A unified method based on pseudo-spectrum for track-before-detect of targets with motion model uncertainty

Abstract

Track-before-detect (TBD) of weak targets with motion model uncertainty is of significance in practical applications, since targets may experience various motions. In this paper, a unified TBD framework is presented for multiframe detection of weak targets with constant velocity (CV) and coordinated turn (CT) motions. This enables detection and parameter estimation of weak CV and CT targets in a same state space. Firstly, according to common CT model in Cartesian coordinates, the state equation of the common model suitable for matched filtering based TBD is derived. In this equation, the speed, turn rate and initial heading are used to determine target motion. Secondly, a heading-speed-turn rate matched filter based on pseudo-spectrum in mixed coordinates is proposed for weak CT or CV target detection in sensor coordinates. The data search before multiframe integration is conducted according to the derived model in x-y plane by matching the constant target speed, turn rate and initial heading. Then, the echo energy is integrated based on the pseudo-spectrum in polar coordinates. This eliminates performance loss caused by model mismatch in sensor coordinates, and facilitates well-maintained target envelope. Thirdly, to deal with the problem that the target motion model may jump at any time during the processing batch, a joint motion parameter and jumping time matching based TBD in mixed coordinates is presented. The jumping time is considered as a matching parameter for multiframe integration in addition to speed, turn rate and heading. This method can supply complete information of the maneuvering target motion in the processing batch. Finally, simulations are conducted to demonstrate the effectiveness of the proposed methods.