Comparison of Extended and Sigma-Point Kalman Filters for Tightly Coupled GPS/INS Integration

Abstract

This paper adresses the fusion of GPS measurements and inertial sensor data in tightly coupled GPS/INS navigation systems. Usually, an extended Kalman lter (EKF) is applied for this task. However, as the system dynamic model as well as the pseudorange and deltarange measurement models are nonlinear, the EKF is a sub-optimal choice from a theoretical point of view, as it approximates the propagation of mean and covariance of Gaussian random vectors through these nonlinear models by a linear transformation, which is accurate to rst-order only. The sigma-point Kalman lter (SPKF) family of algorithms achieve an accurate approximation to at least second-order. Therefore, the performance of EKF and SPKF applied to tightly-coupled GPS/INS integration is compared in numerical simulations. It is found that except in specic situations without practical relevance, both approaches oer an identical performance. This indicates that the SPKF may be an option considering the design of new systems, but a modication of existing EKF-based GPS/INS systems is neither required, nor appropriate to improve their performance.