Session E2, Paper #1
Performance Comparison of ELP and DELP for Multipath Detection
O.M. Mubarak, A.G. Dempster, The University of New South Wales, Australia
Early Late Phase (ELP), which has recently been proposed for multipath detection, exploits the carrier phase difference between the line of sight (LOS) and reflected signals to detect and mitigate multipath. ELP is computed as the difference in phase of early and late correlator outputs. It has been shown that in the absence of multipath, ELP remains close to zero. However, in the presence of multipath, it can attain a higher magnitude because of the presence of signals at two different carrier phases [2]. Thus, an ELP value beyond a certain threshold corresponds to the presence of multipath.
ELP is averaged in time to reduce noise. Averaged ELP has been analysed at different Doppler offsets in the carrier frequency. It has been found that ELP has a higher magnitude in the absence of multipath at certain Doppler offsets, termed "critical Doppler offsets" [1]. Since an increase in ELP magnitude corresponds to the presence of multipath, a higher ELP in the absence of multipath results in a relatively higher probability of false alarm. Differential ELP (DELP) has been proposed to detect multipath at critical Doppler offsets [1]. In order to compute DELP, ELP is locally emulated using tracking loop outputs. It is then subtracted from the ELP obtained from the correlator outputs to give DELP.
Although it has been shown that DELP has a lower magnitude than ELP at critical Doppler offsets, the improvement in multipath detection as a result of its use had not been quantified. Since the computation of DELP requires additional computational resources it is necessary to analyse this improvement, so that the feasibility of using DELP may be assessed for a given application depending on the accuracy required and computational resources available. This motivated the work presented in this paper. Multipath detection performance of ELP and DELP at critical Doppler offsets has been statistically compared. The spread of ELP is indicated in histograms. In the absence of multipath, the variance of the ELP histogram is dependent on the SNR of the signal and its mean is almost zero at all Doppler offsets except critical Doppler offsets. At critical Doppler offsets, the mean moves towards the theoretical ELP value at that Doppler offset. In other words, the whole ELP histogram moves in either a positive or negative direction. Since multipath is detected by defining an ELP threshold on either side of zero, the area of the histogram beyond such a threshold is increased by the histogram movement. The fraction of the area beyond this threshold gives the probability of false alarm, and thus for a given threshold, the probability of false alarm is higher at critical Doppler offsets compared to all other offsets. Since DELP has a significantly lower theoretical value at these critical Doppler offsets in the absence of multipath, it is proposed to be used (instead of ELP) at such Doppler offsets. However it is not recommended to be used at other Doppler offsets as it is computationally more burdensome than ELP and does not provide any advantage.
The increase in the probability of false alarm due to a shift in the ELP histogram is analyzed in this paper for different scales of shift and various ELP thresholds. It is shown that for a given shift in histogram this increase is higher for lower ELP thresholds and vice versa. Because ELP histograms are similar to Gaussian distributions, for a smaller ELP threshold, a given shift of histogram can result in a larger fraction of the histogram area going beyond the threshold, resulting in a relatively higher increase in the probability of false alarm.
The increase in ELP magnitude at critical Doppler offsets can be as high as 0.025 radians. It is shown that depending on the ELP threshold, this can result in up to a 6% increase in the probability of false alarm. On the other hand, DELP shows only an increase of 0.0025 radians at the same Doppler offset, which corresponds to at most a 0.5% increase in the probability of false alarm.
DELP is computed using tracking loop outputs and among them, the carrier phase measurement can become erroneous in the presence of multipath. As a result, DELP performance may be worse than ELP in the presence of multipath, either in the satellite signal being tracked or in an interfering satellite signal. The only exception to this is when the carrier phase difference between the LOS and reflected signals is close to an integer multiple of 2p, as only in this case the carrier phase provided by a tracking loop is similar to that of the LOS signal [1]. Since ELP exploits the phase differences between carriers of the LOS and reflected signals, there is a higher probability of multipath detection when it is not closer to an integer multiple of 2p. This implies that when erroneous tracking loop outputs adversely affect DELP computation, multipath is likely to be detected and the receiver can shift to ELP instead of DELP, even at the critical Doppler offsets. In order to effectively determine whether to use ELP or DELP, this paper also presents an analysis of change in the probability of detection using DELP when multipath is present in the satellite signal being tracked and the probability of false alarm when multipath is present in the interfering satellite signal.
In summary, the paper presents an analysis of performance of ELP and DELP to detect multipath at critical Doppler offsets. Results of this analysis can be useful in determining if and when to use DELP instead of ELP for a given application and computational resources.
References:
1. Mubarak, O. M., and Dempster, A., "Differential early late phase for multipath detection at critical Doppler offsets" in Proc. of the International Symposium on GPS/GNSS (Tokyo), November 11 - 14, 2008 Pages: 939 - 946 2. Mubarak, O. M., "Analysis of Early Late Phase for Multipath Mitigation" in Proc. of the 21st International Technical Meeting of the Satellite Division of the U.S. Institute of Navigation (Savannah) September 16 - 19, 2008.
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Session E2, Paper #2
A Location and Movement Dependent GNSS Multipath Error Model for Pedestrian Applications
A. Lehner, A. Steingass, German Aerospace Center (DLR), Germany
In 2002 the German Aerospace Center (DLR) carried out a high resolution measurement campaign to investigate the land mobile satellite navigation multipath channel. This became necessary because for wideband navigation systems like Galileo there is not enough knowledge about multipath. High bandwidth navigation signals are strongly disturbed by reflections from structures close to the receiver. To model these effects a very high time resolution is required. Especially for the BOC (Binary Offset Carrier) signal structures the delays of echoes have to be known in ns accuracies. Approaches of the past to describe the multipath effects have resolutions of 50 ns which is not satisfying for high precision positioning. Meanwhile we processed the data for car applications and published and analysed the corresponding channel model [1], which is currently undergoing a standardisation as a reference channel model by ITU. The next consecutive step is the extension of the model for pedestrian applications, where multipath reception is most critical due to the relatively slow user speed and strong shadowing effects on the sidewalks close to houses and trees.
For the measurements a Zeppelin simulated the satellite transmitting the measurement signal. During the campaign more than 60 measurements, each lasting for about 15 minutes were taken in several urban, suburban and rural scenarios for car and pedestrian applications in and around Munich. For a sufficient statistic we covered the whole elevation and azimuth range and chose streets containing a relevant mix for each channel type. The measurement signal had a bandwidth of 100 MHz and was transmitted every 3 ms to "sound" the channel, whose impulse response was recorded. For more details on the campaign please refer to [2].
