一类基于神经网络非线性随机系统自适应滤波

Neural networks based adaptive filtering for nonlinear stochastic systems

给出非线性MIMO随机系统可观性定义和条件,将非线性SISO确定性系统局部可观性理论拓展到非线性MIMO随机系统.基于这一理论在系统模型和噪声统计未知情况下,提出一类基于神经网络的非线性离散随机系统自适应滤波器的设计方法.考虑过程方程的动态特性和输出方程的静态特性,设计了动态神经网络作为系统的滤波器,前馈神经网络作为系统的输出预报器.充分利用已知观测信息训练两个神经网络,从而提高了状态估计的精度.该方法克服了扩展Kalman滤波要求模型和统计特性精确已知的不足.仿真例子验证了所提出的估计方法的有效性.

This paper gives the definition and the condition of the locally observability for nonlinear MIMO stochastic system, and extends the locally observable theory from nonlinear SISO determinate system to nonlinear MIMO stochastic system. Without knowing the model of the system and the stochastic characteristics, based on neural networks and the presented theory, this paper presents an adaptive filtering design method for nonlinear discrete stochastic system. Considering dynamical property for the process equation and static property for the output equation, this paper designs a dynamical neural networks as a filter and a feedforward neural network as a predictor. The measured data is adequately utilized to train the two neural networks, so the state estimate reaches higher accuracy. Compared with the extended Kalman filtering method, the requirements of knowing model and stochastic characteristics are avoided. Simulation example shows the proposed theory effectiveness.