辨识动态系统噪声方差Q和R的新方法

对于带未知噪声方差的线性离散定常随机系统，引入左素分解可得到一个新的观测过程，它用两个滑动平均（MA）过程之和表示。用解相关函数矩阵方程组得到了噪声方差Q和R的估值器，进而基于新的观测过程的采样相关函数及其遍历性可得到噪声方差Q和R的强一致估计。算法简单，便于实时应用。一个目标跟踪系统的仿真例子说明了其有效性。

New Approach to Identify the Noise Variances Q and R of Dynamic Systems

For the linear discrete time-invariant stochastic systems with unknown variances, by introducing a left coprime decomposition, a new measurement process is obtained, which is described by the sum of two moving average(MA) process. The estimators of the noise variances Q and R are obtained by solving the matrix equations for correlation function, and based on the sampled correlation function of the new measurement process and its ergodicity, the strong consistent estimators of the noise variances Q and R are obtained. The algorithm is simple, and they are suitable for real time applications. A simulation example for a target tracking system shows their effectiveness.