带不确定参数和噪声方差的鲁棒观测融合Kalman滤波器

对带不确定参数和噪声方差的多传感器定常系统,引入虚拟白噪声补偿不确定参数,可将其转化为带已知参数和不确定噪声方差系统.应用极大极小鲁棒估值原理和加权最小二乘法,基于带噪声方差保守上界的最坏情形保守系统,提出了鲁棒加权观测融合Kalman滤波器,并证明了它与集中式融合鲁棒Kalman滤波器是等价的,且融合器的鲁棒精度高于每个局部滤波器鲁棒精度.一个Monte-Carlo仿真例子说明了如何寻求不确定参数的鲁棒域和如何搜索保守性较小的虚拟噪声方差上界.

Robust measurement fusion Kalman filter with uncertain parameters and noise variances

For the multisensor time-invariant system with uncertain parameters and noise variances, by introducing a fictitious white noise to compensate the uncertain parameters, we can convert the uncertain system into the system with known parameters and uncertain noise variances. Using the minimax robust estimation principle and weighted least squares method, we present a robust weighted measurement fusion Kalman filter based on the worst-case conservative system with the conservative upper bounds of noise variances. We prove that this Kalman filter is equivalent to the robust centralized fusion Kalman filter, and its robust accuracy is higher than that of each local robust Kalman filter. A Monte-Carlo simulation example shows how to find the robust region of uncertain parameter and how to search the less-conservative upper bound of fictitious noise variances.