Maximum likelihood track-before-detect with fluctuating target amplitude

An important problem in target tracking is the detection and tracking of targets in very low signal-to-noise ratio (SNR) environments. In the past, several approaches have been used, including maximum likelihood. The major novelty of this work is the incorporation of a model for fluctuating target amplitude into the maximum likelihood approach for tracking of constant velocity targets. Coupled with a realistic sensor model, this allows the exploitation of signal correlation between resolution cells in the same frame, and also from one frame to the next. The fluctuating amplitude model is a first order model to reflect the inter-frame correlation. The amplitude estimates are obtained using a Kalman filter, from which the likelihood function is derived. A numerical maximization technique avoids problems previously encountered in “velocity filtering” approaches due to mismatch between assumed and actual target velocity, at the cost of additional computation. The Cramer-Rao lower bound (CRLB) is derived for a constant, known amplitude case. Estimation errors are close to this CRLB even when the amplitude is unknown. Results show track detection performance for unknown signal amplitude is nearly the same as that obtained when the correct signal model is used