An Improved Gaussian Mixture CKF Algorithm under Non-Gaussian Observation Noise

Hongjian Wang,Cun Li

doi:10.1155/2016/1082837

Abstract

In order to solve the problems that the weight of Gaussian components of Gaussian mixture filter remains constant during the time update stage, an improved Gaussian Mixture Cubature Kalman Filter (IGMCKF) algorithm is designed by combining a Gaussian mixture density model with a CKF for target tracking. The algorithm adopts Gaussian mixture density function to approximately estimate the observation noise. The observation models based on Mini RadaScan for target tracking on offing are introduced, and the observation noise is modelled as glint noise. The Gaussian components are predicted and updated using CKF. A cost function is designed by integral square difference to update the weight of Gaussian components on the time update stage. Based on comparison experiments of constant angular velocity model and maneuver model with different algorithms, the proposed algorithm has the advantages of fast tracking response and high estimation precision, and the computation time should satisfy real-time target tracking requirements.

Highlights

With the universality of nonlinear problems, the principle and method of nonlinear filtering are being widely used for the nonlinear systems
The Gaussian filtering could sum up three classes according to the different approximate methods: the first is function approximation, which approximates the nonlinear system function using the low-order expansion such as the extended Kalman filtering (EKF) [1] and the improved algorithms (adaptive fading EKF [2], strong tracking EKF [3], and central difference Kalman filtering (CDKF) [4, 5])
We focus on the target tracking problem on offing and design an improved Gaussian mixture Cubature Kalman Filter (CKF) based on the GMCKF algorithm

Summary

Introduction

With the universality of nonlinear problems, the principle and method of nonlinear filtering are being widely used for the nonlinear systems. For the currently nonlinear systems, the possible solution approaches are some approximate methods, such as approximating the probability density of system state as the Gaussian density, which is called Gaussian filtering. The second is deterministic sampling approximation method, which approximates system state and the probability density using deterministic sampling such as the Unscented Kalman Filter (UKF) [6, 7] and the improved algorithms [8, 9]. The third is approximation using quadrature, which approximates the multidimensional integrals of Bayesian recursive equation using some numerical technologies, such as the Gaussian-Hermite Kalman Filter (GHKF) [10] and the Cubature Kalman Filter (CKF) [11,12,13]. GHKF acquires the statistic characteristics after nonlinear transformation by Gaussian-Hermite numerical integral, which has higher accuracy.

Methods

Results

Conclusion