带随机量测时滞和随机丢包的改进无迹卡尔曼滤波

经典卡尔曼滤波要求量测值可实时获取,且仅适用于线性系统.然而,在工程实际应用中,系统多为非线性系统,量测值也会发生滞后或者丢失等现象,此时经典卡尔曼滤波已不适用.因此,本文针对一类带有随机量测一步时滞和随机丢包的非线性离散系统的状态估计问题,用两个满足伯努利分布的独立随机变量来描述随机量测一步滞后和随机丢包的现象.当量测丢失时,用量测值的一步预测值来代替零输入进行补偿.在此基础上应用正交投影理论和无迹变换的方法提出了一种改进的无迹卡尔曼滤波算法.最后,通过仿真例子验证在考虑随机量测一步时滞和随机丢包的情况下,所提出的改进算法相比于经典无迹卡尔曼滤波算法具有更高的精度.

An improved unscented Kalman filter with randomly delayed measurements and randomly missing measurements

The classical Kalman filter requires that the measurements can be obtained in real time, and it is only suitable for linear systems. However, in practical engineering applications, most of the systems are nonlinear systems, and the measurements are sometimes delayed or lost, the classical Kalman filter is no longer applicable in this case. Therefore, in this paper, the problem of state estimation for nonlinear discrete-time systems with randomly one-step delayed measurements and missing measurements is studied. The phenomena of randomly one-step delayed measurements and missing measurements are described by two independent random variables satisfying the Bernoulli distribution. When the measurement is missing, the one-step prediction value of the measurement is used to replace the zero input for compensation. On this basis, an improved unscented Kalman filter is proposed by using the orthogonal projection theory and unscented transformation method. Finally, a simulation example is given to illustrate that the improved algorithm has higher accuracy than the classical unscented Kalman filter in the case of considering randomly one-step delayed measurements and missing measurements.