A dictionary based survival error compensation for robust adaptive filtering

Survival information potential (SIP) is defined by the survival distribution function instead of the probability density function (PDF) of a random variable. SIP can be used as a risk function equipped with learning error compensation ability while this SIP based risk function does not involve the estimation of PDF. This is desirable for a robust learning application in view of the error compensation ability. The learning error compensation scheme provided by SIP requires rank information of learning errors. The accuracy of error compensation desires a large number of input data but is computationally expensive. It is shown that the error compensation can be approximated by an error-related distribution. Based on this approximation, a dictionary based error compensation scheme is proposed to obtain a fixed-budget recursive online learning method. This proposed method is compared with several well-known online learning methods including least-mean-square method, least absolute deviation method, affine projection algorithm, recursive least-mean-square method, and sliding window based SIP method. Simulation results validate the outstanding smooth and consistent convergence performance of the proposed method particularly in α-stable-noise environments.