Study Of Fusion Signed Filtering Algorithm For Cyclostationary Inputs

In recent years,the progress of sensor technology has promoted the rapid development of distributed adaptive filtering theory.Distributed adaptive filtering algorithms are widely used in many fields of wireless sensor networks,distributed image processing,smart grids,array signal processing,biological cluster behavior simulation and so on.Although the distributed adaptive filter represented by the diffusion least mean square(DLMS)algorithm has received intensive theoretical analysis and research,there are still few studies on distributed signed fu-sion algorithms that are often used in the real-time applications.Meanwhile,few researches on the impact of frequently encountered non-Gaussian impulsive noise,cyclostationary input,as well as time-varying non-stationary systems on the error convergence performance of the distributed fusion signed algorithm was fully carried out.Therefore,aiming at the distributed network scenario with high real-time requirements,this thesis designed two robust and small computationally-intensive distributed fusion signed adaptive filtering algorithms based on the time-varying non-stationary system for cyclostationary input and impulsive interference noise.The error transient convergence performance of the two distributed diffusion fusion signed adaptive filters are theoretically analyzed and investigated,and the correctness and effective-ness of the proposed algorithm and analytical models are verified by the numerical simulation experiments.The main research works of this thesis includes the following contents:(1)In the application of distributed adaptive network requiring the high real-time perfor-mance,for the problem of slow convergence speed of diffusion signed error algorithm(DSEA),a novel diffusion dual signed algorithm(DDSA)with adaptive-then-combine strategy is pro-posed in this thesis.When the cyclostationary input passes through a non-stationary system in the presence of non-Gaussian impulsive noise,the theoretical transient performance of the DDSA algorithm has been analyzed in the mean and mean square senses in detail.Numerical simulations demenstrated that the proposed DDSA algorithm has a faster convergence rate than the DSEA algorithm.Moreover,the averaged simulation learning curves coincide with the the-oretical curves predicted by the analytical models verifies the correctness and effectiveness of the theoretical analysis.(2)Aiming at the disadvantage of poor robustness of DRLS algorithm,this thesis proposed a simple and robust diffusion recursive least squares via signed error(DRLS-SE)algorithm.The DRLS-SE algorithm is simple and easy to implement and has strong robustness against impulse noise.Different from the existing theoretical analysis works,most of which are based on the energy conservation relation and only focus on the steady-state characteristics of the DRLS-type algorithms,the first-order mean and second-order mean square transient errors of DDSA algo-rithm are theoretically analyzed and investigated for non-stationary systems and cyclostationary colored input in impulsive noise interference.The numerical simulations not only demenstrated the robustness of the DRLS-SE algorithm against impulsive noise interference,but also proves the correctness and effectiveness of transient theoretical analysis of the DRLS-SE algorithm for the time-varying non-stationary system with the cyclostationary colored input and impulsive interference noise.The above theoretical analysis results can be used to study the impacts on the global transient convergence behavior of the DRLS-type algorithm over network.The two distributed diffusion fusion signed adaptive filtering algorithms mentioned above can be used in different areas.The theoretical transient analysis results for cyclostationary input and impulsive interference noise have very important theoretical significance.Moreover,the analytical models can used to guide the design of the fusion signed adaptive filter in practical applications.