机动目标状态估计的最小均方误差界

Minimum mean square error bound for state estimation of maneuvering targets

基于多项式模型的各种自适应滤波算法被广泛应用于机动目标跟踪领域,但尚没有统一的评估标准来衡量这些跟踪算法的优劣。由于存在确定的时变未知输入,机动目标的状态估计实际为有偏估计。基于状态估计均方误差最小的准则,推导了多项式模型滤波的最小均方误差界计算方法,获得了使状态估计均方误差最小的过程噪声方差变化规律。该方法给出了各种基于多项式模型的机动目标跟踪算法的估计均方误差下限,也为机动目标跟踪中最优过程噪声方差的设定提供了依据。仿真结果验证了算法的有效性。

The adaptive filtering algorithms based on the polynomial model are widely used in the field of maneuvering target tracking, but there is no uniform evaluation criterion to measure the quality of these tracking algorithms. Due to the existence of time-varying unknown inputs, the maneuvering target state estimation is actually biased. To solve this problem, the minimum mean square error bound calculation method for polynomial model Kalman filters was derived based on the minimum mean square error criterion, and the process noise variance law minimizing the state estimation mean square error was obtained. The proposed algorithm provides a unified evaluation standard for maneuvering target tracking algorithms based on the polynomial model, and also provides the basis for the setting of the actual process noise variance in maneuvering target tracking. The effectiveness of the proposed algorithm is demonstrated by the simulation results.