一种基于拟牛顿法的AR模型参数估计

AR model parameters estimate based on quasi-newton method

功率谱是描述随机信号基本特征的重要参数,AR(autoagressive)模型谱估计因其运算量较小,广泛用于各种信号处理中。用AR模型实现谱估计的关键在于寻找AR模型的参数。由AR模型引出Yule-Walker方程,分析说明Yule-Walker方程实质上是线性预测误差功率最小的驻点方程,求AR模型各参数的问题也可归结为求在最小均方误差准则下的线性预测器系数的问题。并由此提出用拟牛顿法来搜索AR模型参数,实现谱估计。通过计算机仿真,对产生的谱漂移现象、谱分裂现象和频率分辨能力进行分析,验证了该算法的有效性。

Power spectral is an important parameter of describing the basic character of random signal. The power spectral estimation of AR model is widely used in various signal processing for its low complexity. The key point of power spectral estimation based on AR model is seeking the parameters of AR model. In this paper,we transform YuleWalker equation from AR model and illustrate that Yule-Walker equation is essentially stagnation point equation of the least linear predictive error power. The Solution of computing the parameters of AR model can also be summarized as the solution of computing the parameters of linear predictor under the principle of the least mean square error. Therefore we propose a method of AR model parameters estimate based on quasi-Newton algorithm and result spectral estimation. Through the computer simulation, we discuss the phenomena of spectrum drifting, spectrum splitting and spectrum resolution. The simulation results show that the algorithm is efficient.