Bayesian Nonlinear Filtering Using Quadrature and Cubature Rules Applied to Sensor Data Fusion for Positioning

Abstract

This paper shows the applicability of recently-developed Gaussian nonlinear filters to sensor data fusion for positioning purposes. After providing a brief review of Bayesian nonlinear filtering, we specially address square-root, derivative-free algorithms based on the Gaussian assumption and approximation rules for numerical integration, namely the Gauss--Hermite quadrature rule and the cubature rule. Then, we propose a motion model based on the observations taken by an Inertial Measurement Unit, that takes into account its possibly biased behavior, and we show how heterogeneous sensors (using time-delay or received-signal-strength based ranging) can be combined in a recursive, online Bayesian estimation scheme. These algorithms show a dramatic performance improvement and better numerical stability when compared to typical nonlinear estimators such as the Extended Kalman Filter or the Unscented Kalman Filter, and require several orders of magnitude less computational load when compared to Sequential Monte Carlo methods, achieving a comparable degree of accuracy.