Sequential Monte Carlo Filters and Integrated Navigation

Abstract: In this thesis we consider recursive Bayesian estimation in general, and sequential Monte Carlo filters in particular, applied to integrated navigation. Based on a large number of simulations of the model, the sequential Monte Carlo filter, also referred to as particle filter, provides an empirical estimate of the full posterior probability density of the system. The particle filter provide a solution to the general nonlinear, non-Gaussian filtering problem. The more nonlinear system, or the more non-Gaussian noise, the more potential particle filters have.Although very promising even for high-dimensional systems, sequential Monte Carlo methods suer from being more or less computer intensive. However, many systems can be divided into two parts, where the first part is nonlinear and the second is (almost) linear conditionally upon the first. By applying the particle filter only on the severly nonlinear part of lower dimension, the computational load can be significantly reduced. For the remaining conditionally (almost) linear partwe apply (linearized) linear filters, such as the (extended) Kalman filter. From a Bayesian point of view, the result from the different filters can be seen as marginal posterior probability densities. The full posterior density is then computed by combining the results from the separate filters using Bayes' rule. The technique of marginalising the complete posterior density and solve the linear parts analytically is referred to as Rao-Blackwellization.The application considered here is integrated aircraft navigation. Integrated navigation refers to the combination of outputs from two or more navigation sensors to yield a more accurate and reliable overall solution. The sensors we are dealing with are inertial navigation and terrain-aided positioning, meaning that we combine two systems which are high-dimensional and highly nonlinear respectively. The integrated navigation application is a typical system which consists of both linearand nonlinear elements. We show that by applying the efficent particle filter based on Rao-Blackwellization we obtain nearly optimal accuracy for a tractable amount of computational load.