| With the rapid development of modern information technology,adaptive filtering,which is an important part of signal processing,has also developed rapidly.The traditional least mean square algorithm,normalized subband adaptive filtering algorithm have been widely used,and these algorithms are proposed under the assumption that the input signal is accurately observable and only the output signal contains noise.In practice,the input signal is usually contaminated with noisy signals due to instrument errors,sampling errors,and human errors,and the adaptive algorithms proposed above will be affected by them and produce biased estimates,and the convergence performance will deteriorate.To solve the above problems,the total least squares method can realize unbiased estimation under the presence of noise in both input and output signals.When the output signal contains impulsive noise,the convergence of the total least squares algorithm deteriorates sharply,so robust algorithm improvements are required.In this paper,based on the study of this algorithm,a relevant improved TLS adaptive algorithm is proposed for several different practical problems,the theoretical performance analysis is performed,and the superior performance of the algorithm is demonstrated in relevant applications(system identification,echo cancellation,and power system frequency estimation).The specific work of this paper can be summarized as follows:1.For the errors-in-variables model under correlated inputs,traditional subband adaptive filtering algorithms produce biased estimates,this paper introduces the total least squares estimation into the subband adaptive filter and proposes the total least squares normalized subband adaptive filtering algorithm that can achieve unbiased estimates.In addition,the mean stability and steady-state mean square performance of the algorithm are analyzed in detail,and the steady-state mean square deviation values are derived.2.For the extreme deterioration of the total least squares algorithm when the output signal in the errors-in-variables is disturbed with impulsive noise,this paper introduces the hyperbolic secant function and proposes a robust hyperbolic secant total least squares algorithm.Meanwhile,to further enhance the efficiency of the algorithm,a robust variable step size strategy is proposed.In addition,the mean stability of the algorithm is analyzed.3.In distributed adaptive networks,the convergence behavior of the diffusion gradient descent total least squares algorithm deteriorates sharply when the output signal is disturbed by impact noise.To address this problem,a robust diffusion total least mean M-estimate(DTLMM)algorithm is proposed in combination with the M-estimate function.The algorithm significantly enhances the robustness of the diffusion gradient descent total least squares algorithm in suppressing impulsive noise.Meanwhile,to further enhance the efficiency of the algorithm,a robust diffusion variable step size strategy is proposed.The mean value condition and steady-state mean square behavior of the DTLMM algorithm are derived in detail under impulsive noise conditions.Finally,the DTLMM algorithm is extended to the complex domain,and the diffusion augmented complex TLMM algorithm is derived,and the frequency estimation performance of the proposed algorithm is verified in the measured unbalanced three-phase voltage signal.Finally,the convergence performance of the TLS-type adaptive algorithms proposed in this thesis and the accuracy of the algorithmic rational performance verification are demonstrated by simulation experiments. |
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