Long-Time Coherent Integration Enhancement of Moving Target Line Spectrum Based on Matched Frequency-Trajectory Estimation

Abstract

Line spectra radiated by moving targets are important features for passive sonar detection and classification. Relative motion between a target and the receiver induces time-varying Doppler shifts in the received line spectra, causing phase misalignment during long-time Fourier integration and resulting in spectral broadening, energy dispersion and coherent integration loss. To address this problem, this paper proposes a matched frequency-trajectory estimation method for long-time coherent integration enhancement (MFT-LTCIE). The method transforms the received signal into its analytic representation, extracts the narrowband component around the target line spectrum and partitions the signal into short-time segments. For each segment, matching responses are computed over a candidate frequency grid, and a maximum-matching criterion is used to estimate the segment-wise frequency trajectory. The estimated trajectory is interpolated onto the sample-time axis and used to construct a phase-compensation function relative to a reference frequency. Trajectory-guided phase compensation restores phase coherence, and a full-duration FFT of the compensated signal yields an enhanced coherent integration spectrum. Simulations show that MFT-LTCIE suppresses Doppler-induced spectral broadening and maintains sharp spectral peaks under different signal-to-noise ratios and target speeds. Experimental ship-radiated noise data further demonstrate its ability to track line-spectrum variations and refocus dispersed energy.