基于ARMA辨识的色噪系统状态参数鲁棒估计

Robust State Estimation for Systems with Colored Measurement Noise Based on ARMA Identification

实际环境中观测系统的噪声,同时存在着白噪、色噪声和尖点噪声的影响。已有的研究都仅考虑白噪或色噪声,首次将实际系统中可能出现的所有噪声纳入观测方程,推导出统一的带白噪形式的观测方程。新观测方程在色噪声ARMA辨识基础上,可以直接用于传统的卡尔曼滤波算法,避免了扩维滤波。于是状态参数的稳健估计归结为ARMA参数的辨识。重点研究了自由参数选取与输入噪声之间的关系,将鲁棒支持向量回归机的优化问题转换成最大后验估计问题,为合理选择自由参数提供了理论依据。仿真结果验证了新算法的有效性。

In practical application, the observation systems is influenced by white noise, colored noise and outliers. Till now, most research considered the noise as white noise or colored noise respectively. In the paper, both of them are considered, a new measurement equation is derived by denoting the colored noise with white noise, and Kalman filtering model for systems with white noise and colored noise is presented in order to avoid complicated computation and expansion of the dimension of the filter. Hence, the state estimation can be interpreted into an equivalent ARMA identification problem. The dependency relationship between the parameter selection and input noise in robust SVR is studied using maximum a posteriori estimation. The simulation also shows that based on ARMA identification robust state estimation for systems with unstable and colored measurement noise performs well.