In transportation networks, the majority of moving vehicles are route-based or trajectory-scheduled. Taking advantage of such predictive information generally produces more accurate dynamic models and better surveillance performance. This paper is concerned with the route-based dynamic modeling along with the route-aided tracking. First, the evolution of the positions across the route is formulated as a stationary Markov process from the characteristics of the route-based dynamics, which follows that the second- and third-order models of the straight-line route-based motions are constructed. This novel modeling strategy is in reverse to the conventional ones starting from the acceleration and its resultant dynamic models are easy to implement due to the linearity with respect to the system states. Second, an optimal initialization technique for route-aided tracking is proposed by utilizing the stationary process information sufficiently. Furthermore, an extension to the circular route-based dynamic modeling and a combinational modeling structure are also presented. Finally, in the context of aerial surveillance, numerical simulations are provided to show the effectiveness of the proposed dynamic modeling and to verify the theoretical results given in the paper.

Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data.

In this paper, a trajectory shape constraint on target motion is investigated, and the corresponding state estimation method is presented. This type of constraint occurs when only the shape of the target trajectory is known a priori, without any other necessary information to exactly describe the specific trajectory. For example, one may only know that the target moves along a straight line. This prior knowledge of trajectory can be considered as a constraint to improve tracking performance. To describe the shape constraint arising from the straight line assumption, the state vector is augmented by the states at previous time steps. This facilitates the description of the shape constraint using the components of the state vector. Pseudomeasurements are then constructed based on these relationships to incorporate the constraint into an estimation process to improve the performance. The redundancy of the complete set of pseudomeasurements for a given augmented state vector is analyzed, and the minimal set of pseudomeasurements, which describes the constraint exactly, is proposed. The time evolution equation for the augmented state and the measurement equation using the minimal pseudomeasurement set are formulated. A trajectory shape constraint Kalman filter (TSCKF) is then proposed for simultaneous filtering and smoothing. Since both the measurement vector and the state vector are high dimensional, the cubature Kalman filter is used in the proposed TSCKF to deal with the strong nonlinearity in this problem. Monte Carlo simulations illustrate the effectiveness of the proposed TSCKF and the improvement in both filtering and smoothing accuracies by incorporating the trajectory shape constraint.

This study proposes a coupled velocity model (CVM) that establishes the relation between the orientation and velocity using their correlation, avoiding that the existing extended object tracking (EOT) models treat them as two independent quantities. As a result, CVM detects the mismatch between the prior dynamic model and actual motion pattern to correct the filtering gain, and simultaneously becomes a nonlinear and state-coupled model with multiplicative noise. The study considers CVM to design a feasible distributed weighted least squares (WLS) filter. The WLS criterion requires a linear state-space model containing only additive noise about the estimated state. To meet the requirement, we derive such two separate pseudo-linearized models by using the first-order Taylor series expansion. The separation is merely in form, and the estimates of interested states are embedded as parameters into each other’s model, which implies that their interdependency is still preserved in the iterative operation of two linear filters. With the two models, we first propose a centralized WLS filter by converting the measurements from all nodes into a summation form. Then, a distributed consensus scheme, which directly performs an inner iteration on the priors across different nodes, is proposed to incorporate the cross-covariances between nodes. Under the consensus scheme, a distributed WLS filter over a realistic network with “naive” node is developed by proper weighting of the priors and measurements. Finally, the performance of proposed filters in terms of accuracy, robustness, and consistency is testified under different prior situations.

The performance of track initialization methods based on real-time filtering depends heavily on the state estimation accuracy of the track head, which cannot be accurately obtained in many cases. This paper proposes the joint optimization problem of multi-target track initialization, in which the data association and track parameters of targets are obtained simultaneously. To this end, the target trajectory is first modeled as a weighted sum of a set of continuous time basis functions, and the corresponding track initialization is to determine discrete-value decision related to data association and continuous-value estimate related to function weights (i.e., track parameters). Such binary optimization is further transformed into the equivalent quadratic concave optimization of the data association vector by track parameter elimination, while each target definitely corresponds to one of the local minima that satisfy the target existence condition. In implementation, a modified normal rectangular algorithm is presented to obtain such minima, instead of the global minimum gotten by the standard normal rectangular algorithm. Finally, simulation results show the effectiveness of the proposed algorithm.