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This paper proposes an accurate quantitative segmentation method by analyzing the probability distribution of tracking variance and strict derivation based on the tracking loop theory. The segmentation points are taken as characteristics of phase lock loop (PLL) and frequency lock loop (FLL) performances, and the two factors that cause the performance difference are discriminator gain and filtering coefficient, which denote proportional and integration coefficients, respectively. The filtering coefficients lead to a difference of 2.5 dB-Hz between the FLL and PLL. Moreover, through the analysis of the normalized bandwidth and phase margin, it is found that the integration time and bandwidth need a dynamic balance to achieve the best performance. Finally, the simulation results and real data are in good agreement with the theoretical analysis results. The minimum mean error rate of the deviation between the real data and the theoretical data is only 1.8%. In the proposed method, the influence of external hardware factors on the tracking loop is removed, and the loop design factors are modeled directly. Instead of testing the denoising performance based on the ranging and angle measuring error after location calculation, the filter coefficient is proposed to evaluate the processing performance of the tracking loop objectively and directly at the theoretical level, which proposes a new performance evaluation method at the theoretical level. The results presented in this study provide theoretical support for the design of a new-type tracking loop with enhanced performances.

Adaptive notch filters have been the focus of intense research for more than three decades. Low computational requirements and good performance make them attractive for tracking frequency modulated signals. Despite the extensive literature on adaptive notch filters, algorithm extensions and new models for describing the dynamics of the notch frequency continue to be proposed. In this study, the equivalence between adaptive notch filters using a plain gradient (PG) algorithm and frequency lock loops (FLLs) with exponential filtering is established. FLL theory is then used to analyse the noise performance and signal tracking capabilities of adaptive notch filters. A linear model describing the dynamics of the filter adaptation process is derived and the concepts of loop and Doppler bandwidths are introduced. Criteria based on the loop and Doppler bandwidths are suggested to set the PG adaptation step. Finally, algorithm extensions based on the FLL theory are proposed. Theoretical results are supported by Monte Carlo simulations which show the validity of the analysis performed. [ABSTRACT FROM AUTHOR]

This paper proposes an accurate quantitative segmentation method by analyzing the probability distribution of tracking variance and strict derivation based on the tracking loop theory. The segmentation points are taken as characteristics of phase lock loop (PLL) and frequency lock loop (FLL) performances, and the two factors that cause the performance difference are discriminator gain and filtering coefficient, which denote proportional and integration coefficients, respectively. The filtering coefficients lead to a difference of 2.5 dB-Hz between the FLL and PLL. Moreover, through the analysis of the normalized bandwidth and phase margin, it is found that the integration time and bandwidth need a dynamic balance to achieve the best performance. Finally, the simulation results and real data are in good agreement with the theoretical analysis results. The minimum mean error rate of the deviation between the real data and the theoretical data is only 1.8%. In the proposed method, the influence of external hardware factors on the tracking loop is removed, and the loop design factors are modeled directly. Instead of testing the denoising performance based on the ranging and angle measuring error after location calculation, the filter coefficient is proposed to evaluate the processing performance of the tracking loop objectively and directly at the theoretical level, which proposes a new performance evaluation method at the theoretical level. The results presented in this study provide theoretical support for the design of a new-type tracking loop with enhanced performances. [ABSTRACT FROM AUTHOR]