Theoretical Analysis And Algorithm Studies On Resolution And Parameter Estimation For The Time-frequency Closed Multi-signal

Resolution and parameters estimation on the time-frequency domain overlapped signals appears in many applications, such as radar, wireless communications, acoustic, seismic waves, and so on. From about the 1950s, this problem attracted more and more attention among foreign scholars. The various methods to the time-frequency domain overlapped signals resolution and parameters esti-mation have been reported, and the theoretical analysis of the performance of estimators and detector were studied. With the development of digital signal processing technology, and the increase of track-ing and positioning demand, the precision of estimation and detection on time-frequency overlapped signal will be more higher.Firstly, we conducted a theoretical analysis on this problem. In the second chapter, we derive the maximum likelihood estimation and the CRLB on multiple signal parameters. As can been seen from the conclusions, the multiple pulse signal estimation affected not only by SNR, but also by the signal waveform, particularly when the pulse signals overlapped in the time domain. Due to the orthogonality of frequency components, the frequency estimate for the multiple signal is equal to the single-frequency signal. In the third chapter, we get the detector based on GLRT and derive the false alarm probabilityPFA and the detect probability PD.In the fourth chapter, we propose two methods to solve multi-pulses resolution and get parame-ters estimation. The first is the interior point method which achieve the time-closed pulse resolution by minimise cost function. Because the algorithm tend to converge to local minima, we consider combining it with the traditional methods in future work. Subsequently, we propose a Taylor series expansion based CLEAN algorithm which resolve the time-closed pulse and get parameter estimation without knowing the number of pulse in advance. In addition, this algorithm can estimate decimal sampling delay for non-ideal sampling pulse.In the fifth chapter, we focused on multi-frequency resolution and parameters estimation. We preprocess the received signal by using the polynomial fitting method, then resolving frequency-closed signals by combining with MUSIC and ESPRIT algorithms. In order to choice the fitting order, we propose an improved differential generalized likelihood ratio test (IDGLRT). Comparing the GLRT fit, the IDGLRT fitting has a slight error in the low SNR regional and the significant improvement in parameters estimation in the high SNR regional.In the final section, we summarize our main contributions and results, and discuss directions of future research.