Terrain Referenced Navigation Based on Robust Point Mass Filter Using Variance Adjusted Discrete Normal PDF and Mean Valued Likelihood

Abstract

Terrain referenced navigation (TRN) provides complementary technology when Global Navigation Satellite System (GNSS) is unavailable. TRN estimates the vehicle’s position by comparing the measured terrain heights with the embedded ones such as Digital Terrain Elevation Data (DTED). However, its sequential estimation problem is beyond linear because terrain itself is highly nonlinear and its solutions are not explicit function form as well. There are lots of algorithms applicable to TRN estimation problem including Point mass filter (PMF). PMF implements the nonlinear Bayesian estimator by using a grid of point masses such that converts the integrals to finite sum over this grid. It’s generally known that the PMF based TRN outperforms that with particle filter (PF) in terms of accuracy and robustness. There have been lots of efforts to improve its performance and robustness since Bergman had proposed PMF with 2- dimensional position error states for TRN. The previous results had focused on the grid selection or adaption algorithm. In spite of those efforts, however, PMF still shows the tendency of overconfidence and point mass impoverishment when its grid resolution is limited due to computational issue. So two new methods are proposed in this paper in order to overcome those problems. First, the kernel design technique with variance adjusted discrete normal pdf implementation for time propagation of weights is suggested. The proposed kernel implementation scheme exactly draws the second moments when system noise follows normal distribution and it soothes the overconfidence problem. Second, mean valued likelihood for measurement update is proposed. The previous results calculate its likelihood only on grids. The proposed scheme calculates its likelihood over the area which grid covers instead of just one point on grid. This method might degrade performance but guarantee its robustness. Simulation result shows the effectiveness of the PMF with the proposed two schemes for TRN. The simulation assumes that interferometric radar altimeter(IRA) is used as a sensor measuring altitude above the ground. IRA measures the range and look angle from vehicle to the closest point in zero-doppler area. Because 3-dimensional relative position can be calculated, it gives more accurate relative altitude over the ground than previous radar altimeter. With this accurate altimeter, it is expected that the proposed PMF schemes outperform the original filter on both accuracy and robustness.