  This paper addresses the problem of real-time detection and tracking of a
non-cooperative target in the challenging scenario with almost no a-priori
information about target birth, death, dynamics and detection probability.
Furthermore, there are false and missing data at an unknown yet low rate in the
measurements. The only information given in advance is about the
target-measurement model and the constraint that there is no more than one
target in the scenario. To solve these challenges, we model the movement of the
target by using a polynomial trajectory function of time (T-FoT), which aims to
estimate the continuous-time trajectory of the target rather than a series of
discrete-time point estimates as is done in most existing filters/trackers.
Data-driven T-FoT initiation and termination strategies are proposed for
identifying the (re-)appearance and disappearance of the target. During the
existence of the target, real target measurements are distinguished from
clutter if the target indeed exists and is detected, in order to update the
T-FoT at each scan for which we design a least-squares estimator. Overall, our
approach is Markov-free, data-driven yet analytical. Simulations using either
linear or nonlinear systems are conducted to demonstrate the effectiveness of
our approach in comparison with the Bayes optimal Bernoulli filters. The
results show that our approach is comparable to the perfectly modeled filters,
even outperforms them in some cases while requiring much less a-priori
information and computing much faster.
