Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting (original) (raw)

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

—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 trajec-tory 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.

Smoothing for maneuvering target tracking

2006 9th International Conference on Information Fusion, 2006

Smoothing algorithms for maneuvering target tracking with nonlinear target dynamic and measurement equations are described and investigated. Target motion is represented using a multiple model approach. Techniques based on the interacting multiple model filter (IMMF), hypothesis pruning and maximum a posteriori (MAP) estimation of the maneuvering mode are described. All three techniques are based on the use of the unscented transformation with an augmented state model. A procedure for selecting the sigma points which exploits the partial lineairty of the augmented state model is used. The performances of the algorithms are analysed using a scenario involving a target which undergoes coordinated turn maneuvers. In this scenario, for a sufficiently large number of smoothing lags, the MAP approach and the pruning algorithm have almost equal performance and significanty superior performance to the augmented state IMMF. The MAP approach has the benefit of a reduced computational expense.

A Learning Gaussian Process Approach for Maneuvering Target Tracking and Smoothing

IEEE Transactions on Aerospace and Electronic Systems

Model-based approaches for target tracking and smoothing estimate the infinite number of possible target trajectories using a finite set of models. This paper proposes a data-driven approach that represents the possible target trajectories using a distribution over an infinite number of functions. Recursive Gaussian process and derivative based Gaussian process approaches for target tracking and smoothing are developed, with online training and parameter learning. The performance evaluation over two highly maneuvering scenarios, shows that the proposed approach provides 80% and 62% performance improvement in the position and 49% and 22% in the velocity estimation, respectively, as compared to the best model-based filter.

Novel Approach for Nonlinear Maneuvering Target Tracking Based on Input Estimation

Applied Mechanics and Materials, 2011

Trajectories of aerial and marine vehicles are typically made of a succession of smooth trajectories, linked by abrupt changes, i.e., maneuvers. Notably, modern highly maneuvering targets are capable of very brutal changes in the heading with accelerations up to 15 g. As a result, we model the target behavior using piecewise deterministic Markov models, driven by parameters that jump at unknown times. Over the past years, real-time (or incremental) optimization based smoothing methods have become a popular alternative to nonlinear filters, such as the Extended Kalman Filter (EKF), owing to the successive relinearizations that mitigate the linearization errors that inherently affect the EKF estimates. In the present paper, we propose to combine such methods for tracking the target during non-jumping phases with a probabilistic approach to detect jumps. Our algorithm is shown to compare favorably to the state of the art Interacting Multiple Model (IMM) algorithm, especially in terms of target's velocity estimation, on a set of meaningful and challenging trajectories.

Target tracking by time difference of arrival using recursive smoothing

Signal processing, 2005

The paper presents a simple recursive solution to passive tracking of maneuvering targets using time difference of arrival (TDOA) measurements. Firstly, an iterative Gauss-Newton algorithm is developed for stationary target localization based on a constrained weighted least-squares (CWLS) criterion. The advantages of the CWLS estimate are its inherent stability due to the absence of local minima at infinity and its capability to match the performance of the maximum-likelihood (ML) estimate. To track maneuvering targets, a computationally efficient recursive least-squares (RLS) algorithm is developed, which smoothes successive stationary target location estimates obtained from the ML or CWLS solution using a constant-acceleration motion model. In simulation studies, the proposed recursive tracking algorithm is compared with a Kalman tracking algorithm that estimates the target track directly from the TDOA measurements, and is shown to be capable of outperforming the Kalman tracker. r

Smoothing data association for target trajectory estimation in cluttered environments

EURASIP Journal on Advances in Signal Processing

For heavily cluttered environments with low target detection probabilities, tracking filters may fail to estimate the true number of targets and their trajectories. Smoothing may be needed to refine the estimates based on collected measurements. However, due to uncertainties in target motions, heavy clutter, and low target detection probabilities, the forward prediction and the backward prediction may not be properly matched in the smoothing algorithms, so that the smoothing algorithms may fail to detect the true target trajectories. In this paper, we propose a new smoothing algorithm to overcome such difficulties. This algorithm employs two independent integrated probabilistic data association (IPDA) tracking filters: one running forward in time (fIPDA) and the other running backward in time (bIPDA). The proposed algorithm utilizes bIPDA multi-tracks in each fIPDA path track for fusing through data association to obtain the smoothing innovation in a fixed-lag interval. The smoothing innovation is used to obtain the smoothing data association probabilities which update the target trajectory state and the probability of target existence. The fIPDA tracks are updated after smoothing using the smoothing data association probabilities, which makes the fIPDA path tracks robust for maneuvering target tracking in clutter. This significantly improves the target state estimation accuracy compared to the IPDA. The proposed algorithm is called fixed-lag smoothing data association based on IPDA (FLIPDA-S). A simulation study shows that the proposed algorithm improves false track discrimination performance for maneuvering target tracking in clutter.