In addition the Zeppelin transmitted a 18.8 GHz carrier whose Doppler shift was logged by a ground station in order to measure the airship´s movement which was in the same order as the movement of the pedestrian. These data are necessary to calculate the Doppler spreads caused by the receiver and its environment only. For the measurements a team member, simulating the average pedestrian, carried the receiver antenna in his hand, while walking along the sidewalks accompanied by a special measurement bus equipped with the channel sounder receiver and several sensors.
In this paper we will present statistical analyses of the measured data for pedestrian applications in urban and suburban environments. The raw data has a delay resolution of 10 ns and was post processed with an ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) based super resolution algorithm guaranteeing a delay resolution in ns. We will give detailed information about echo occurrences, birth and death rates, life times of echoes and their power and delay distributions. In addition we have accurate information about their Doppler shifts and bandwidths. We will present dependencies of the channel characteristics (e.g. visibility) on elevation and azimuth and compare urban and suburban scenarios. Furthermore we are able to identify worst case scenarios and can give verified examples, where positioning errors of more than 100 meters occurred due to multipath, when using a standard GPS receiver.
This pedestrian channel model allows the realistic simulation of the multipath channel by approximating every single reflection. It is based on a new approach: The combination of statistical data from a measurement and a deterministic scenario. The deterministic scenario is used for the direct path modelling. This includes effects such as shadowing by house fronts, tree damping or refracting lampposts. For house fronts and lampposts a knife edge diffraction model can be used due to its almost perfect matching to the measurement. For trees a new approach of deterministic and stochastic combined modelling is used to allow short simulation times.
The echo paths in this channel model are generated statistically in the geometric scenario. Their generation is driven by data obtained from the measurement only. The delay and Doppler trend of each measured echo and the transmitter and receiver position and speed, respectively, allowed to identify the fictive localization of the reflectors seen by the receive antenna. This data was used to determine a position distribution function relative to the receiver, which is strongly dependent on the satellite elevation and azimuth.
The model includes time variant reflectors approaching and receding, and a dependency on the azimuth and elevation of the satellite. Another input parameter is the receiver speed, which allows investigation of typical user movements, like an alternating stop and walk situation. The process of variable number of reflectors in different types of streets is modelled according to the observed occurrence of echoes. The output of the model is a series of channel impulse responses.
Due to the measurement approach the channel model is independent on the transmitted signal. Therefore the usability for all satellite navigation or communication systems in L-band is given. For better understanding and visualisation we will present a video of an animated walk through an urban scenario using the new channel model.
[1] Andreas Lehner, Alexander Steingass, "A novel channel model for land mobile satellite navigation", Institute of Navigation Conference ION 2005, Long Beach, USA. [2] Alexander Steingass. Andreas Lehner, "Measuring GALILEO´s multipath channel", GNSS 2003, Graz, Austria.
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Session E2, Paper #3
Post-Correlation Peak Sharpening
C. Yang, Sigtem Technology, Inc.; T. Nguyen, Air Force Research Lab/RYRN; M. Miller, Air Force Research Lab/RWG
Correlation between an incoming signal and a replica code is a fundamental operation in a GNSS receiver. The height of the correlation peak above the noise floor indicates the presence or absence of a desired signal while the location of the peak provides an estimate of the time and frequency of the acquired signal. However, due to limited bandwidth and inherent code structure, the correlation function is not an ideal delta function but rather has a certain size and shape. The spreading of energy into neighboring code and frequency bins not only makes the peak location imprecise in the presence of noise (thus also called the ambiguity function) but also renders it vulnerable to such interference as multipath. Methods have been introduced in the past to sharpen the correlation peak either prior to or during the correlation process. In this paper, two post-correlation peak sharpening methods are investigated, namely, the nonlinear Teager-Kaiser (TK) operator and the two-dimensional (2D) deconvolution. The TK operator was shown to outperform the classical narrow-correlator method against multipath. The 2D deconvolution, implemented either as a modified inverse filter or a Wiener filter, is analogy to image-deblurring but in the delay-Doppler domain. Simulation results are presented to illustrate the functionality and performance of post-correlation peak sharpening methods.
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Session E2, Paper #4
A Statistical Detector of Multipath and Interferences for Antenna-array based GNSS Receivers
C. Fernandez, Centre Tecnologic de Telecomunicacions de Catalunya, Spain; P. Closas, J.A. Fernandez-Rubio, Universidad Politecnica de Catalunya, Spain
This paper presents a statistical-based test for close multipath and interference detection for antenna-array based GNSS software receivers.
The problem of multipath mitigation has been extensively tackled both in single and multiple antenna configurations. In the case of single-antenna receivers several DLL-based methods have been proposed, such as the Narrow Correlator or different kinds of the Double Delta Correlator. However, multipath mitigation in single-antenna receivers has inherent drawbacks, such as the difficulty to resolve close reflections [Wei95].
In the case of multiple-antenna receivers, spatial diversity has revealed as an effective tool in the design of adaptive multipath and interference mitigation techniques for GNSS receivers. [Seco05] and [Fernandez06] proposed algorithms that effectively mitigate the effect of multipath and interferences without any previous knowledge of their characteristics and even without a explicit modeling of such harmful signals, but gathering them in a colored Gaussian noise term. These algorithms perform well and achieve coherent multipath mitigation when it is present, at the cost of an (often to a great extend) increased computational burden when compared to the regular DLL. However, the application of such methods in scenarios where multipath or interferences are not present implies a waste of computational load, and thus power consumption, at no benefit. Thus, there is a need of multipath detectors operating as close as possible to the antennas, that is, just at the output of the ADC converters.
Existing detectors operate at higher layers. For instance, at the observable level, day-to-day correlation can be used to identify and remove the multipath errors [Kamarudin04]. Other strategies are based on on pseudoranges [Brown97], the SNR [Comp98], the instantaneous difference between the pseudorange and the carrier-phase [Braasch95], linear combinations of the pseudorange and the L1 and L2 carrier-phases [Bisnath01], or successive-time double-differences [Lee]. Recent works try to deal with the synchronization of all the impinging signals in order to isolate the line-of-sight one, or using an independent component analysis (ICA) algorithm [Tarhuni07], but these techniques are unable to cope with coherent multipath, that is, echoes that have a relative delay with respect to the line-of-sight signal smaller that a chip period. There are also proposals of algorithms that operates at the tracking loop level: given an antenna array with a GPS software receiver in tracking mode, the signal from each channel is correlated with a reference signal in blocks of one C/A code period. When the relative phase delay for the direct GPS signal is stripped off from each channel, the expected values of the correlates is the same for all of the channels only if no multipath is present. This can be exploited to define a multipath detector by means of an Analysis of Variance (ANOVA) algorithm [Brenneman08]. However, this method cannot be applied directly to the input signal. This is due to the fact that the GPS signal is by construction a weak direct spread-spectrum signal which is not statistically detectable, and thus we have to assume that the receiver is already in tracking mode before applying the multipath detection algorithm.
