连续系统下的一种容偏估计策略

A bias-allowable estimator for continuous-time system

目标跟踪系统中为降低系统复杂度和保证估计的平稳性常常选择尽可能低阶次的模型,当目标出现较高阶次的机动时,则很容易丢失目标.在假定目标的机动时间与强度均有限时,提出了容偏估计的思想,将稳态误差系数约束连同区域极点、估计误差方差上界指标一起构成估计系统的约束指标集,寻求使得稳态误差系数尽可能小的滤波器,以使得对机动目标跟踪的系统偏差尽可能小.通过将约束指标集转化为一组双线性矩阵不等式(BMIs),并利用迭代求解线性矩阵不等式(LMIs)近似BMIs的方法,得到了满足给定指标约束要求的容偏估计策略,所设计的容偏估计策略可同时保证估计的准确性和精确性的要求,从而保证了在目标出现机动时,估计输出具有尽可能小的系统偏差.最后数值算例对所提出的结论进行了说明.

In an object-tracking system, the order of system model is often chosen as low as possible for reducing the computational complexity and ensuring the estimation smoothness. If the object makes a higher order maneuvering, the tracking system may lose the object. By assuming that the intensity and duration of the target maneuver are finite, we introduce the idea of bias-allowable estimation. The purpose is to find an estimator that makes the steady error coefficient as small as possible for minimizing the tracking system bias, under the constraints of regional poles and the upper bound of the error variance, along with the constraint of steady error coefficient index. The constraint index set is transformed to a set of bilinear matrix inequalities（BMIs）. The expected bias-allowable estimator is obtained by iteratively solving linear matrix inequalities（LMIs） to approximate the solutions of BMIs. The proposed bias-allowable estimator ensures the accuracy and smoothness of the estimation output and guarantees the tracking system bias to be small as possible, when the target is maneuvering. Finally, a numerical example is given to illustrate the design of the bias-allowable estimation.