Sequential Importance Resampling Particle Filter for Ambiguity Resolution
Creators: name: Manzano Islas, Roberto Rene
Publisher: name: Arts
Year: 2023
Subjects: subject: GNSS ambiguity resolution
subject: Particle filter
subject: Non linear estimators
subject: satellite navigation
subject: satellite positioning
subject: Statistics
subject: FOS: Mathematics
subject: Geodesy

description: In this thesis the sequential importance resampling particle filter for estimating the full geometry-based float solution state vector for Global Navigation Satellite System (GNSS) ambiguity resolution is implemented. The full geometry-based state vector, consisting on position, velocity, acceleration, and float ambiguities, is estimated using a particle filter in RTK mode. In contrast to utilizing multi-frequency and multi-constellation GNSS measurements, this study employed solely L1 GPS code and carrier phase observations. This approach simulates scenarios wherein the signal reception environment is suboptimal and only a restricted number of satellites are visible. However, it should be noted that the methodology outlined in this thesis can be expanded for cases involving multiple frequencies and constellations. The distribution of particles after the resampling step is used to compute an empirical covariance matrix Pk based on the incorporated observations at each epoch. This covariance matrix is then used to transform the distribution using the decorrelating Z transformation of the LAMBDA method [1]. The performance of a float solution based on point mass representation is compared to the typically used extended Kalman filter (EKF) for searching the integer ambiguities using the three common search methods described in [2]: Integer Rounding, Integer Bootstrapping, and Integer Least Squares with and without the Z transformation. As Bayesian estimators are able to include highly non-linear elements and accurately describe non-Gaussian posterior densities, the particle filter outperforms the EKF when a constraint leading to highly non-Gaussian distributions is added to the estimator. Such is the case of the map-aiding constraint, which integrates digital road maps with GPS observations to compute a more accurate position state. The comparison between the position accuracy of the particle filter solution with and without the map-aiding constraint to the solution estimated with the EKF is made. The algorithm is tested in different segments of data and shows how the position convergence improves when adding digital road map information within the first thirty seconds of initializing the Particle Filter in different scenarios that include driving in a straight line, turning, and changing lanes. The assessment of the effect of the map-aiding algorithm on the ambiguity domain is carried out as well and it is shown how the convergence time of the float ambiguities improves when the position accuracy is improved by the constraint. The particle filter is able to weight the measurements according to any kind of distribution, unlike the EKF which always assumes a Gaussian distribution. The performance of the PF when having non-Gaussian measurements is assessed, such as when the measurements are distorted by multipath. Two additional steps are implemented, an outlier detection technique based on the predicted set of particles, and the use of a mixture of Gaussians to weight the measurements detected as outliers. The implemented outlier detection algorithm is based on the residual (or innovation) testing technique which is commonly applied into the EKF. The innovation and its covariance matrix are estimated from a predicted set of residuals using the transitional prior distribution and the measurement model. Then, the innovation is compared against the critical value of N (0, 1) at a level of significance α. The mixture of Gaussians is the weighted sum of two Gaussians, one from the measurement noise matrix, and the second being a scaled version of the first one describing the multipath error. This procedure de-weights the measurements with multipath, and reduces the bias in the position estimate. The proposed map-aiding algorithm improves the ambiguity convergence time by approximately 80%, while the deweighting process enhances it by around 25% for the segments of the vehicle dataset that were analyzed. This work serves as a demonstration of cases wherein the particle filter addresses the limitations of the EKF in estimating the float solution in ambiguity resolution. Such limitations include constraints that give rise to non-Gaussian probability density functions and the utilization of a distinct likelihood function for outlier measurements, as opposed to the Gaussian assumption made by the EKF. The proposed map-aided particle filter can be implemented in real-time to enhance the float ambiguity during the initial epochs after the filter has been initialized. This implementation proves beneficial in urban environments where there is a loss or complete obstruction of the GNSS signal.