Under the common state space model for tracking a maneuvering target, the tracker needs to adapt its state transition model timely to match the target maneuver, which is usually carried out by finding the best one from a bank of candidate Markov models or employing all of them simultaneously but assigning different probabilities. Both methods suffer from time delay for confirming the target maneuver. To avoid these problems, we model the target motion by a continuous time trajectory function and the tracking problem is formulated as an optimization problem with the goal of finding the trajectory function that best fits the observation over a sliding time window. The trajectory function can be used for smoothing, filtering and even prediction. The approach is particularly applicable to a class of target motion patterns such as passenger aircraft, where little prior statistical information is available on the target dynamics or even the sensor observation except the linguistic information that “the target moves in a smooth trajectory” (as being called smoothly maneuvering target). Simulation is provided to demonstrate the supremacy of our approach with comparison to a number of classical Markov-Bayes approaches, based on Hartikainen et al.'s example.