The method proposed in this paper operates directly on the digitized signal, in parallel to the acquisition and tracking processes, and have no need of inferring the number of multipath components and computing their delays. Therefore, it can be considered a step towards a cognitive GNSS receiver: a device that could adapt its correlation strategies according to the results of a ´scenario sensing´. Since the Software-Defined-Radio approach allows the coexistence of different algorithms for synchronization that can be stored in memory and applied as required, this new detector can be used as a metric for the existence of multipath or interferences in the scenario. The proposed detector is based on the relation between the arithmetic and the geometric means of the covariance matrix eigenvalues. The full derivation and justification of this metric will be found on the final paper. In addition, simulation results will be presented showing the probability of false alarm of the detector as a function of a number of parameters, such as signal-to-multipath ratio, signal-to-interference ratio, relative angle-of-arrival and relative delay between LOS signal and its replica.
[Seco05] Gonzalo Seco et al., "ML estimator and Hybrid Beamformer for multipath and interference mitigation in GNSS receivers", IEEE Transactions on Signal Processing, vol. 53, no. 3, pp. 1194-1208, March 2005.
[Fernandez06] Carles Fern ndez Prades, "Advanced Signal Processing Techniques for Global Navigation Satellite Systems Receivers", PhD Dissertation, UPC, April 2006.
[Brenneman08] M.T. Brenneman et al., An ANOVA-Based GPS Multipath Detection Algorithm Using Multi-Channel Software Receivers, Proc. 2008 Joint IEEE PLANS and ION Annual Meeting. Monterey, CA. May 6-8, 2008.
[Kamarudin04] N. Kamarudin et al., Multipath Error Detection Using Different GPS Receivers Antenna, 3rd FIG Regional Conference. Jakarta, Indonesia, October 3-7, 2004.
[Tarhuni07] M. El-Tarhuni et al., An ICA-Based Multipath Detection Algorithm for DS-SS Communication Systems, 9th International Symposium on Signal Processing and Its Applications, ISSPA 2007, Sharjah, United Arab Emirate, 12-15 Feb. 2007
[Brown97] R. G. Brown et al., "GPS RAIM: Calculation of threshold and protection radius using chi-square methods-a geometric approach," in Global Positioning System: Inst. Navigat., 1997, vol. V, pp. 155-179.
[Comp98] C. J. Comp et al., "Adaptive SNR-based carrier phase multipath mitigation technique," IEEE Trans. Aerosp. Electron. Syst., vol. 34, pp. 264-276, Jan. 1998.
[Braasch95] M. S. Braasch, "Isolation of GPS multipath and receiver tracking errors," J. Inst. Navigat., vol. 41, pp. 415-434, 1995.
[Bisnath01] S. B. Bisnath et al., "Pseudorange multipath mitigation by means of multipath monitoring and deweighting," in Proc. IEEE 4th Int. Symp. Kinematic Systems in Geodesy Geomatics, and Navigation, 2001, pp. 392-400.
[Wei95] L. R. Weill, "Achieving Theoretical Accuracy Limits for Pseudoranging in Presence of Multipath", Proceedings of the ION GPS, Palm Springs, CA, 1995.
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Session E2, Paper #5
Real-Time Low-Cost Multipath Mitigation Technique Calibrated Through Real Data Repeatable Testing
M-A. Fortin, R. Jr Landry, Ecole de technologie superieure, Canada
Satellite navigation receivers can now remove most error sources from the positioning equation, thanks to the continuously improving measurement corrections and signals´ characteristics. Ionospheric delays are addressed through SBAS corrections and even better by multi-frequency measurements, becoming progressively available. Also, tropospheric delays can be modeled for standard weather conditions and precise ephemerides are being broadcast for more accurate satellite orbit estimations. Hence, current GPS receivers are basically left with a potential ñ10 m error due to multipath, which cannot be differentially corrected, modeled nor predicted (except for static reference stations). Hence, efforts such as Signal Quality Monitoring (SQM) have been deployed to characterize multipath. Most mitigation techniques, usually based on signal processing and implemented in the receiver´s channels, only address the static specular multipath case, which is the simplest form to simulate and test. Nevertheless, commercial receivers cannot usually afford the extra resources required by such techniques. This paper reviews an adaptive, low-cost multipath mitigation technique based on an additional correlator per channel. As introduced at ION 2008, each of these Variable Spacing Correlators (VSC) scans the Auto-Correlation Function (ACF). Now, to use this tool as a real-time multipath mitigation technique looking for biases affecting the pseudo-range measurement, 4 VSC configurable parameters (i.e. chip span of the ACF, number of measurement points, coherent integration time and non-coherent smoothing) are set to obtain a total scan time matching the non-coherent integration period used for the Delay Lock Loop (DLL) feedback. Thus, depending on the signal´s navigation message´s period, different optimum "real-time" targets may be achieved according to the signal´s characteristics. This constraint allows for a snapshot of the current multipath to be quantified and used to correct the Pseudo-Range (PR) measurement, thus improving the navigation solution´s accuracy in presence of multipath. In the case of GPS L1 Coarse Acquisition (CA), a minimum coherent integration time of 1 ms over a total of 20 points around the Prompt correlator could be evaluated at each 20 ms, the upper unaided coherent integration limit due to the navigation message rate. This approach´s drawback is that thermal noise becomes more important as the dwell time is reduced, resulting in a real-time, but noisier ACF. To begin with, the chip span may be larger and adaptively reduced to narrow down and mitigate the impact of multipath on the ACF.
