多传感器系统估计的稳健切比雪夫中心估计融合

摘要

针对多传感器线性回归模型的参数估计融合问题,在观测噪声是范数有界的情况下,提出了稳健切比雪夫中心估计融合方法.描述参数的可行集合,为线性系统的所有可行解.可行集合的切比雪夫中心是最坏情况下使得估计误差最小的点,可用它作为多传感器系统参数估计的稳健融合.该问题在复数域上的某些情况可以精确求解,但目前的研究在实数域上只能得到近似解,即松弛的切比雪夫中心.严格证明了在实平面上可行集合的切比雪夫中心可以通过有限个约束的凸优化问题求解,因此,切比雪夫中心可以通过高效优化算法得到.在高维情况下,通过将可行集合投影到各坐标平面,设计了近似的切比雪夫中心融合方法.数值实验结果表明:该方法优于松弛的切比雪夫中心融合.%Aiming at the problem of the parameter estimation fusion of multisensor linear regression model,where the noise of the observation is unknown but norm-bounded. The feasible parameter set ( FPS) is described as all admissible solution to the linear system. Chebyshev center of FPS is the point of in the worst-case which make the estimation error minimize, which is used as a robust estimation fusion of the parameter. This problem can be solved in the complex domain in some cases, but in real domain only get the relaxed Chebyshev center (RCC) estimator in present research. It is demonstrated Chebyshev center of FPS on real plane can be solved by convex optimization of a set of finite restrain, so Chebyshev center can be obtained via efficient optimization algorithms. An approximate Chebyshev center(ACC) fusion algorithm is designed via the projections of the FPS to each coordinate planes. The numerical experiment results show that the method is prior to relaxed Chebyshev center fusion.