Novel Nonlinear Filtering & Prediction Method for Maneuvering Target Tracking

IEEE Transactions on Aerospace and Electronic Systems, 2009

A new nonlinear filtering and prediction (NFP) algorithm with input estimation is proposed for maneuvering target tracking. In the proposed method, the acceleration level is determined by a decision process, where a least squares (LS) estimator plays a major role in detecting target maneuvering within a sliding window. We first illustrate that the optimal solution to minimize the mean squared error (MSE) must consider a trade-off between the bias and error variance. For the application of target tracking, we then derive the MSE of target positions in a closed form by using orthogonal space decompositions. Then we discuss the NFP estimator, and evaluate how well the approach potentially works in the case of a set of given system parameters. Comparing with the traditional unbiased minimum variance filter (UMVF), Kalman filter, and interactive multiple model (IMM) algorithms, numerical results show that the newly proposed NFP method performs comparable or better in all scenarios with significantly less computational requirements.

Estimating the motion of a maneuvering target with time-sequentially sampled imagery

Journal of the Optical Society of America A, 1986

We describe an approach to motion estimation that enables the trajectory of a target undergoing substantial changes in motion between frames to be reconstructed from a single frame of data. The approach is based on the fact that time-sequentially obtained samples from a moving object form a set of noisy measurements of the trajectory. Approximation methods are used to construct a smooth estimate of the trajectory based on these samples. The methods considered here are least squares and smoothing splines. The order in which the spatial points in the field of view are sampled is shown to have a significant effect on how reliably motion is detected and estimated. The effect of object size and velocity on the motion estimate is also considered.

Interacting multiple model forward filtering and backward smoothing for maneuvering target tracking

2009

The Interacting Multiple Model (IMM) estimator has been proven to be effective in tracking agile targets. Smoothing or retrodiction, which uses measurements beyond the current estimation time, provides better estimates of target states. Various methods have been proposed for multiple model smoothing in the literature. In this paper, a new smoothing method, which involves forward filtering followed by backward smoothing while maintaining the fundamental spirit of the IMM, is proposed. The forward filtering is performed using the standard IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion. This backward recursion mimics the IMM estimator in the backward direction, where each mode conditioned smoother uses standard Kalman smoothing recursion. Resulting algorithm provides improved but delayed estimates of target states. Simulation studies are performed to demonstrate the improved performance with a maneuvering target scenario. The comparison with existing methods confirms the improved smoothing accuracy. This improvement results from avoiding the augmented state vector used by other algorithms. In addition, the new technique to account for model switching in smoothing is a key in improving the performance.

Tracking highly maneuverable targets with unknown behavior

Proceedings of The IEEE, 2004

Tracking of highly maneuvering targets with unknown behavior is a difficult problem in sequential state estimation. The performance of predictive-model-based Bayesian state estimators deteriorates quickly when their models are no longer accurate or their process noise is large. A data-driven approach to tracking, the segmenting track identifier (STI), is presented as an algorithm that operates well in environments where the measurement system is well understood but target motion is either or both highly unpredictable or poorly characterized. The STI achieves improved state estimates by the least-squares fitting of a motion model to a segment of data that has been partitioned from the total track such that it represents a single maneuver. Real-world STI tracking performance is demonstrated using sonar data collected from free-swimming fish, where the STI is shown to be effective at tracking highly maneuvering targets while relatively insensitive to its tuning parameters. Additionally, an extension of the STI to allow its use in the most common multiple target and cluttered environment data association frameworks is presented, and an STI-based joint probabilistic data association filter (STIJPDAF) is derived as a specific example. The STIJPDAF is shown by simulation to be effective at tracking a single fish in clutter and through empirical results from video data to be effective at simultaneously tracking multiple free-swimming fish.