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T. Li, H. Chen, S. Sun and J. M. Corchado. Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting, IEEE Trans. Automation Science and Engineering, @ IEEE Xplore . Doi: 10.1109/TASE.2018.2882641, arXiv:1708.02196 [stat.AP]
In the above paper, 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, conditioned on a priori model information if any. 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 schedule, (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.
For the sake of generality and reproduction of the results, the first two simulations are taken from an excellent MATLAB-maneuvering-target-tracking toolbox due to Hartikainen, Solin, and Särkkä : one uses linear and non-deterministic target dynamics and linear observation model, while the other utilizes deterministic target dynamics and nonlinear observation model. This toolbox features a large body of popular filters and smooths for discrete-time state space models, including the KF, extended KF (EKF) and unscented KF (UKF) and their corresponding smoothers implemented on the basis of the rauch-tung-striebel (RTS) algorithm. In addition, the interacting multiple model (IMM) approach, as well as its nonlinear extensions based on the mentioned filters and RTS smoothers, has also been simulated. --- The M codes are attached in maneuvering_TLi below.
In contrast, the third simulation is described in a continuous-time system for tracking a non-maneuvering ballistic target in which a particle filter (PF)，EKF and UKF are compared. --- The M codes are attached in freebody_TLi below.
The results as presented in the paper can be reproduced by running the xxx_demo main Scripts in the following attached M codes. The source data for the results presented in the paper are included in the files as well.
This series of work is a part of a project sponsored by Marie Skłodowska-Curie Individual Fellowship (H2020-MSCA-IF-2015)
See also T-Constrained tracking by fitting
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