Pseudo-Spectrum Based Speed Square Filter for Track-Before-Detect in Range-Doppler Domain

Track-before-detect (TBD) in range-Doppler plane is of significance for Doppler radars. Existing methods suffer from approximate motion models in range-Doppler plane and inefficiency of energy integration. In this paper, an accurate evolution equation of target range and Doppler with respect to time is presented and a new pseudo-spectrum based TBD method is proposed to effectively integrate target energy and detect weak target in range-Doppler domain. According to common constant velocity motion in Cartesian coordinates, the evolution of range and Doppler is correctly described by a nonlinear function of target range-Doppler and time invariant speed square. Consequently, a novel TBD method, which matches target speed instead of velocity in each direction, is proposed. Each cell in range-Doppler plane is predicted to the last frame according to the time evolution equation. Then, a pseudo-spectrum is constructed around the predicted position according to a point spread function. Multiframe accumulation is achieved by adding the sampling values of the pseudo-spectrum over several cells to the last frame. To match the unknown target speed square, a bank of pseudo-spectrum based speed square filter (PS-SSF) is presented. The target output envelopes in both range-Doppler and speed square domains are derived theoretically and a feasible parameter estimation method is proposed. Numerical results demonstrate that the proposed PS-SSF method can not only achieve effective weak target detection in range-Doppler domain, but also produce precise parameter estimates of range and Doppler, as well as target speed.