Comparison of Nonlinear Filtering Methods for Terrain Referenced Aircraft Navigation

Abstract

Inertial Navigation Systems (INS) are the main part of the integrated navigation for most of the aerial vehicles. However, the accuracy of an inertial navigation solution decreases with time as the inertial instrument (e.g., gyroscope and accelerometer) errors are integrated through the navigation equations. Therefore, different aiding techniques are used to bound the drift in these systems. One of the commonly used techniques is the integration of INS with Global Navigation Satellite System (GNSS) signals. By means of this integration, the advantages of both technologies are combined to give a complete navigation solution. The need for Terrain Referenced Navigation (TRN) arises when these satellite based radio signals are unavailable. In recent years, research on the application of TRN to aerial vehicles has been increased rapidly with the developments in the accuracy of digital terrain elevation database (DTED). Since the land profile is inherently nonlinear, TRN becomes a nonlinear estimation problem. Because of the highly nonlinear problem, linear or linearized estimation techniques such as Kalman or Extended Kalman Filter (EKF) do not work properly for many terrain profiles. Hence, this paper focuses on nonlinear filtering techniques and presents the main principles of two different TRN methods. These methods will be compared and advantages of both methods will be presented. The first method is the Sequential Monte Carlo (SMC) technique namely the particle filter (PF) for dealing with nonlinearities and different types of probability distributions even multi-modal. PF is an approximate optimal filter on correct model and based on particle representation of probability density function. The second method is the Unscented Kalman Filter (UKF) based on the Unscented Transform (UT) of sigma points. The basic idea is to approximate the probability density function with deterministically selected and weighted small number of sigma points. Simulations with different inertial measurement units (IMUs), with different initial errors, over maps with various resolutions are performed and investigated. The performance of both nonlinear filtering algorithms will be presented through Monte Carlo simulations.