The Effect of Linear Approximation and Gaussian Noise Assumption in Multi-Sensor Positioning Through Experimental Evaluation

Assumptions of Gaussianity in describing the errors of ranging data and linearization of the measurement models are well-accepted techniques for wireless tracking multi-sensor fusion. The main contribution of this paper is the empirical study on the effect of these assumptions on positioning accuracy. A local positioning system (LPS) was set up and raw data were collected using both the global satellite navigation system (GNSS) and the LPS. These data were fused to estimate position using both an extended Kalman filter (EKF) and a particle filter (PF). For these data, it was shown that the PF had an improvement in accuracy over the EKF of 67 cm (72%) with achieved accuracy of 26 cm. This improvement was attributed to the PF handling the non-linear system dynamics, rather than a linear approximation as in the EKF. Furthermore, when the PF used the fitted three-component Gaussian mixture model as the better approximation of the actual LPS ranging error distribution, rather than a Gaussian approximation, a further 3 cm (13%) reduction in positioning error was observed. Overall, the average accuracy of 23 cm was achieved for the proposed multi-sensor positioning system when the assumptions of Gaussianity are not made and the non-linear measurement model is not linearized.