Underwater Propeller Target Feature Extraction Based on Robust Micro-Doppler Frequency Shift Estimation

The micro-Doppler frequency shift generated by the rotation of propellers is not only higher than the Doppler frequency shift caused by the target translation but also contains information about the size and rotational speed， making it an important feature for underwater target detection and identification. However， the estimation of the instantaneous frequency of underwater propellers is affected by the intersection points， line target spectrum， and noise， leading to numerous outliers that severely impede subsequent feature extraction. To address this issue， this paper first establishes a short-pulse point-line mixture model for underwater propeller targets and then proposes a robust multi-frame joint estimation method. The method employs a decision-directed approach to eliminate samples with significant deviations in each upper envelope of instantaneous frequency estimation， subsequently leverages its sparsity to reconstruct the instantaneous frequency at the corresponding time instances， and finally accomplishes target feature extraction based on the accurate time-frequency ridge path of each component. Simulation results demonstrate that when the input signal-to-noise ratio （SNR） is above 4 dB， the relative errors （RE） of the proposed algorithm in estimating the maximum frequency shift and rotational frequency are below 5% and 2%， respectively. As the rotational speed increases， the effective operational range of the algorithm can be extended to SNRs above -2 dB， and it successfully performs feature extraction for propellers with 2 to 5 blades. In contrast， the JMDFE algorithm， which also relies on instantaneous frequency estimation， achieves relative errors of approximately 25% and 4%， only under conditions where the SNR is above 6 dB and propellers have 2 blades. Real-world experimental results on measured data show that the REs of the maximum frequency shift estimation of the two rotational components are 3.60% and 3.97%， respectively， while the relative error of the rotational frequency estimation is 0.79%.