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.

Cooperative localization in wireless sensor network (WSN) using biased received signal strength (RSS) measurements is investigated in this letter. In the existing work on cooperative RSS localization, measurements of sensor nodes (including both target-anchor and target-target measurements) are generally assumed bias-free. However, in practice, they may be subject to biases, which directly affect localization accuracy. As a result, the existing localization methods are not applicable any more. In this letter, RSS observation biases are considered as the extra parameters to be estimated as well as locations of target nodes. To overcome the nonconvexity of the maximum likelihood (ML) estimator, semidefinite programming (SDP) is applied with $l_{1}$ and $l_{2}$ norms, respectively. Then, the locations of multiple target nodes and observation biases are simultaneously estimated through convex optimization. Numerical examples demonstrate the performance superiority of the proposed methods compared to the existing bias-free SDP methods for wireless cooperative localization.

Received signal strength (RSS) based techniques are promising for location estimation due to low cost and easy implementation. The RSS measurements can be used to determine a receiver's location given the positions of multiple emitters. Also, the RSS measurements at receivers with known positions can be used to determine the location of an emitter. This paper investigates both 3D receiver navigation and source localization using RSS measurements. In practice, sensor mea9 surements are often biased due to design problems or other effects. However, almost all existing methods deal with bias11 free cases. In contrast, we focus on biased cases. For both receiver navigation and source localization, we propose united- RSS (URSS) and differential-RSS (DRSS) approaches, where URSS estimates the location and sensor bias together while DRSS estimates the location by eliminating the effect of bias. They are based on semidefinite programming (SDP) and constrained least squares (CLS), respectively. The proposed methods avoid the nonconvexity in the maximum likelihood (ML) method. Numerical examples verify the necessity for sensor registration in RSS based location estimation and show better performance of the proposed methods.

The Kalman filter has successful applications in many fields. The applicability of the standard Kalman filter critically hinges on the accurate prior knowledge of all the system model parameters. However, in practical applications, it can be difficult or unrealistic to obtain these parameters, in which case it is a common practice to employ some pre-determined alternatives for the unknown model parameters. This letter investigates the case of unknown initial state priors by assessing how their pre-determined alternatives affect the performance of the Kalman filter. The ranking of three types of mean squared errors is established. It is found that the definiteness of the initial state prior deviation is critical, which determine the ranking of the three types of mean squared errors. Such results provide guideline on the choice of the pre-determined initial state prior. Numerical examples are provided to validate the results.

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.

The problem of distributed fusion of Gaussian mixture models (GMMs) provided by the local multiple model (MM) estimators is addressed in this paper. Taking GMMs instead of combined Gaussian assumed probability density functions (pdfs) as the output of local MM estimators can retain more detailed (or internal) information of local estimations, but the accompanying challenge is how to perform the fusion of GMMs. For this problem, a distributed fusion framework of GMMs under the minimum forward Kullback-Leibler (KL) divergence sum criterion is proposed first. Then because the KL divergence between GMMs is not analytically tractable, two suboptimal distributed fusion algorithms are further developed within this framework. These two fusion algorithms all have closed forms. Numerical examples verify their effectiveness in both computational efficiency and estimation accuracy.