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This paper considers tracking of extended objects using the measurements of down-range and cross-range extent. This type of measurement can be naturally and intuitively expressed in terms of support functions. Based on support functions, we propose a general approach to model smooth shapes of objects. Another approach based on extended Gaussian image is proposed to model nonsmooth shapes such as polygons. Compared with existing approaches, a larger range of object shapes can be modeled by the proposed approaches, which have concise mathematical forms and favorable properties. Specifically for elliptical and rectangular objects, our approaches can be implemented easily utilizing simple parametric representations without the need to assume that the major axis of the object is parallel to its velocity vector. Based on these models, a Bayesian algorithm for extended object tracking is easily obtained, where the kinematic state and object extension can be jointly estimated effectively. The benefits of the proposed modeling approaches are illustrated by simulation results.

The pseudo measurement method is a main approach to equality-constrained state estimation due to its simplicity. It is, however, not popular due to possible numerical problems and increased computational complexity. The work presented here further develops the pseudo measurement method. To avoid numerical problems resulting from singular measurement noise when a matrix inverse is used, the Moore-Penrose (MP) inverse is used instead. Also, to reduce the computational load without performance loss and to simplify the analysis of this type of estimation problem, two sequential forms are obtained. They differ only in the processing order of the physical measurement and the pseudo measurement (i.e., the equality constraint). Although form 1 is the same as some existing results, form 2 is new. This motivates the discussion of processing order for this type of estimation problem, especially in the extension to the nonlinear case. It is found that under certain conditions, the use of the pseudo measurement for filtering is redundant. This differs in effect from update by the physically error-free measurement. However, if there exists model mismatch, update by the pseudo measurement is necessary and helpful. Supporting numerical examples are provided.

A multiple-model algorithm for maneuvering target tracking is proposed. It is referred to as a second-order Markov chain (SOMC)-based interacting multiple-model (SIMM) algorithm. The target maneuver process is modeled by a SOMC to incorporate more information. SIMM adopts a merging strategy similar to that of the interacting multiple-model (IMM) algorithm, except that the one-step model transition probabilities are updated based on the SOMC. A scheme is proposed to design the transition probabilities of the SOMC for target tracking. The performance of the proposed SIMM algorithm is evaluated via several scenarios for maneuvering target tracking. Simulation results demonstrate the effectiveness of SIMM compared with IMM, the second-order IMM (IMM2) algorithm, and the likely-model set (LMS) algorithm. It is shown that SIMM performs about the same as IMM2 but requires only n filters versus n2 filters in IMM2 for n models. The effectiveness and efficiency of combining SIMM and LMS for state estimation are also demonstrated in the simulation.

A new approach to route planning for joint search and track missions by coordinated unmanned aerial vehicles (UAVs) is presented. The cornerstone is a novel objective function that integrates naturally and coherently the conflicting objectives of target detection, target tracking, and vehicle survivability into a single scalar index for path optimization. This objective function is the value of information gained by the mission on average in terms of a summation, where the number of terms reflects the number of targets detected while how large each term is reflects how well each detected target is tracked. The UAV following the path that maximizes this objective function is expected to gain the most valuable information by detecting the most important targets and tracking them during the most critical times. Although many optimization algorithms exist, we use a modified particle swarm optimization algorithm along with our proposed objective function to determine which trajectory is the best on the average at detecting and tracking targets. For simplicity, perfect communication with centralized fusion is assumed and the problems of false alarm, data association, and model mismatch are not considered. For analysis, we provide several simplified examples along with a more realistic simulation. Simulation results show that by adjusting the parameters of the objective function, solutions can be optimized according to the desired tradeoff between the conflicting objectives of detecting new targets and tracking previously detected targets. Our approach can also be used to update plans in real time by incorporating the information obtained up to the time (and then reusing our approach).

The work presented here deals with estimation fusion of smoothed state estimates. Two problems of fusion for smoothing are considered: fixed point and fixed interval. Optimal linear fusion rules in the sense of the optimal weighted least squares (OWLS) and the linear minimum mean-square error (LMMSE) are obtained. These rules are in recursive forms convenient for implementation. We also propose a more practical method for real-time smoothing, which in essence is fusing smoothed and filtered estimates. Illustrative numerical results are provided to verify the performance and credibility of the fusion rules.

Model-set design is one of the most important topics of the multiple-model (MM) approach, which is the state of the art for many estimation, control, and modeling problems. The work presented here proposes a general systematic model-set design method in the parameter space of a system based on number theoretic (NT) methods for design of statistical experiments. The system is characterized by uncertain parameters that describe the mode space, and the models used in the model set are designed to approximate the mode by minimizing distribution mismatch. Two types of F-uniform model sets that perform well are proposed: one by the NT methods, the other according to an F-centered discrepancy. In order to improve the performance of the F-uniform model sets further, two types of expected mode augmentation (EMA) are applied. Simulation examples are given and compared with results from the Monte-Carlo method to demonstrate the designs and their performance.

The problem of distributed fusion for estimation when the cross-correlation of errors of local estimates is unavailable is addressed. We discuss a general estimation fusion approach for this problem-generalized convex combination (GCC) - and classify various GCC fusion approaches in three categories. We develop three GCC fusion algorithms for the problem under consideration. First, based on a set-theoretic formulation of the problem, we propose a relaxed Chebyshev center covariance intersection (RCC-CI) algorithm to fuse the local estimates. Second, based on an information-theoretic criterion, we develop a fast covariance intersection (IT-FCI) algorithm with weights in a closed form. The proposed RCC-CI and IT-FCI algorithms are characterized by both the local estimates and the mean-square error (MSE) matrices being taken into account. Third, to fuse incoherent local estimates, we propose a fault-tolerant GCC fusion algorithm by introducing an adaptive parameter, which can obtain robust fusion and the degree of robustness varies with that of incoherency between estimates to be fused.

For single-target multisensor systems, two fusion methods are presented for distributed recursive state estimation of dynamic systems without knowledge of noise covariances. The estimator at every local sensor embeds the dynamics and the forgetting factor into the recursive least squares (RLS) method to remedy the lack of knowledge of noise statistics, developed before as the extended forgetting factor recursive least squares (EFRLS) estimator. It is proved that the two fusion methods are equivalent to the centralized EFRLS that uses all measurements from local sensors directly and their good performance is shown by simulation examples.

Theoretical design of a tracker with respect to the so-called target perceivability is presented. Basic rules and analytic formulas for the determination of tracker parameters are presented for making better tracking decisions (i.e., track initiation, confirmation, and termination) toward enhancing tracking performance. Simulation results are provided that support the theoretical design and demonstrate the enhancement of the tracker in tracking performance.

An approach to detection and diagnosis of multiple failures in a dynamic system is proposed. It is based on the interacting multiple-model (IMM) estimation algorithm, which is one of the most cost-effective adaptive estimation techniques for systems involving structural as well as parametric changes. The proposed approach provides an integrated framework for fault detection, diagnosis, and state estimation. It is able to detect and isolate multiple faults substantially more quickly and more reliably than many existing approaches. Its superiority is illustrated in two aircraft examples for single and double faults of both sensors and actuators, in the forms of "total", "partial", and simultaneous failures. Both deterministic and random fault scenarios are designed and used for testing and comparing the performance fairly. Some new performance indices are presented. The robustness of the proposed approach to the design of model transition probabilities, fault modeling errors, and the uncertainties of noise statistics are also evaluated.