离散系统状态和参数鲁棒滤波分离算法

Separated robust filtering algorithm of state and uncertain coefficient matrix for discrete-time system

提出了一种离散系统的鲁棒分离滤波方法.为了对状态向量进行较准确估计,将鲁棒滤波器分为:1)零误差状态估计器;2)不确定矩阵估计器;3)鲁棒合成器.零偏差状态估计器是假定系统的不确定部分为零时的状态估计器;其新息作为不确定部分的估计变量,并由此估计系统的不确定部分;最后,根据系统不确定部分估计误差的上下界,用鲁棒合成器对状态向量的估计值进行鲁棒修正.为了在合成器中得到鲁棒滤波的逼近计算式,通过变换状态估计误差的协方差阵,得到了系统矩阵不确定部分的误差上界不等式逼近,并且得到了估计误差协方差阵逆阵的下界不等式逼近,从而给出了鲁棒合成滤波的完整算法.

Recent research papers on estimating the effect of inaccurate model are still quite difficult to apply in engineering computations. To decrease the error caused by model uncertainty, a separated robust filter for estimating both the state and uncertain coefficient matrix of discrete-time system was presented. To get accurate estimation of both the state and uncertain matrix, the new robust filter was built up by three parts: First, uncertainty-free state estimator. Second, uncertain matrix identification; Third, robust mix filter. In uncertainty-free state estimator, the uncertain parts of both the system matrix and observation matrix are all considered as zero. In uncertain matrix identification part, the innovation of uncertainty-free state estimator was used to get uncertain matrix identification. In the robust mix filter, the state was further improved by the result of both identified uncertain matrices and uncertainty-free state estimates. By estimating upper bound of state-error-covariance matrix in the time update and by estimating lower bound of observation-inverse-covariance matrix in the measurement update, the mix-filter gain matrix was obtained. Thus state estimating errors caused by uncertain matrix can be decreased. Finally, the proposed approach was applied to a certain aircraft, and the numerical simulation results showed fairly good agreement between flight-testing data and the data obtained by the proposed filtering method.