Reliability of GNSS Measurements via Pseudorange Prediction Using an Odometer for Robust Land-Vehicle Navigation

Abstract : Reliable GNSS positioning is difficult to be achieved in dense urban areas, because in these environments typically the satellite signals are often obscured or reflected by buildings and receiver-surrounding objects to cause multipath signal reflections, which distort measurements and bias the calculated position. Diffracted and reflected signals received with the direct signal can result in ten-meter-order positioning errors, and hundreds of meters of positioning error can be present in non-line-of-sight signals (NLOS) situations. Thus, degraded receptions due to these phenomena are the dominant causes of reduced reliability in urban environments positioning. The standard way to solve the NLOS problem in GNSS receivers is to identify and exclude the associated measurements in the navigation algorithm, with techniques such as RAIM, when the induced error is not acceptable. However, this approach is not adapted to positioning in harsh environments (urban canyons, deep urban and indoor), where only few satellites in NLOS situations may be available and PVT solution has to be computed even from these degraded measurements. Under such poor conditions of satellites visibility, the positioning algorithm has to take into account the fact that the received signal may be received from a non-direct path with an additional distance. The objective of this work is to introduce a new methodology of exploiting these NLOS measurements, usually removed by GNSS receivers in good availability conditions. In traditional RAIM, a local test checks the reliability of PR measurements, and the global test checks the reliability of position solution in presence of contaminated observables. In this paper, we apply robust statistics as a powerful tool for statistical analysis in presence of outliers. However using robust tests, (e.g. robust covariance estimation), achieve their limits when most of the data resemble outliers. The robustness of a robust estimation method is measured by the breakdown point, representing the proportion of incorrect observations that this estimator can handle when computing the robust estimate [1]. The maximum breakdown point in M-estimation methods is up to 50%, thus when the percentage of biased pseudorange (PR) exceeds the half, as in urban environments, robust RAIM techniques will fail also. To overcome this issue, a realistic NLOS bias model is developed based on the predicted PRs. When the number of reliable satellites measurements is insufficient, other sources of information need to be used to increase information redundancy and improve the PVT solution. The usual approach is to use dead-reckoning sensors (IMU, odometer, etc.) together with the GNSS measurements as inputs of a fusion algorithm. They can be integrated with the GNSS to compensate the navigation error even when the PRs are not available [2]. On the other hand, the PRs can calibrate the sensor when they are available. While there are many works describing the fusion of other sensors with GNSS to improve accuracy and availability, the aspect on the reliability of the navigation solutions based on such configurations are still needed. Instead of using least square residuals as in standard RAIM we propose in this paper to estimate the size of multipath errors in the observed PR using Doppler observables and odometer measurements. The size of multipath (MP) errors is computed as the difference between observations and predicted values, then used for reliability checking and measurements error modeling. More precisely we use the odometer to predict reliable PR measurements, such that PR(t) = PR(t-1) + DeltaR, where DeltaR is computed from the odometer and satellite velocity. Then the measured PR and predicted ones will be compared using a consistency checking metric such as Kullback-Leibler Divergence that permit us to compute the adaptive variance of the PR observation from the area of PDFs overlapping [3]. Therefore, we may use the odometer error distribution to compute the error distribution of the NLOS PR which can be exploited for reliability analysis in the range domain. In other words, this scheme provides a way to correct the NLOS bias of PRs from a trusted external sensor. Reliability checking is a challenging task in harsh urban environment because modeling the GNSS errors is quite complex. The work in [4] has demonstrated that using principle component analysis (PCA) for stochastic fault detection is viable without knowing the state-model a priori. This has sparked our interest to also investigate the PR reliability checking by means of PCA in this paper. However, the PRs measurement errors in deep urban areas could be correlated and as such, PCA is not optimal in this situation. In order to overcome this limitation, the PR reliability checking is implemented using a robust PCA. A robust PCA can be obtained by robust estimation of the measurements covariance [1] and the robust residuals permit us to address the identification of the biases. In the analysis, the validity of the predicted PR values and the model of the PR prediction error are studied as a function of time using a reference trajectory system (SPAN FSAS Novatel/iMAR IMU). The NLOS PR error distribution is estimated and validated from data. The reliability checking approaches described above will be discussed and analyzed in different scenarios for evaluation using real GPS signals. In summary, this work implements robust reliability checking with robust statistics to exploit NLOS measurements which are usually removed by GNSS receivers in urban navigation. Inclusive in the study are modeling of multipath errors, RAIM with MP residuals, use of odometer to predict reliable PR measurements, and applying PCA for GNSS reliability.
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Contributor : Céline Smith <>
Submitted on : Monday, January 27, 2014 - 3:18:29 PM
Last modification on : Friday, February 9, 2018 - 8:36:01 PM

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Khariol Bin Ahmad, Mohamed Sahmoudi, Christophe Macabiau. Reliability of GNSS Measurements via Pseudorange Prediction Using an Odometer for Robust Land-Vehicle Navigation. ION GNSS 2013, 26th International Technical Meeting of The Satellite Division of the Institute of Navigation, Sep 2013, Nashville, United States. pp 1299-1307. ⟨hal-00936884⟩

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