基于BLPN算法的AR SαS过程共变谱估计方法

Covariation Spectrum Method for AR SαS Processes Based on BLPN Algorithm

研究了一种新的AR SαS过程的谱估计算法。该算法将整个数据作为一个整体,利用分数低阶p阶矩从前向、后向两个方向对数据进行处理,获得了一种高分辨率的参数估计算法——双向最小p范数法(Bidirectional Least p Norm,BLPN)。利用得到的参数,结合共变谱的定义,构建了AR SαS过程下的共变谱估计表达式,并分别对AR SαS过程参数估计、α稳定分布噪声中的正弦信号的谱估计进行仿真。仿真结果表明,基于BLPN的ARSαS模型的共变谱估计方法对于不同的α值均具有良好的韧性,特别是在α值较小或者短时数据时,本文方法的性能明显优于基于FLOM的AR SαS模型共变谱估计方法。

A new spectrum estimation algorithm is studied based on AR SαS process. The new algorithm makes all data as a whole,thus obtaining a high precision parameter estimation method—bidirectional least p norm（BLPN） by disposing the datum from forward,backward with fractional lower order p order square.Combined with the define of the covariation spectrum,the obtained parameter is used to form the covariation spectrum estimation expression of AR SαS process.The parameter estimation of AR SαS processes are simulated,as well as the sepctrum estimation of sine signal embedded in the α-stable nosie.Simulation results show that the covariation spectrum estimation method for the AR SαS processes based on BLPN is robust for different values of α（1α≤2）,especially when α is small or short time data,the proposed covatiation spectrum estimation method for AR SαS processes based on BLPN can provide better performances than that of based on FLOM.