Research On Parameter Estimation And Tracking Method In Array Signal Processing

Parameter estimation and tracking is one of the most important research subjects in array signal processing. It is widely used in many civil and military fields, such as radar, sonar, wireless communication, seismic exploration, radio astronomy, biomedical engineering, and so on. This subject involves two parts: parameter estimation and parameter tracking. The basic theoretical framework and algorithms about array signal parameter estimation have been quite mature after decades of development. However, when the attention are paid to the practical application in engineering, higher requirements for the robustness, estimation accuracy and computational complexity of array signal parameter estimation algorithms are emphasized. As for array signal parameter tracking, there are still many problems to be solved currently. This thesis investigates several critical issues in array signal parameter estimation and tracking, including source number estimation in the presence of white Gaussian noise and colored Gaussian noise, DOA(Direction of Arrival) estimation of coherent signals, joint estimation of DOA and Doppler frequency of coherent/same direction signals, DOA tracking and Doppler frequency tracking. Focusing on the above issues, we have proposed a series of effective algorithms, and have obtained some meaningful results. The main work and results of this thesis are summarized as follows:First, an Otsu method based on pseudo covariance matrix is proposed to estimate the source number in the presence of complex noise. The pseudo covariance matrix composed of delay correlation of array output signals is immune to white Gaussian noise and colored Gaussian noise under certain conditions. In addition, the array's effective aperture is improved by using the time correlation between arrays, and then the differences between signal singular values and noise singular values, which are got from the singular value decomposition of pseudo covariance matrix, are also improved. At last, by utilizing Otsu method to classify the signal singular values and noise singular values, the probability of successful estimation of source number is further improved.Second, for the DOA estimation of coherent signals, an eigenspace-based MUSIC(Multiple Signal Classification) algorithm for spatial smoothing estimation is presented. The coherent signals are processed through spatial smoothing first, and then the eigenspace-based MUSIC algorithm is applied to estimate the DOA effectively, making full use of the signal and noise subspaces information. Moreover, the proposed method has no effect on the DOA estimation when the uncorrelated signals exist, and it also can be used to estimate the power of source signals effectively. Compared with the conventional spatial smoothing technique and the modified MUSIC algorithm for DOA estimation of coherent signals, the proposed method has lower SNR(Signal Noise Ratio) threshold and higher resolution and estimation accuracy.Third, out of different considerations, two algorithms are investigated for joint DOAs and Doppler frequencies estimation. 1) Considering that the estimation performance of the two-dimensional MUSIC(2D-MUSIC) algorithm deteriorates under non-ideal conditions, such as low SNR and small snapshots, a modified 2D-MUSIC algorithm via the signal subspace projection method is proposed. A signal subspace projection method weighted by the reciprocal of signals power is presented, and then it is combined with the 2D-MUSIC for spatial spectrum synthesis. Using the information of both signal subspace and noise subspace, the resolution performance of the proposed algorithm in joint DOAs and Doppler frequencies estimation for multiple targets under non-ideal conditions is improved. 2) Considering the joint DOAs and Doppler frequencies estimation of coherent signals and/or same-direction signals, a modified 2D-MUSIC algorithm based on conjugate data reconstruction is proposed. At first, establish the generalized array signal model, which involves the information of DOAs and Doppler frequencies, and reconstruct the array covariance matrix through conjugate data rearrangement, to make it applicable to this joint estimation problem. Then this algorithm is further modified by the foregoing signal subspace projection method in 1) to obtain better resolution performance. Besides, the proposed algorithms can also estimate the signals power effectively, and the estimated parameters can be paired automatically.Fourth, considering the high computational complexity of the maximum likelihood method, an improved algorithm based on SQP(Sequential Quadratic Programming) is presented to jointly estimate DOAs and Doppler frequencies. The maximum likelihood method is a Bayesian optimal estimation method in the condition of known white noise, it has much better performance than the eigen-subspace based algorithm in estimating parameters like DOA and Doppler frequency, and it can process coherent signals directly. However, nonlinear multidimensional optimization is necessary when using the maximum likelihood method, and the traditional grid searching method needs extensive calculation. For this consideration, a global optimal SQP method with local superlinear convergence property is proposed to solve the optimization problem of the maximum likelihood method. At last, numerical simulation results verify the effectiveness of the proposed method.Fifth, considering the DOA tracking problem of moving targets, an adaptive updating algorithm with a variable forgetting factor for the covariance matrix of samples is proposed. The time-varying forgetting factor can adjust its value adaptively according to the change rate of DOA, so as to adaptively adjust the weights of current and historical sample data in the covariance matrix during the update. In order to avoid the repeated eigenvalue decomposition or singular value decomposition, and be able to track the coherent signals, the updated covariance matrix is used for DOA estimation via maximum likelihood method directly. Considering the extensive computation due to the maximum likelihood method, artificial bee colony algorithm and SQP are employed to solve the optimization problem, thus, the computational complexity is reduced, and the optimization procedure is sped up, thereby ensuring the real-time tracking performance.Sixth, considering the Doppler frequency tracking problem of radar signals, a tracking algorithm based on dynamic compressed sensing is proposed. The time-varying sparse signal model of radar signals is established first. Then construct the redundant dictionary of current moment according to the priori sparse location information extracted from the sparse vector of last moment, obtain the distribution probability of the nonzero elements in the sparse vector of current moment, and establish the sparse probabilistic model of Doppler frequency. Finally, the sparse signal of current moment is reconstructed by solving a weighted l1-norm minimization problem to obtain the nonzero element location, thus, the dynamic real-time tracking of Doppler frequency is achieved. Simulation results clarify the validity of the proposed algorithm.