Bayesian nonlinear filters for Direct Position Estimation

The use of a Direct Position Estimation approach has recently deserved some attention in the satellite-based navigation topic. In this paper, the core idea is to merge a motion model based on the observations of an Inertial Measurement Unit, accounting for possible biased measures, with a signal model parameterized by the position of the receiver. Indeed, this position is to be estimated. Bayesian nonlinear filtering theory is reviewed in the paper. Particularly, we focus our attention on the study of particle filtering and square-root derivative-free algorithms based on the Gaussian assumption and approximation rules for numerical integration, namely the Gauss-Hermite quadrature rule or the third-degree spherical-radial cubature rule. These algorithms exhibit a dramatic improvement and better numerical stability than classical Kalman filter-like methods, for example the extended Kalman filter or the unscented Kalman filter. The paper presents an analysis of the computational complexity of each algorithm and a performance comparison using computer simulations under a realistic scenario.