In order to reliably reproduce a sharp ACF, a 24 MHz double-sided front-end bandwidth is used. Also, not all 120 points around the prompt correlator (ñ1 chip at 60 MHz) need to be analysed. The inverse of the sampling frequency imposes the maximum resolution achievable while the large bandwidth prevents high-frequency components filtering, thus preserving the triangular shape of the auto-correlation curve, typical of Binary Phase Shift Keying (BPSK) modulated signals. Since it is practically impossible to completely simulate real multipath scenarios with a deterministic algorithm (i.e. simulations, no matter how complex they may be, never account for 100% of the targeted phenomenon), this multipath mitigation technique has been calibrated through repeatability analysis based on playing-back pre-recorded live, 20 MHz wide signals. Nevertheless, before using Averna´s RF Record and Playback (R&P), a 2-step validation methodology was used. First, the new version of the VSC was tested with known simulated signals, using Spirent´s 7700 simulator (generating GPS L1 C/A signals) to determine an optimal parameters´ configuration. Then, to validate that the insertion of the R&P does not compromise the signal processing chain, the simulated signals were recorded and played-back, achieving the same multipath mitigation results. Once characterized, the R&P is used to analyse real multipath-affected signals, offering a new insight on true multipath behaviour, hence improving the characterisation of real world multipath´s evolution in time. Furthermore, this experiment has been replicated for different environmental conditions (i.e. multipath scenarios in both static and dynamic user configurations), reproducing in the lab true repeatable signals (with real multipath, blockage, attenuation, etc.). In the current experiment, the advantage of replaying several times the same RF data is twofold: multipath characterization/analysis and multipath mitigation parameters´ fine tuning. This paper concentrates on the latter. More explicitly, repeatedly submitting the receiver loops to the same data allows us to measure the noise variance from step to step (same direct and multipath signals with same power); only the receiver noise will vary one time to another. This experimental setup is the best of both worlds: simulation repeatability of real data.
This paper has shown that no configuration of fixed correlators can reliably attest of all the multipath scenarios. On the other hand, the VSC approach can easily adapt to different types of multipath (learned or not). It is hence the most versatile (i.e. it equally applies to any GNSS signal tracking channel) and least consuming real-time multipath mitigation technique. With the proposed methodology combining R&P and VSC, a more representative study of multipath can now be performed. It is believed that the presented findings will influence the way multipath mitigation efforts will be oriented in the future, both on the receiver and simulator sides. Obviously, not all new GNSS civil signals have been studied in this paper. It is believed that interesting findings will result of further investigations, as new signals become available, at least on one satellite. An even more promising avenue is the multiband mitigation of multipath. Joint analysis of multi-frequency signal´s auto-correlation curves may teach us something new. Now introducing multi-frequency signals, such a multipath analysis on L1 C/A could provide corrections to be applied on all the signals transmitted from the same satellite. Hence, determining on which GNSS signal multipath mitigation is more effective would reduce the tracking complexity of other signals, assuming the Kalman filter deduces the corrections to be applied from a single ACF. Finally, the proposed methodology could just as well be applied to characterize the performances of other multipath mitigation techniques and new signals/frequencies under realistic scenarios and for multipath scenarios characterization and classification. This better understanding of multipath could also influence the way its mitigation ways will be developed.
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Session E2, Paper #6
A Novel Real-time Platform for Digital Beamforming with GNSS Software Defined Receivers
J. Arribas, Centre Tecnologic de Telecomunicacions de Catalunya, Spain; D. Bernal, Universidad Politecnica de Catalunya, Spain; C. Fernandez, Centre Tecnologic de Telecomunicacions de Catalunya, Spain; P. Closas, J.A. Fernandez-Rubio, Universidad Politecn
Sources of accuracy degradation in satellite-based navigation systems are well known, and their mitigation has deserved the attention of a number of researchers in latter times. While atmospheric-dependant sources (delays that depend on the ionosphere and troposphere conditions) can be greatly mitigated by differential systems external to the receiver´s operation, the multipath effect is location-dependant and remains as the most important cause of accuracy degradation in time delay estimation, and consequently in position estimation, becoming a challenging issue. In the latest years, a number of multipath mitigation techniques have been proposed, most of them are based on single-antenna receivers; an approach that has inherent drawbacks. In the literature it has been proved that the Cram‚r-Rao bound for any single antenna time delay estimator increases when the multipath reflections impinge the receiver with small time-delay with respect to the line of sight (LOS) signal [Wei95]. By contrast, the multi-antenna receiver approach can exploit the spatial diversity as a possible solution for the mitigation of reflections that are highly correlated with the direct signal path, usually referred to as coherent multipath [Sec05, Fer06]. An antenna-array based receiver can make use of Digital Beamforming (DBF) techniques, providing appealing spatial multipath mitigation capabilities.
The goal of this paper is to provide details about the design and implementation of DBF architecture on an FPGA for a GNSS antenna array receiver. Our work deals with the design of DBF algorithms from a real-time implementation point of view, in contrast to theoretic studies regarding DBF techniques. Hence, practical aspects of DBF implementation such as weight quantization and required computational resources are studied. We also present the generation of simulated-multipath scenarios capable to recreate a variety of conditions with real GNSS signals comparing three different DBF implementations. The DBF techniques cover the use of spatial references, the use of temporal references and a technique combining both spatial and temporal references. Namely, we refer to these DBF strategies as Spatial Reference Beamforming (SRB), Temporal Reference Beamforming (TRB) and Hybrid Beamforming (HB), respectively.
The SRB algorithm is based on the assumption that the receiver has the knowledge of the satellite ephemerides and a rough estimation of the receiver´s position. At this point, the receiver calculates the directions of arrival (DOA) for each satellite in order to feed the beamforming module with a spatial reference. With this set of information a SRB can be implemented using the well-known Minimum Variance Beamforming (MVB) algorithm also named Capon Beamformer. This beamformer is array-calibration sensitive and array-attitude dependent, which complicates its implementation, especially in a mobile receiver because the need of inertial sensors. On the other hand, the TRB approach selects all the correlated signals and attenuates the uncorrelated noise and interferences, minimizing the Mean Squared Error (MSE) between the reference and the array output. Consequently, the TRB technique does require neither a calibrated array nor attitude determination of the receiver, but a locally generated reference signal. [Bro00, Wax96, Sah07] HB is a hybridization of the SRB and TRB strategies, which was proposed in [Sec05]. HB takes advantage of both approaches to mitigate multipath and interference contributions. The technique is implemented in the DBF platform, being specially suited to the particularities of a GNSS receiver.
