In this paper, a recursive $t$-distribution noise model based maximum likelihood estimation algorithm for discrete-time dynamic state estimation is proposed. The proposed estimator is robust to outliers because the “thick tail” of the $t$-distribution reduces the effect of large errors in the likelihood function. A computationally efficient recursive algorithm is derived using the influence function. As the $t$-distribution reduces to the Gaussian distribution when its degree of freedom tends to infinity, the proposed estimator reduces to the Kalman filter. The mean squared error is used to evaluate the performance of the proposed estimator. Compared with the Kalman filter, the proposed estimator is more robust to outliers in the process and measurement noise. Simulations show that for the particle filter to give a better mean squared error, its computational time is two orders of magnitude slower than the proposed estimator.

在本文中，递归 $吨$提出了基于分布噪声模型的离散时间动态状态估计最大似然估计算法。建议的估计量对异常值具有鲁棒性，因为$吨$-分布减少了似然函数中大误差的影响。使用影响函数导出计算效率高的递归算法。作为$吨$-分布在其自由度趋于无穷大时简化为高斯分布，建议的估计量简化为卡尔曼滤波器。均方误差用于评估建议估计器的性能。与卡尔曼滤波器相比，所提出的估计器对过程和测量噪声中的异常值具有更强的鲁棒性。模拟表明，粒子滤波器要提供更好的均方误差，其计算时间比建议的估计器慢两个数量级。