Adaptive multi-scale singular spectrum analysis for laser micro-Doppler signal denoising at low SNR

To address the issue of low signal-to-noise ratio (SNR) in micro-Doppler signals of space targets during long-range detection, this paper proposes a signal denoising method based on Adaptive Multi-scale Singular Spectrum Analysis (AMSSA). AMSSA constructs a multi-scale iterative mechanism with dynamic coarse-to-fine window length shrinkage and a joint Energy Contribution Rate and Minimum Description Length (ECR-MDL) separation criterion, achieving adaptive and robust separation of signal and noise. To evaluate the efficacy of AMSSA, accurate estimation of the parameters is subsequently accomplished using a standard nonlinear least squares fit based on the high-quality reconstructed spectrograms. Simulation results demonstrate that at the low SNR of −5 dB, AMSSA achieves a significant SNR gain of 9.38 dB, outperforming traditional single-stage SSA and fixed-window iterative SSA by margins of 9.06 and 5.39 dB. The extraction of the spin frequency, precession frequency and precession angle transitions from being “completely unusable” to “high-precision estimation” with minimum relative errors of 9.88%, 2.57% and 11.19%. Experimental data further validate the denoising performance of the proposed method, yielding an output SNR improvement of 8.14 dB. The minimum relative errors for the three parameters reach 15.32%, 3.36% and 15.24%, realizing highly accurate estimation. This study provides an effective technical approach for the micro-Doppler signal denoising at low SNR, thereby offering reliable data support for subsequent parameter estimation.