The integration between a DBF module and a GNSS receiver will be presented. The platform is designed to provide enough bandwidth and flexibility for present and forthcoming GNSS signals, being focused on GPS L1 C/A and GALILEO E1 signals. The prototype digitizes the signal coming from eight antenna elements synchronously, and is able to execute SRB, TRB and HB techniques. The core of the DBF platform is a Xilinx Virtex5 FPGA connected to a Texas Instruments eight channels 12 bits analog-to-digital converter (ADC) with a maximum sample rate of 70 Msps. The beamforming module takes the input samples coming from each ADC, computes the beamweights and obtains a single output. Next, the samples are sent, via Gigabit Ethernet port, to a GNSS software receiver running on a PC. In addition, the estimated delay and DOA (at the PC) are fed-back to the beamweight calculation algorithm by a serial bus. We designed and tested hardware and software blocks of the FPGA, presenting the conceptual description, schematics and simulation. All blocks are programmed in VHDL, except the block in charge of the computation of the antenna weights, which is implemented using the Xilinx MicroBlaze soft-processor of the FPGA, programmed in C.
In order to test the implemented algorithms, the performance is measured and compared to the theoretical limits over different virtual multipath scenarios [Fer06]. The simulated antenna array outputs coming from the channel emulator are fed to the ADC at intermediate frequency. The testing equipment consist of a GPS real-time signal generator Agilent GPS Personality for the E4438C ESG Vector Signal Generator connected to a Elektrobit channel emulator model Propsim C8 to set up a variety of multipath situations. [Agi00, Ele00].
References:
[Wax96] M. Wax, et al. "Performance analysis of the minimum variance beamformer", IEEE Transactions on Signal Processing, vol. 44, no. 4, April 1996.
[Wei95] L. R. Weill, "Achieving Theoretical Accuracy Limits for Pseudoranging in Presence of Multipath", Proceedings of the ION GPS, Palm Springs, CA, 1995.
[Bro00] A. Brown, et al. "Multipath Rejection through Spatial Processing" Proceedings of ION GSP 2000, Salt Lake City, Utah, September, 2000.
[Fer06] C. Fern ndez, "Advanced Signal Processing Techniques for Global Navigation Satellite Systems Receivers", PhD dissertation, UPC, April 2006
[Sec05] G. Seco, et al. "ML estimator and Hybrid Beamformer for multipath and interference mitigation in GNSS receivers," IEEE Trans. Signal Processing, vol. 53, no. 3, pp, March 2005.
[Agi00] Agilent GPS Personality for the E4438C ESG Vector Signal Generator Option 409, Product overview, http://cp.literature.agilent.com/litweb/pdf/5988-6256EN.pdf
[Ele00] EB Propsim C8 - Multi-Channel Emulator, Product overview, http://www.elektrobit.com/index.php?955
[Sah07] M. Sahmoudi, et al. "Optimal Robust Beamforming for Interference and Multipath Mitigation in GNSS Arrays", Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on Volume 3, 15-20 April 2007.
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Session E2, Paper #7
The Aid of Wavelets Correlator in Carrier Phase Multipath Reduction and Motion Detection
A. El-Ghazouly , Dept. of Geomatics Engineering, University of Calgary, Canada
Student Paper: Please download the paper from ION FTP Site. Instructions will be sent to you by e-mail.
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Session E2, Paper #8
Effects of Rotor Blade Modulation on GNSS Receiver Measurements
A. O´Brien, K. Hayhurst, I.J. Gupta, The Ohio State University
GNSS signals received by antennas mounted on airborne platforms are affected by platform generated multipath. If the aircraft is a helicopter or has propeller blades, this multipath has the potential to be very complex and periodically time-varying. This leads to time-varying distortion of the received signals which is commonly referred to as rotor blade modulation. When a GNSS receiver is mounted on a rotor craft, one needs to include the rotor blade modulation in the receiver measurements for good estimation of the position and time solutions. However, there is very little information available (in the open literature) on how to model the effects of rotor blade modulation in GNSS measurements.
In this paper, we will address the rotor blade modulation problem through two primary contributions. First, we will provide a methodology for incorporating rotor blade modulation effects into an analytic GNSS model. We will present analytic expressions for the receiver cross-correlation and use these expressions to derive GNSS performance metrics such as C/N, carrier phase bias, and code phase bias when the antenna response is time-varying. Second, we will quantify the rotor blade modulation effects by modeling a simple GNSS antenna on a model helicopter platform. We have used numerical electromagnetic (EM) software to rigorously simulate the effects of the platform and obtain antenna patterns in the presence of rotor blade modulation. In these simulations, the antenna is a single crossed-slot mounted on a flat plate that represents a helicopter body. Above the antenna, a set of large, rotating plates represent the helicopter rotor blades. EM simulations are performed over the entire upper-hemisphere, which includes signals received through the plane of the rotor blades and also near the horizon. The antenna is placed at varying distances from the axis of rotation. Antenna patterns are obtained by simulating this platform with the rotor blades at various rotation increments and composing these into a single time-varying antenna response. It will be shown that the effects of rotor blade modulation -- as expected -- is to introduce time-varying C/N and antenna-induced biases as well as minor C/N degradation. The amount of variation is strongly dependent on the antenna placement on the platform and the ratio of the receiver integration period to the blade rotation period. The consequences of these effects on GNSS signal tracking in the receiver depend on the specific receiver implementations. We have also carried out computer simulations using numerical antenna data signals to verify the accuracy of the analytic models. Some computer simulations results will also be presented.
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Session E2, Alternate #1
WAAS Geostationary Satellite Orbital Perturbations and its Impact on Signal Multipath
S. Ramakrishnan, D. Akos, T. Walter, P. Enge, Stanford University; D. Brekke, The Boeing Company
Augmentation Systems such as WAAS, EGNOS and GAGAN are air navigation aids which augment signals from Global Navigation Satellite Systems. These augmentation systems improve the accuracy, integrity, continuity, and availability of GNSS signals for purposes of aircraft navigation. Correction messages are uploaded from a Master Control Station to Geostationary Satellites using a C-band uplink. The signals are converted to the desired L-band frequency onboard the satellite and then broadcast back to the users.
Geostationary satellite orbits cannot be modeled accurately as a "Two-Body Problem" comprising the satellite and a spherical symmetric Earth gravity. At geostationary altitudes, the perturbing forces of the Sun and Moon´s gravitational attraction are significant. Further, forces arising from solar radiation pressure and the non-spherical nature of the Earth´s gravitational attraction cause significant perturbations. Consequently, a geostationary satellite orbit must be modeled as a "Four-Body Problem" comprising of the Sun-Moon-Earth-Satellite system. Each of the perturbing forces causes a change in one or more of the orbital parameters. Long-Term or secular perturbations with periods ranging from a few weeks to several years are accounted for through station keeping maneuvers. It is the short-term perturbations periodic over one day or shorter which influence the characteristics of Standing Waves observed at the user receiver.
