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

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.

arXiv comment16 pages, 8 figures, 5 tables, 80 references; Codes available

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• Multiple Object Tracking: A Literature Review
• Recursive Bayesian Filtering in Circular State Spaces
• On Statistical Methods of Parameter Estimation for Deterministically Chaotic Time-Series
• Smoothing and filtering with a class of outer measures
• Sensitivity And Out-Of-Sample Error in Continuous Time Data Assimilation
• Displacement Data Assimilation
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Cited by in corpus (6)

• DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup
• Graphical Inference in Linear-Gaussian State-Space Models
• Poisson Multi-Bernoulli Mixtures for Sets of Trajectories
• From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation
• From Target Tracking to Targeting Track: A Data-Driven Yet Analytical Approach to Joint Target Detection and Tracking
• From Target Tracking to Targeting Track -- Part II: Regularized Polynomial Trajectory Optimization