Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting

TL;DR

This paper introduces a continuous-time state estimation framework that unifies smoothing, tracking, and forecasting by fitting a continuous trajectory function to observations, enabling real-time, flexible target motion analysis without strict statistical assumptions.

Contribution

It proposes a novel continuous trajectory fitting approach for STF tasks, relaxing traditional statistical models and handling arbitrary sensor revisit times and target maneuvers.

Findings

Outperforms traditional estimators in maneuvering scenarios

Handles arbitrary sensor revisit times effectively

Applicable to real-world targets like aircraft and ships

Abstract

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.