Recursive estimation of three-dimensional aircraft position using terrain-aided positioning

As a part of aircraft navigation, three-dimensional position must be computed continuously. For accuracy and reliability reasons, several sensors are integrated together, and here we are dealing with dead-reckoning integrated with terrain-aided positioning. Terrain-aided positioning suffers from severe nonlinear structure, meaning that we have to solve a nonlinear recursive Bayesian estimation problem. This is not possible to do exactly, but recursive Monte Carlo methods, also known as particle filters, provide a promising approximate solution. To reduce the computational load of the normally rather computer intensive particle filter we present an algorithm which takes advantage of linear structure. The algorithm is based on a Rao-Blackwellisation technique, meaning that we marginalise the full conditional posterior density with respect to the linear part. The linear part of the state vector is estimated using multiple Kalman filters, and the particle filter is then used for the remaining part. Simulations show that the computational load is reduced significantly.