欠观测条件下的高斯和增量卡尔曼滤波算法

Gaussian sum incremental Kalman filter under poor observation condition

欠观测条件下的增量卡尔曼滤波算法能够消除未知的量测系统误差,提高滤波精度。当系统的过程噪声和量测噪声为非高斯分布时,该算法不能直接使用。针对该问题,结合高斯和滤波算法,提出一种欠观测条件下的高斯和增量卡尔曼滤波算法。该算法将初始状态、过程噪声和量测噪声近似为高斯和的形式,然后按照增量卡尔曼滤波的思想对每个高斯项进行预测和更新,最后以累加和的形式对状态向量进行近似。仿真结果表明,该算法在非高斯噪声分布的情况下,既能成功地消除量测系统误差,又能有效地提高滤波估计的准确度和可靠性。

Incremental Kalman filter under poor observation condition can eliminate unknown measurement system errors and improve the precision of filter. However,when the system process noise and measurement noise are subject to non-Gaussian distributions,the algorithm cannot be used directly. Addressing this problem,this paper presented a Gaussian sum incremental Kalman filter under poor observation condition though combining with the Gaussian sum filtering algorithm. In the algorithm,it approximated the initial state,process noise and measurement noise by the form of Gaussian sum. Then it used each Gaussian item to predict and update according to the incremental Kalman filter theory. Finally,it approximated state value by using the form of accumulated sum. Simulation results show,in systems with non-Gaussian noise distribution,the proposed algorithm can eliminate the measurement system successfully,and can improve the accuracy and reliability effectively.