Research On Iterative Parameter Estimation Based On Matched Filter Bank Theory

Harmonic frequency and direction of arrival(DOA) estimation are typical parameters play an important role in numerous fields, such as speech signal processing, mechanical fault diagnosis, radar, communications, biomedicine, seismic exploration and etc. In practical application, the requirements of high performance of parameter estimation in accuracy, resolution and computationa l efficiency are inevitable research challenges. As a result of the existence of random noises in the observed data sequences, the probability density function(PDF) and the power spectral density(PSD) are adopted as typical parameter estimation methods. To achieve accurate parameter estimate, the modern PSD estimation methods with high spectral resolution become the primary choice. Among them, the method based on the matched filter bank(MAFI) theory achieves high spectral resolution by suppressing random noises, and attracts various research attentions without signal modeling. Based on MAFI theory, iterative algorithms are studied for matched filters design and characteristic parameters estimation, in order to improve the filter spectral resolution, parameter estimation accuracy, and the computational efficiency.The main contents of this dissertation are organized as follows:(1) To achieve high resolution on limited data samples, higher dimension covariance matrix is needed, while suffering from the matr ix inverse and rank-deficient matrix problem. Based on the theory of convex quadratic programming(CQP), we propose two iterative algorithms(Conjugate Gradient method for Convex Quadratic Problem, CG-CQP) and(New Iterative Algorithm for Rank-Deficient matrix, NIARD) to calculate the optimal matched filters. The simplified CQP reformulation and the nonlinear gradient function are used to avoid the matrix inversion and matrix decomposition. Experiment results show that, for the same solution precision, the iteration times of the new algorithms is about 1/25~1/8 of the existing iterative method, the computing consumption is about 4%~18% of the latter. Higher computational efficiency is achieved.(2) Because of the lack of priori knowledge of spectral peak sea rching grids division, the signal mismatch problem(SMP) is common on sparse grids, with the damped spectral peak and the biased parameter estimation. Traditional methods are based on spectrogram, but with the limited application in multiple component signals. Firstly, PSD spectrum based on canonical correlation analysis(CCA) method is proposed, which has higher spectral peaks and can be used in the coarse search process to save the computation. Then, we present an iterative algorithm DSSP(Dichotomous Search for Spectral Peaks) via dichotomous search method in fine search process, where PSD spectrum with higher resolution is applied to achieve accurate parameter estimation. Experiment results show that, the damped spectral peak is remitted, and accurate estimation is achieved. The computing consumption is about 1/50~1/40 of the traditional methods. While, the DSSP algorithm based on the magnitude squared coherent spectral is applied to pick out the weak components from the strong random noises.(3) Higher estimation accuracy can be achieved on dense grids, while suffering by the heavy computational burden and poor real-time performance. Firstly, a scalar cost function is developed on typical MAFI PSD spectrum, where the frequency grids division and related spectral peak search are avoided. The harmonic frequencies are estimated by the location of each local minimum of the cost function. Then, to remit the computational burden on dense frequency grids, we present an iterative frequency estimation algorithm SITER(Single local minimum ITERative search), and adaptive initial frequency selection strategies are presented for single and multiple component signals respectively. The experiment results indicate that, with the same accuracy, the computing consumption is about 2.56% of the traditional methods. Higher accuracy and lower computation are obtained.(4) Based on data interception by sliding window and based on the stationary assumption, the MAFI PSD spectrum is extended to time-frequency analysis. Firstly, we derive the time-variant MAFI PSD spectrum, where high resolution is achieved and the cross-terms are suppressed as well. Then, we propose a T-SITER(Time-variant SITER) algorithm based on time-variant MAFI PSD spectrum, to continuously estimate the time-variant frequencies on sampled data with high precision. Experiment results show that, with high parameter estimation accuracy, the computing consumption is only 0.067% of the traditional spectral peak search methods. With the T-SITER algorithm, the time-variant frequencies of the sampled data are tracked with high accuracy and high efficiency.