| The adaptive filters constitute an important part of the statistical signal processing. As the development of the investigation in this field, the theory and the techniques of adaptive signal processing become more perfect. Aiming at the problems of adaptive estimation of signal parameters in different practical environments, this dissertation provides several efficient and robust algorithms and verifies them by computer simulations. The main contents of this dissertation can be summarized as follows:·Aiming at the problems of low computational efficiency and long-time numerical unstability in RLS algorithms, a fast surface search (FSS) algorithm used for adaptive FIR filter is studied. In this algorithm, data symbol vector and unit vector with periodic shift structure are defined as search surface in order to predigest the form of fast gain vector. The least estimation error is achieved by updating the direction vector's weight factor, and then highly efficient recursive algorithm for computing the filter factor is given. The computational complexity of this algorithm is lower than the fast recursive least square (FRLS) algorithm. The convergence of the algorithm is analyzed theoretically, and the tracking performance and the estimation error of the algorithm are evaluated via simulations.·The XS-RTLS and E-RTLS algorithm are developed for fast iteratively computing the TLS solution for FIR system whose input and output signal have Gaussian noise. In the XS-RTLS algorithm, augmenting observation data symbol is used for constructing search direction vector. By modifying the direction vector's weight factor, generalized Rayleigh quotation of a least square cost function is minimized and the system parameter vector is updated. The global convergence of the new algorithm is studied. In time-invariant system and time-variant system, the performances of the relevant algorithms are compared via simulations. The steady-state error and search range are considered in E-RTLS algorithm. On the basis of FSS and XS-RTLS algorithms, augmenting observation data symbol and cycle-switch unit vectors are used for constructing special search direction vector. The estimation error and tracking performance are verified via simulations.·Because the input and output signals of infinite impulse response system are corrupted by a steady noise, adaptiveⅡR filter total least Lp-norm (IIR-TLMP) algorithm is presented. In this algorithm, a steady noise of input and output signal is considered, an augmented data vector and corresponding system parameter vector are constructed. By minimizing the Lp-norm of Rayleigh quotation constructed by two generalized vectors, the solution with least Lp-norm is gained. In this algorithm instantaneous gradient is used to simplify computation. The influence of primary parameters such as character index and step factor to the performance of TLMP algorithm is evaluated via simulations, and the performances of TLMP algorithm and LMP algorithm are compared.·In order to improve the low convergence speed ofⅡR-TLMP algorithm, recursive total least lp norm (ⅡR-RTLP) algorithm of adaptiveⅡR filter is presented. In this algorithm, recursive method is used to solve the least lp-norm of Rayleigh quotation. Matrix inversion lemma and power iteration method are used to recursive update the factors of adaptive filter. System estimation error and convergence speed ofⅡR-RTLP and TLMP algorithm are tested by simulations.·Aiming at the conflict between the convergence rate and stable state mean square error of fixed step LMS algorithm, using the information of instantaneous error square and instantaneous error correlation, integrating the advantage of VSS algorithm and RVSS algorithm, a robust variable step adaptive algorithm is given. The stable performance, and tracking ability are analyzed theoretically. The simulation result has shown that this algorithm has faster convergence rate and lower stable state square error.This paper is supported by National Natural Science Foundation of China.
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