNSS only solution and red ones with the algorithm we proposed. The lowest Integrity Risk used was 10 -7 , as a consequence true limit could be lower. Even with a very low integrity risk our map-matching solution was able to give non-ambiguous results; the 90-th percentile is 10 -4 . On the contrary, the GNSS only solution median is 0.18 which shows that integrity would not be respected most of the time even if a high risk is set, typically 0.05.

VI. CONCLUSIONS

In this paper, a new method for lane level localization has been presented which aims at providing results with high integrity. This method combines pose protection levels and over-bounding of errors when the underlying distributions are unknown. The algorithm advantages lie in its efficiency and its ability to give reliable lane level localization, with an IR as low as 10 -7 , while keeping a high availability. The algorithm efficiency relies on the basic idea of using polygon intersections to express hypotheses. Furthermore, the algorithm is simple and easy to implement and contrary to classical geometrical approaches, the algorithm is insensitive to map imprecision.

The output of the map-matching can further serve as an input to a localization estimator in order to improve the pose estimation itself. One issue that was not considered in this paper is the case of missing markings in the map. The proposed algorithm may not be resilient to such a problem, especially when only few detected markings are available. One possible solution to alleviate such an issue would be to consider temporal consistency in the map-matching process.

Fig. 1 .

 1 Fig. 1. Reference frames. The vehicle body frame R M is located at point M and the camera frame R C is located at point C. C 0 represents the lateral distance between the camera frame and a lane marking [AB].

Fig. 2 .

 2 Fig. 2. Representation of map, camera and localization uncertainties. Points A and B are supposed to be within a circle of radius l. The lateral distance of the detected marking is C 0 with its uncertainty ∆C 0 .

Fig. 3 .Fig. 4 .

 34 Fig. 3. Steps of the search area construction. Step 1: without using P L θ . Step 2: introducing P L θ to compute intermediate areas. Step 3: final area (green) over-bounding previous areas of step 2.

Fig. 5 .

 5 Fig. 5. Road configuration with three lanes and four lane markings M i , i ∈ {1, 2, 3, 4}. M ij is the j-th segment of the i-th marking.

Fig. 6 .

 6 Fig. 6. Top: overview of the test site with the trajectory from point A to B. Bottom : colored map-matched marking. Matched markings with restrictions on quality levels and marking types are in dark blue and matched markings without restriction on quality or type are in light blue.

Fig. 7 .Fig. 8 .

 78 Fig. 7. System availability with TIR = 10 -4 .

  Frisch and Ph. Xu are with Sorbonne universités, Université de technologie de Compiègne, CNRS, Heudiasyc UMR 7253, 60203 Compiègne Cedex, France.

G. E. Stawiarski is with Renault s.a.s, Guyancourt, France. This research has been carried out in the scope of the SIVALab laboratory shared between Renault, UTC and CNRS.