In the first part of this paper, we derive analytical expressions to characterize the impact of satellite perturbations on the extent of Standing Wave or Multipath that can be observed at a user receiver. In particular, we analyze the extent of perturbations required to change the differential path length between the direct and reflected wave by integer multiples of the wavelength corresponds to the GPS WAAS L1 and L5 signals. The periodic nature of the satellite perturbations can be used to estimate the extent of multipath observed at the receiver. Appropriate the errors resulting from these standing waves can be compensated for in the receiver.
In the second part of this paper, we validate our analytical efforts with experimental data. We collect and process data over longs periods ranging between 20 to 24hours over several days in a near real-time basis. This was done through a flexible and robust FPGA-based receiver we designed. The design of this dual-frequency multi-channel receiver is based upon a Xilinx Virtex series FPGA chipset. The receiver is capable of acquiring and tracking both the WAAS/GPS L1 and L5 navigation signals.
Apart from the L1 C/A ranging signals, the two WAAS geostationary satellites also currently broadcast the GPS L5 signal. Since the L5 signal lies within the Aeronautical Radio Navigation Services (ARNS) band, it is subjected to pulsed interference from Distance Measurement Equipment (DME) and Tactical Air Navigation (TACAN) systems operating in the ARNS band. Efficient DME/TACAN interference mitigation techniques developed by us have been included in the receiver processing algorithms to prevent frequent loss of receiver loss of lock. The experimental data processed using our FPGA based receiver is in close agreement with our analytical results. We can efficiently estimate errors resulting from multipath due to the satellite perturbations and compensate for the same.
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Session E2, Alternate #2
Empirical Analysis and Characterization of GNSS Indoor Multipath Conditions using Deconvolution Techniques
H. Blunck, M.B. Kaergard, D.L. Christensen, T. Godsk, K. Gronbaek, Aarhus University, Denmark
Moving GNSS towards indoor positioning is an important challenge. Increases in receiver sensitivity, the forthcoming increase in number of GNSS satellites and signal design improvements all contribute to addressing this challenge. However, coping with the impact of signal multipath phenomena in indoor environments is a main issue for realizing GNSS-based indoor positioning. The main objective of our paper is to analyse and categorize real world multipath phenomena, measured in indoor environments. The work can contribute with an empirical understanding of the phenomena that enables future improvements of GNSS receiver design specifically in challenging indoor environments.
One way of assessing multipath phenomena as experienced when receiving GNSS signals indoors, is by inspection of correlation results, that is by analyzing the cross correlation of a received signal with a local PRN code replica of a GNSS satellite. Given ideal signal conditions, such a correlation function exhibits a single and symmetric peak, from the position-in-time of which the code phase and ultimately the pseudorange to the signal source can be computed. While such correlations are the basis for every GNSS receiver, little attention is traditionally paid to the correlation function´s overall shape - apart from a single pronounced peak, which then is tracked over time by the GNSS receiver.
Especially in indoor environments, though, correlation functions usually contain multiple and convoluted peaks, stemming from both the line-of-sight signal as well as from echos of the same signal. Such convolution may distort the most pronounced peak´s position and complicate it´s tracking. Furthermore, in severe multipath conditions the line-of-sight signal might not even be the strongest apparent at the receiver; in this case the most pronounced peak stems from an echo; if this peak is consequently chosen for being tracked, the subsequent pseudorange calculation will lead to an error linear in the tracked echo´s delay with respect to the line-of-sight signal.
Provided a signal sampling rate higher than used in traditional receivers, though, the shape of the correlation function can be adequately analyzed: The higher time-resolution allows for reliable deconvolution of the correlation function yielding a decomposition into the line-of-sight-signal and individual echo components, thus enabling identification and tracking of just the line-of-sight signal version. Not surprisingly, in the recent GNSS literature many variants of such and similar correlation deconvolution techniques have been proposed to enhance or even replace traditional delay lock loops as a state-of-the-art GNSS tracking procedure. The evaluation of such proposals, though, has yet been mostly by means of software/hardware-based simulation and not by thorough empirical analysis as documented in this paper.
Although, real-world experiments have not yet been rigorously used specifically to evaluate correlation deconvolution techniques for GNSS, they are in general in the GNSS literature considered important for the purpose of gaining more insight in indoor signal conditions. Recent campaigns to characterize such signal conditions use a variety of measurements machinery such as channel sounders, mobile signal generators and spectrum analyzers and have been prominently published.
In this paper, we investigate indoor multipath phenomena through inspection of high-resolution correlation results in real-world indoor environments. Deconvolution techniques are then used as a central tool for assessing and analyzing real-world signal conditions and multipath patterns in a broad variety of indoor environments including a shopping mall and a loose cattle barn.
For a diverse number of chosen in-building locations, we undertake a series of measurements, recording high-resolution correlation results. We chose the individual experimental setups carefully to cover a variety of instances of parameters known to influence multipath and indoor signal reception: Additional to satellite elevation and azimuth we take into consideration architecture parameters of the building and room such as building superstructure and building materials that the signals penetrate to reach the receiver. Furthermore, we carry out measurements for various receiver positions within every room chosen for experiments, specifically we vary proximity and angles to building elements such as walls, windows, doors and room corners.
Our proposed methodology and the anticipated experimental results can foremost be seen as an effort to characterize indoor GNSS signal conditions, and can therefore be seen as an addition to recent characterization campaigns, e.g., by Hein, Teubner, and others. While the latter also briefly investigate the shape of correlation functions as an indicator for signal conditions, we look at these shapes much closer - with a significantly higher sampling rate, which is also essential for our subsequent analysis by decomposition to deliver meaningful results. Having gathered and analyzed emperical data as proposed above, we also revisit published results and models regarding indoor signal propagation to compare them with our findings.
Finally, our contribution is worthwhile also from an engineering point of view for two reasons: First, although GNSS receivers process raw signals, they ultimately do so by inspecting the cross correlation result of the signal with a local PRN code copy; thus investigating in detail such correlation results stemming from challenging indoor environments should add to the characterization of GNSS signal conditions in a way that directly points to potential improvements to GNSS receiver design. Additionally, as our investigation makes experimental use of correlation deconvolution techniques, our paper will also contain insights into the behavior of these techniques, when faced with various real-world indoor signal measurements.
