A Pseudo-Spectrum Approach for Weak Target Detection and Tracking

Conventional velocity-filtering-based track-before-detect (VF-TBD) methods integrate the energy of a cell in a frame with that of the cell closest to the predicted target position in the last frame of the processing batch, assuming a certain target velocity. However, the target may not exactly be on the quantized cell and its echo envelope may occupy multiple adjacent cells. This often leads to significant energy loss and echo envelope degradation. In this paper, a novel VF-TBD method based on pseudo-spectrum (PS-VF-TBD) is presented to address this problem. For every cell, a pseudo-spectrum is constructed around the predicted position according to the assumed velocity using a truncated point spread function. Samples of the pseudo-spectrum on the cells that are located in the truncated spread area are added onto the last frame of the processing batch to integrate the target energy within multiple cells. Due to the use of the point spread model and the accurate sampling of the predicted spectrum, energy loss can be mitigated and the echo envelope is well maintained. This approach simultaneously maximizes the signal-to-noise ratio (SNR) gain and enables improved parameter estimation utilizing the envelope characteristics. The procedure for pseudo-spectrum construction and multiframe accumulation is derived in detail and the output SNR is analyzed theoretically. It is found that the proposed PS-VF-TBD can achieve an SNR gain greater than that by the conventional VF-TBD method. To deal with a target with unknown velocity, a bank of pseudo-spectrum-based velocity filters is proposed. The signal gain loss resulting from velocity mismatch is investigated and the $\mu$-width of the envelope in the velocity domain is analyzed. Finally, a method for improved position and velocity estimation is presented. Simulation results demonstrate the superiority of the proposed method in terms of SNR gain, detection probability, and estimation accuracy at the expense of increased computational complexity.