Linfeng Xu

Numerous human activities and object motions are intrinsically motivated by a goal or guided towards a destination. Exploring and exploiting such valuable intent information is expected to lead to considerably improved modeling and inference. This paper delves into a class of more practical destination constrained (DC) systems, where the arrival time is unavailable in advance, and addresses two critical issues: DC dynamics modeling and estimation of DC state and arrival time. First, a generalized DC dynamic model is constructed by conforming a relaxed dynamics to the destination constraint. This modeling is not only easy to implement in practice but also produces a congruous DC dynamic model that has superior properties, e.g., applicable to various arrival time, whether known or uncertain. Second, a connection between the proposed DC dynamic model and the pseudo-observation-based bridge distribution model is established. For a linear Gaussian system with a linear destination constraint, these two models are mathematically equivalent despite their different modeling strategies and resultant model forms. Third, two DC state estimation algorithms are developed by incorporating the spatial information of the destination into state prediction. The two algorithms differ in computational efficiency and estimation capability. In particular, one of them can estimate more accurately the state and the arrival time simultaneously. Finally, for tracking of adversarial destination guided targets, numerical simulations are provided to validate the effectiveness of the proposed modeling and estimation algorithms.

This paper addresses the filtering problem of a reentry vehicle (RV) using a passive sensor onboard an aircraft. The passive sensor measures the azimuth and elevation angles of the RV. We use the continuous-discrete filtering (CDF) paradigm that combines the continuous-time dynamic model with the discrete-time measurement model. Our approach benefits from a highly accurate RV dynamic model formulated as an Itô stochastic differential equation, which takes into account spherical-Earth gravity, atmospheric drag, and stochastic process noise. The RV's state is defined by its 3D Cartesian position, velocity, and a random drag parameter. For the prediction step, we present two distinct variants of the continuous extended Kalman filter, namely the CEKF and CEKF2, while for the measurement update step, we employ a cubature Kalman filter (CKF). These combined CDF algorithms are named the CEKF-CKF and CEKF2-CKF. These two filters are compared with an existing approximate discrete filter called the EKF-CKF. To assess their performance, we conduct Monte Carlo simulations to compute the root mean square errors for position, velocity, and the drag parameter. Additionally, we assess the filter's consistency by calculating the average normalized estimation error squared and the average normalized innovation squared. The simulation results show that the CEKF-CKF outperforms the CEKF2-CKF in the two scenarios examined. At higher process noise levels, the CEKF-CKF has a higher covariance consistency than the EKF-CKF.

This work aims to design a distributed extended object tracking (EOT) system over a realistic network, where both the extent and kinematics are required to retain consensus within the entire network. To this end, we resort to the multiplicative error model (MEM) that allows the extent parameters of perpendicular axis-symmetric objects to have individual uncertainty. To incorporate the MEM into the information filter (IF) style, we use the moment-matching technique to derive two pair linear models with only additive noise. The separation is merely in a fashion, and the cross-correlation between states is preserved as parameters in each other's model. As a result, the closed-form expressions are transferred into an alternating iteration of two linear IFs. With the two models, a centralized IF is proposed wherein the measurements are converted into a summation of innovation parts. Later, under a sensor network with the communication nodes and sensor nodes, we present two distributed IFs through the consensus on information and consensus on measurement schemes, respectively. Moreover, we prove the estimation errors of the proposed filter are exponentially bounded in the mean square. The benefits are testified by numerical experiments in comparison to state-of-the-art filters in literature.

This article presents the state estimation problem of nonlinear dynamic stochastic systems with temporal constraints, depicting the nonlinear interval relationship between states at two successive time instants for the first time. To this end, a hybrid sampling-based particle filter (HSPF) with temporal constraints is proposed by integrating the acceptance–rejection sampling, the repeat sampling, and the sample-to-sample sampling via online optimization, where a decision criterion of improving sampling efficiency is designed to determine whether or not the repeat sampling is activated and a simple sequential quadratic programming (SSQP) is derived to mitigate the computational burden of particle optimizations. Next, compared with filters without introducing temporal constraints, we find that the number of effective particles increases, and the differential entropy of the probability density function as a measure of uncertainty is small, implying that fusing more extra information will help to improve the accuracy of estimates. Finally, two simulation scenarios verify the performance of the proposed filter with temporal constraints.

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.

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.

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.

The paper presents the problem of multi-target tracking with heavy-tailed process and measurement noises. Such heavy-tailed noises can reflect unmodeled anomalies, sudden disturbance, or temporary sensor failures. A robust Students t-based labeled multi-Bernoulli (RSTLMB) filter is designed for such systems, where the state predicted probability density and measurement likelihood function of individual targets are modeled as Students t distributions. A closed form recursion of the RSTLMB filter to jointly estimate the target state and the parameters of the Students t distribution is derived in the variational Bayesian framework. Simulations on multi-target tracking with heavy tailed process and measurement noises demonstrate the effectiveness and superiority of the proposed RSTLMB filter.

Constrained filters, through utilising the prior state constraint information, are designed to obtain more accurate state estimates in applications, and most of them deal with the estimation problem of systems with deterministic constraints. In practice, complex environmental disturbance, incomplete information or uncooperative behaviour often brings out uncertainties of the constraints. This paper tackles the filtering problem of dynamic systems subject to the stochastic linear equality constraints expressed by random weighted basis matrices. The corresponding constrained dynamic model is constructed first and the linear-minimum-mean-square-error filter is derived based on the orthogonality principle. Due to the effect of constraint randomness, the resultant filter encounters the problem of nonlinear stochastic calculation of random parameters, which is solved by the Taylor-based and the UT-based schemes, respectively, and the computational complexity as well as the tractability of both schemes are analysed. Finally, a simulation study on a road-constrained vehicle tracking demonstrates that the proposed filter has better performance than the classical estimation projection method in terms of estimation accuracy and computational complexity.