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Session E2, Alternate #3
Modeling the GNSS Rural Radio Channel: Wave Propagation Effects Caused by Trees and Alleys
F. Schubert, A. Lehner, A. Steingass, P. Robertson, German Aerospace Center, Insitute of Communications and Navigation, Germany; B.H. Fleury, Aalborg University, Institute of Electronic Systems, Denmark
Compared to radio channel modeling in the digital communication domain, channel modeling for satellite positioning, and especially for GNSS positioning applications, is still in its beginnings. It is only since recent years that realistic channel models for urban [1], sub-urban [2] and aeronautical [3] scenarios have been developed. Only the most recent models have been derived based on empirical wide-band channel sounding measurement data (with a measurement bandwidth of 100 MHz in the case of [1], [3], and [4]).
The wave propagation effects caused by roadside trees and alleys are very pertinent to channel modelling aspects for GNSS applications:
- Trees close to the road cause periodic deep fades in the order of -10 to -30 dB of the received signal.
- the trees´ canopies show strong reflective and scattering behaviour that sometimes lead to re-scattered signals exceeding the direct signal.
Both effects, i.e. the deep fades and the strong reflections of the satellite signal in close proximity of the vehicle happen frequently and repetitively, which exposes GNSS receivers to a demanding situation in rural surroundings dominated by tree vegetation. The modeling of the GNSS rural radio channel presented in this paper focuses on shadowing, diffraction, and scattering of trees and alleys along the road.
This paper presents an analysis of the characteristics of wave propagation effects caused by single trees and alleys and of the influences of these effects on the performance of GNSS receivers. The following effects were identified as being dominant in this setting:
- treetops attenuation and scattering,
- diffraction by the tree trunks, and
- ground reflection.
The scenario defined by the user vehicle trajectory, the tree positions, and the geometric and electrical parameters for the tree trunk and canopy serve as inputs to the model.
The proposed model approximates the tree canopies by spherical volumes which contain a plethora of point scatterers defined by given dielectricity and permeability. The scatterers represent the characteristic speckle-like reflective behaviour caused by the tree´s heterogeneous structures at wavelength scale such as branches, forks, and leaves. The scatterer positions with respect to satellite and vehicle position play also a vital role. This dependency and the treetops´ attenuation are modelled using a ray-tracing approach. The tree trunks are modelled by cylinders with given radii and heights. Again, a geometrical ray-tracing approach is applied to reproduce specular, diffractive and attenuating behaviour of the trunks.
Channel sounder measurements at a center frequency of 1.51 GHz and a bandwidth of 100MHz performed in a rural environment are available to determine the model parameters.
Complex-valued time series at a specified sampling frequency will be the output of the model. Comparative simulations of the model output and out-of-sample measurements (which were not used for the modelling) will be provided. Also, power delay profiles which are yielded from the measurements will be given.
Although detailed investigations of wave propagation effects induced by trees were conducted in the past [5], [6], [7], only the attenuation caused by trees was mostly regarded. To the authors´ best knowledge it is the first time that an accurate time-variant, trajectory-dependent, and descriptive model based on wide-band measurement of rural sceneries for the GNSS use case is proposed.
References
[1] A. Lehner et al.: "A channel model for land mobile satellite navigation", Proceedings of the 18th International Technical Meeting of the Institute of Navigation Satellite Division (ION GNSS 2005), Long Beach, California, USA.
[2] F. Perez-Fontan et al.: "Statistical modeling of the LMS channel", IEEE Transactions on Vehicular Technology (50), 2001.
[3] A. Steingass et al.: "Navigation in multipath environments for suburban applications", Proceedings of the 20th International Technical Meeting of the Institute of Navigation Satellite Division (ION GNSS 2007), Fort Worth, Texas, USA.
[4] A. Steingass et al.: "Characterization of the aeronautical satellite navigation channel through high-resolution measurement and physical optics simulation," International Journal of Satellite Communications and Networking (26), John Wiley & Sons, 2008.
[5] Y.L.C. de Jong and M.H.A.J. Herben: "A tree-scattering model for improved propagation prediction in urban microcells", IEEE Transactions Vehicular Technology (53), 2004
[6] G. Lachapelle et al.: "Seasonal effect of tree foliage on GPS signal availability and accuracy for vehicular navigation", Proceedings of the 7th International Technical Meeting of the Satellite Division of the Institute of Navigation ION GPS 1994, Salt Lake City, UT, 1994.
[7] R.H. Lang et al.: "Microwave tree scattering experiment: comparison of theory and experiment", IEEE International Geoscience and Remote Sensing Symposium Proceedings (5), 1998.
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Session E2, Alternate #4
Development of a GPS Deterministic Multipath Simulator for an Efficient Computation of the Positioning Errors
A. Chen, A. Chabory, A-C. Escher, C. Macabiau, ENAC, France
From the satellite to the receiver antenna, the GPS signal is confronted to a number of propagation effects which may constitute sources of positioning error. For instance, when passing through the atmosphere, the signal undergoes ionospheric and tropospheric effects which affect its magnitude and delay. Among the different propagation phenomena, multipath has been identified in the literature as the most challenging source of positioning error. Therefore, it is important to get information about the potential multipath affecting the signal reception. This is particularly the case in man-made environments when precise positioning is required. Multipath is defined by echoes associated with the fields reflected and diffracted by the surrounding environment. In multipath situations, the received signal is not only the direct one but also a sum of attenuated and delayed versions of the direct signal. For this reason, a multipath channel is usually characterized by a set of three parameters: the amplitude, the delay and the phase-shift of each multipath. When characterizing a multipath channel, the main issue is the prediction of these parameters. Number of prediction tools already exist. We can distinguish three kinds of models: deterministic models, statistic models and finally hybrid models which mix both deterministic and statistic prediction. Here we focus on deterministic models. When defining a multipath prediction simulator, many possibilities are available at each stage of the conception [1], and it appears that the best solutions may not be obvious. For instance, the choice of an electromagnetic prediction method, the number of interactions to consider or suitable criteria for the 3D environment description are of major concerns. In this paper, we propose a GPS multipath prediction simulator based on physical optics (PO) adapted to man-made environments for which we aim at justifying each design choice carefully. Thus the paper is organized as follow. In Section 1, we expose the simulator principle. The input parameters of the multipath generator are the satellite position, the receiver position, and the 3D modeling of the environment composed of planar dielectric and metallic facets. The role of the multipath generator is to predict the channel parameters. These parameters become the input of the GPS receiver simulator which returns the receiver position error. The multipath generator is composed of two main blocks. The first block predicts the list of the electromagnetic fields associated with each multipath assuming a narrow-band signal. Within this assumption, the multipath channel is obtained from the fields computed only at the central L1 frequency only. These fields are computed by means of PO and multiple-order reflections are considered. The second block of the generator takes into account the GPS receiver antenna. It allows the computation of the multipath parameters from the electromagnetic fields via the use of the effective vectorial height of the antenna. In Section 2, we justify the prediction method employed in the multipath generator by means of simulations on comprehensive test-cases. We expose the interest of PO compared to two different approaches. The first one is the Uniform Theory of Diffraction (UTD) which is the most popular electromagnetic method to predict multipath. The second one is the Method of Moments (MoM) which can be considered as a time-consuming but reference method. Besides in this section, we justify the narrow-band hypothesis. For this purpose the multipath channel is also computed without this assumption, that is to say the field is computed on a regular sampling of the L1 band, and compared to the result obtain when considering the field computation at the L1 frequency only. In Section 3, we evaluate how the simulator should be used to obtain a reliable estimation of the position error within acceptable computational efforts. For the multipath generator settings, the influence of multiple-order reflections is studied. Moreover, in dynamic situations, i.e. for a mobile receiver, we also consider how the Doppler shift of each multipath impacts the position error. Concerning the 3D environment modeling, we propose criteria for a suitable description. First we assess the influence of small details by performing simulations either with or without small elements in the 3D modeling. Then, the influence of material characteristics is studied by performing simulations with a realistic representation of the environment and different modeling: either with metallic facets or with multilayer dielectric facets.
