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Discrete-time min-max tracking

机译：离散时间最小-最大跟踪

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摘要

The problem of optimal state estimation of linear discrete-time systems with measured outputs that are corrupted by additive white noise is addressed. Such estimation is often encountered in problems of target tracking where the target dynamics is driven by finite energy signals, whereas the measurement noise is approximated by white noise. The relevant cost function for such tracking problems is the expected value of the standard H/sub /spl infin// performance index, with respect to the measurement noise statistics. The estimator, serving as a tracking filter, tries to minimize the mean-square estimation error, and the exogenous disturbance, which may represent the target maneuvers, tries to maximize this error while being penalized for its energy. The solution, which is obtained by completing the cost function to squares, is shown to satisfy also the matrix version of the maximum principle. The solution is derived in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated discrete-time Kalman filter is recovered. A local iterations scheme which is based on linear matrix inequalities is proposed to solve these equations. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the target position.
机译：解决了线性离散时间系统的最优状态估计问题，该系统的测量输出受到加性白噪声的破坏。在目标跟踪问题中经常会遇到这种估计，其中目标动态是由有限的能量信号驱动的，而测量噪声是由白噪声近似的。对于此类跟踪问题，相关的成本函数是标准H / sub / spl infin //性能指标相对于测量噪声统计的期望值。用作跟踪滤波器的估计器试图使均方估计误差最小，而可能代表目标操纵的外源性干扰则试图使该误差最大化，同时对其能量进行惩罚。通过将成本函数求平方得到的解也显示为也满足最大原理的矩阵形式。该解决方案是根据两个耦合的Riccati差分方程式得出的，从中可以得出滤波器增益。在外来干扰的能量受到无限惩罚的情况下，恢复了著名的离散时间卡尔曼滤波器。提出了一种基于线性矩阵不等式的局部迭代方案来求解这些方程。给出了说明性示例，其中必须利用目标位置的噪声测量来估计机动目标的速度。

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