Robust Kalman Filters Based on Gaussian Scale Mixture Distributions With Application to Target Tracking
针对非高斯重尾或偏斜噪声，提出将一步预测和似然概率密度函数建模为高斯尺度混合分布，并用变分贝叶斯推断状态、混合参数等，在机动目标跟踪中精度和偏差优于现有卡尔曼滤波器。
In this paper, a new robust Kalman filtering framework for a linear system with non-Gaussian heavy-tailed and/or skewed state and measurement noises is proposed through modeling one-step prediction and likelihood probability density functions as Gaussian scale mixture (GSM) distributions. The state vector, mixing parameters, scale matrices, and shape parameters are simultaneously inferred utilizing standard variational Bayesian approach. As the implementations of the proposed method, several solutions corresponding to some special GSM distributions are derived. The proposed robust Kalman filters are tested in a manoeuvring target tracking example. Simulation results show that the proposed robust Kalman filters have a better estimation accuracy and smaller biases compared to the existing state-of-the-art Kalman filters.