线性系统在非线性等式约束下的集员卡尔曼滤波

Set-membership Kalman filtering for linear systems with nonlinear equality constraints

为了解决运行系统要求的100%估计包含真实最小域的需要和计算机的实时计算问题,使用集员卡尔曼滤波算法解决非线性状态约束.采用最小迹椭球算法对状态向量的椭球域进行更新,同时分别在预测和滤波的2个阶段用投影的方法把没有约束的状态估计投影到有约束的状态估计表面来处理约束问题.最后将所设计的集员卡尔曼滤波器应用到汽车追踪实例中.实验结果表明:采用所提算法的系统只是在初始值有比较大的误差,在后续的跟踪过程中都能在最大最小界之内跟踪上真实值.所提算法相比于传统的卡尔曼算法,其误差能迅速减小.实例仿真结果证明了所提方法的可行性和有效性.

The set-membership Kalman filtering is proposed to solve the problems of the system requiring 100% confidence to be estimated and the real-time calculation for systems w ith nonlinear equality constraints.The algorithm of the minimum trace ellipsoid is adopted to optimize the stage of time updating.At the steps of prediction and filter,the unconstrained set-membership Kalman filtering is projected onto the state constraint surface to deal w ith the constraint problem.The proposed algorithm is tested on a vehicle tracking application.The results show that the true values by using the constrained set-membership filter always reside between their upper bounds and lower bounds during the later tracing,despite the original values have great error which rapidly decreases compared to the Kalman filtering.The simulation results show that the proposed method is available and effective.