时变有色观测噪声下基于变分贝叶斯学习的自适应卡尔曼滤波

针对卡尔曼滤波中观测噪声是有色的且随时间变化这一情形，该文提出基于变分贝叶斯学习的自适应卡尔曼滤波算法。该算法先利用差分法，将时变噪声模型当中的有色观测噪声进行白化处理，从而使模型转换成了过程噪声与观测噪声相关的白噪声模型。考虑噪声相关条件下的卡尔曼滤波，并使之与变分贝叶斯学习结合，将白噪声方差与系统状态变量一起作为参数进行联合的递推估计。仿真结果表明，该自适应算法对时变的噪声具有较好的跟踪效果，相对经典卡尔曼滤波有着较高的滤波精度，最终得到时变有色观测噪声下的状态估计。

Adaptive Kalman Filtering with Time-varying Colored Measurement Noise by Variational Bayesian Learning

An adaptive Kalman filtering algorithm based on variational Bayesian learning is suggested to cope with the problem in which colored and time-varying measurement noise is introduced. By use of differencing, the model is converted back to a normal model in which measurement noise is white but correlated with process noise. Kalman filtering is modified owing to the correlation and variational Bayesian learning is combined to jointly estimate the measurement noise and the state in a recursive manner. The simulation results demonstrate that this adaptive algorithm is capable of tracking time-varying noise and provides more accurate state estimation than standard Kalman filtering with colored and time-varying noise.