基于可变遗忘因子广义RLS算法的频率估计

传统的递推最小二乘(RLS)算法有良好的抑制噪声的能力,但在非稳态环境下跟踪能力弱,导致误差大.RLS和Kalman滤波之间存在一一对应的关系,引入Kalman滤波的一步预测估计和新的状态转移矩阵,可以得到广义的RLS算法,该算法改进了跟踪能力.同时,考虑到加权遗忘因子对算法的收敛速度和跟踪能力也有很大影响,故在广义RLS算法中再引入可变的遗忘因子,以确保对时变参数的快速跟踪能力和小的参数估计误差.对基于可变遗忘因子的广义RLS自适应算法和按指数加权的传统RLS算法进行了仿真比较,分析了在稳态下加入谐波、输入幅值变化、输入频率变化等情况下,2种方法所得的频率估计值和均方误差,结果显示所提方法在精度和收敛速度上都更优越.

Frequency estimation based on extended RLS with variable forgetting factor

The conventional RLS(Recursive Least-Squares) algorithm is excellent in noise suppres -sion,but its tracking performance is poor,which causes big error in nonstationary condition.Because of the one -to -one correspondence between RLS and Kalman filtering,the extended RLS algorithm is obtained by introducing the one -step forecast estimation of Kalman filtering and new state transfer matrix into it to improve its tracking performance.As the variable forgetting factor has great impact on convergence speed and tracking performance,it is further introduced into the extended RLS algorithm to ensure the fast tracking and small estimation error.The simulative comparison between the extended RLS algorithm and the conventional RLS algorithm are carried out in estimated frequency and mean square error for three cases:injected harmonics,changed input amplitude and changed input frequency in stationary condition.Results show that the proposed method is better in both precision and convergence speed.