Tracking a time-varying number of targets is a challenging
dynamic state estimation problem whose complexity is intensified
under low signal-to-noise ratio (SNR) or high clutter conditions.
This is important, for example, when tracking
multiple, closely spaced targets moving in the same direction such as a
convoy of low observable vehicles moving through a forest or multiple
targets moving in a crisscross pattern. The SNR in
these applications is usually low as the reflected signals from
the targets are weak or the noise level is very high.
An effective approach for detecting and tracking a single target
under low SNR conditions is the track-before-detect filter (TBDF)
that uses unthresholded measurements. However, the TBDF has only been used to
track a small fixed number of targets at low SNR.
This work proposes a new multiple target TBDF approach to track a
dynamically varying number of targets under the recursive Bayesian framework.
For a given maximum number of
targets, the state estimates are obtained by estimating the joint
multiple target posterior probability density function under all possible
existence combinations. The estimation of the corresponding target existence
combination probabilities and the target existence probabilities are also
derived. A feasible sequential Monte Carlo (SMC) based implementation
algorithm is proposed. The approximation accuracy of the SMC
method with a reduced number of particles is improved by an efficient
proposal density function that partitions the multiple target space into a
single target space.
The proposed multiple target TBDF method is extended to track targets in sea
clutter using highly time-varying radar measurements. A generalized
likelihood function for closely spaced multiple targets in compound Gaussian
sea clutter is derived together with the maximum likelihood estimate of
the model parameters using an iterative fixed point algorithm.
The TBDF performance is improved by proposing a computationally feasible
method to estimate the space-time covariance matrix of rapidly-varying sea
clutter. The method applies the Kronecker product approximation to the
covariance matrix and uses particle filtering to solve the resulting dynamic
state space model formulation.