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.