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文中提出了一个通过多项式预测模型来描述待辨识系统冲击响应系数的最优自适应滤波算法.该算法首先利用具有时不变参数的多项式预测模型,来描述系统冲击响应的时变/时不变系数.当视描述的模型为其待辨识系统冲击响应时变/时不变系数进化的状态方程,而待辨识系统的输入和输出联系视为对这些状态的观测方程时,自适应滤波问题可以在Kalman滤波的框架下得以解决.由于在Gauss白噪声环境中以及状态方程准确的情况下,Kalman滤波是最大似然、最大后验和最小均方等统计意义下的最优滤波,因此当待辨识的系统冲击响应系数可以由多项式模型建模时,文中模型和相应算法也是这些统计意义下的最优自适应滤波.在分析的结果验证上述结论的同时,仿真的结果也表明:文中提出的自适应滤波算法的性能优于已知的自适应滤波算法.
A polynomial prediction model is proposed in this paper to describe the optimal adaptive filtering algorithm of the impulse response coefficient of the system to be identified.The algorithm first uses the polynomial prediction model with time invariant parameters to describe the time-varying / time-invariant When the model to be described is the equation of state of the variable / time invariant coef fi cient for the system to be identified, the input and output relations of the system to be identified are treated as observational equations for these states, and the adaptive filtering problem can be solved Which can be solved in the framework of Kalman filter.Because Gaussian white noise environment and the state equation is accurate, Kalman filter is the optimal filter in the statistical sense such as maximum likelihood, maximum a posteriori and minimum mean square, so when When the identified system impulse response coefficient can be modeled by polynomial model, the model and the corresponding algorithm are also the optimal adaptive filtering in these statistical senses.At the same time, the simulation results also show that the proposed system The performance of adaptive filtering algorithm is better than the known adaptive filtering algorithm.