Variable frequency-based multi-frame coherent track-before-detect method for weak tones in passive sonar

Passive detection for weak tones remains a challenging topic. Tonal frequency trajectory can be extracted by combining the pre-processing based on the multi-frame coherent integration with track-before-detect (TBD) method. However, complex target maneuvers can lead to intricate variations in tonal frequency, limiting the coherent processing gain. To address this issue, a variable frequency-based multi-frame coherent track-before-detect method is proposed. The evolution of tonal frequency and phase across time frames is modeled using polynomial functions. We propose a state-space dynamical system model for the time-evolving tonal signal, where the state variables are defined as the tonal amplitude and the coefficients of the polynomial used to represent the tonal frequency. The optimal model order is then analyzed based on minimizing the coherent gain loss. Furthermore, an improved particle filtering algorithm is employed to implement the established TBD model. We design a data-adaptive sequential importance sampling method. By optimizing particle sampling based on high transition probabilities, a majority of particles can be distributed in high-likelihood regions. This enables high adaptability when the tonal frequency undergoes complex variations. Both simulation and processing results from SwellEx-96 experiment demonstrate that the proposed method can improve detection performance and reduce frequency estimation error.