  Trajectory estimation of maneuvering objects is applied in numerous tasks
like navigation, path planning and visual tracking. Many previous works get
impressive results in the strictly controlled condition with accurate prior
statistics and dedicated dynamic model for certain object. But in challenging
conditions without dedicated dynamic model and precise prior statistics, the
performance of these methods significantly declines. To solve the problem, a
dynamic model called the power-limited steering model (PLS) is proposed to
describe the motion of non-cooperative object. It is a natural combination of
instantaneous power and instantaneous angular velocity, which relies on the
nonlinearity instead of the state switching probability to achieve switching of
states. And the renormalization group is introduced to compensate the nonlinear
effect of perturbation in PLS model. For robust and efficient trajectory
estimation, an adaptive trajectory estimation (AdaTE) algorithm is proposed. By
updating the statistics and truncation time online, it corrects the estimation
error caused by biased prior statistics and observation drift, while reducing
the computational complexity lower than O(n). The experiment of trajectory
estimation demonstrates the convergence of AdaTE, and the better robust to the
biased prior statistics and the observation drift compared with EKF, UKF and
sparse MAP. Other experiments demonstrate through slight modification, AdaTE
can also be applied to local navigation in random obstacle environment, and
trajectory optimization in visual tracking.
