  We present a continuous time state estimation framework that unifies
traditionally individual tasks of smoothing, tracking, and forecasting (STF),
for a class of targets subject to smooth motion processes, e.g., the target
moves with nearly constant acceleration or affected by insignificant noises.
Fundamentally different from the conventional Markov transition formulation,
the state process is modeled by a continuous trajectory function of time (FoT)
and the STF problem is formulated as an online data fitting problem with the
goal of finding the trajectory FoT that best fits the observations in a sliding
time-window. Then, the state of the target, whether the past (namely,
smoothing), the current (filtering) or the near-future (forecasting), can be
inferred from the FoT. Our framework releases stringent statistical modeling of
the target motion in real time, and is applicable to a broad range of real
world targets of significance such as passenger aircraft and ships which move
on scheduled, (segmented) smooth paths but little statistical knowledge is
given about their real time movement and even about the sensors. In addition,
the proposed STF framework inherits the advantages of data fitting for
accommodating arbitrary sensor revisit time, target maneuvering and missed
detection. The proposed method is compared with state of the art estimators in
scenarios of either maneuvering or non-maneuvering target.