Acknowledgments: the authors wish to thank Airbus for funding this work.
[1] A. Chen, A. Chabory, A.C. Escher, C. Macabiau, "Comparisons of Multipath Modeling Strategies for the Estimation of GPS Positioning Error", EUCAP, Berlin (Germany), march 2009.
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Session E2, Alternate #5
Using Dirichlet Process Mixtures for the Modelling of GNSS Pseudorange Errors in Urban Canyon
A. Rabaoui, N. Viandier, J. Marais, INRETS-LEOST, France; E. Duflos, Laboratoire d´Automatique, Genie Informatique et Signal, France
Modern GPS receivers achieve high position accuracy in line-of-sight (LOS) conditions but multipath propagation highly degrades GPS tracking performance. For safety transport applications, the performances require to be stringent in terms of accuracy, availability and integrity. These applications are used in different propagation environment, resulting in signal propagation variations. This increases difficulty of getting the best reception conditions for each available satellite signal.
The key point in GNSS is to efficiently mitigate the multipath effect because we use only the satellite receiver transit time offset of the LOS signal for positioning. Multipath occurs when the satellite signal is reflected on different surfaces before arriving to the receiver. Therefore, the incoming signal is the sum of the direct signal and several delayed replica. Simulations carried out in many previous works show that multipath can result in biases of up to 100 m. Consequently, multipath appears as a critical issue. Here, we consider positioning accuracy degradation problem when we don´t receive the direct signal but just reflected replica.
Since the observations delivered by some sensors may be easily blurred because of hard external conditions in urban canyons; they may deliver totally erroneous measurements in some conditions. In fact, the signal reaches the receiver after interaction with one or more objects/obstacles in the environment. In urban area, some obstacles (buildings, trees, etc) can be modelled using a simulator. However, some other obstacles (cars, pedestrians, etc) can appear suddenly and thus can induce a random error in the pseudorange measure. In order to ensure high accuracy positioning and external environment mapping a good estimation of the observation error in such cases is required.
It´s important to notice that there has been considerable investigation into development of multipath mitigation techniques in the past few years. The proposed solutions are aimed either to recover the unbiased propagation delay or to compensate for the induced errors on GPS measurements. Our study focuses on the second class of methods which track multipath errors on the GPS pseudoranges. We consider mainly the alternate path when the signal is received after reflexions or diffractions on obstacles and we assume in this case that there is no direct signal. The objective is to improve the position accuracy in these environments without coupling different sensors; we choose to work only with GNSS signals and thus to help in developing low cost systems.
In our previous work, we considered two different cases. In the first case, when the signal is received from the satellite in LOS, the pseudorange error distribution is considered Gaussian. In the second case, when the signal can´t arrive to the antenna in LOS but only after one or more reflections, the pseudorange error distribution is represented by a Gaussian Mixture. In real urban environment, such assumptions are in some way restrictive. To tackle this problem, the overall localization system must be considered as a multisensor system. A straightforward approach consists of estimating jointly the navigation states and the pseudorange errors from the corrupted GPS measurements. A number of considerations arise in assessing such multipath mitigation techniques, mainly a good performance in realistic multipath conditions must be provided.
We know that the main reason for these errors is the maladjustment between the modelling of the received signal and the processing realized inside the receiver. Kalman filters and extended Kalman filters which are widely used as optimal solution in case of Gaussian systems are not suitable for treating the models which exhibit non Gaussian distributions. However, the sequential Monte Carlo-based filtering methods (particle filters) are able to cope with noises of any distribution. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. The DPMs were too complex to handle numerically before the introduction of Monte Carlo simulation based methods.
This paper proposes two main contributions. First, the unknown noise distribution in the linear dynamic model is assumed to be DPMs, these are flexible Bayesian nonparametric models which have become very popular in statistics over the last few years, to perform nonparametric density estimation. Second, the efficiency of this approach is demonstrated by applying a validation step involving real GPS signals. Hence, the paper will contain two main parts. The first part focuses on the modelling of the pseudorange noises using DPMs and its suitability in the estimation problem handled by a particle filter. The other part contains interesting validation schemes using different methods.
Some modelling techniques of the pseudorange error distributions are proposed from both simulated and real signals. Simulated data is obtained from a 3D model through Ergospacer (Ergospace use the Ray Tracing method to simulate propagation of GNSS signals, between transmitters and a receiver, in 3D environments). However, real samples are raw pseudorange measurements obtained from a bi-frequency GNSS receiver (Septentrio).
To prove that the Dirichlet Process Mixture is more adapted than the previous models, we will use a graphical method based on the Quantile-Quantile Plot and two statistical tests called chi2 and Kolmogorov-Smirnov. These methods were used to compare real samples with referenced probability distribution by computing an adequacy quantification measure between the specific and data distributions. We will show that our approach outperforms standard models commonly used to represent observation noise distributions.
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