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The Sequential Probability Ratio Test (SPRT) is a classical detector for problems with an unfixed sample size. Though it is optimal under some conditions, SPRT can be directly used only for a binary hypothesis with exactly known distributions. In this paper, sequential detection problem with an uncertain hypothesis distribution is considered, in which the uncertain distribution is formulated in a...
Detection with multiple distributions is considered. Rather than formulating the problem with multiple hypotheses, we formulate the problem in a binary hypothesis testing framework by a multiple model approach. Three classes of the Multi-Model Detection (MMD) problems are considered: simplex, compound, and mixture. Three concepts of optimality are given for these three problems, including Uniformly...
For highly nonlinear problems, the linear minimum mean-square error (LMMSE) estimation using a nonlinearly converted measurement can outperform the one using the original measurement. For a function space of measurement conversions, every function in the space can be represented as a linear combination of a basis of the space. Then the LMMSE estimator using a vector with its entries forming a basis...
A fault detection, identification, estimation and state estimation (FDIESE) problem involves joint decision and estimation (JDE). Decision contains detection and identification, while estimation is for fault severeness and system state. Both detection and identification are highly coupled with estimation and a fault is identified after detection. To solve this problem, an approach named nested joint...
For the over-the-horizon radar (OTHR) based target tracking, the reflecting height of the ionosphere, which reflects radar signals, is important. Existing methods assume that this height is exactly known a priori. In practice, however, we can only determine its range, not its specific value. To circumvent this problem, we propose to use a multiple-model approach in which each model corresponds to...
This paper studies and formulates the problem of distributed filtering with a diffusion strategy for state estimation of a dynamic system by using observations from sensors in a network. The sensor-nodes have estimation ability and work in a collaborative manner. The information transmission across the network abides by the diffusion strategy that each node communicates only with its neighbors. First,...
This paper proposes a new approach for constrained multiple model (MM) maximum a posteriori (MAP) estimation through the expectation-maximization (EM) method by using our previously developed constrained sequential list Viterbi algorithm (CSLVA). The approach is general and applicable for any type of constraints provided they are verifiable. Specific algorithms for implementation are designed, and...
This paper deals with the problem of estimating the state of a discrete-time stochastic linear system based on data collected from multiple sensors with limited communication resources. For the cases of transmitting measurements and local state estimates, respectively, we design data-driven communication schemes based on a normalized innovation vector and corresponding fusion rules in the (approximate)...
This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent....
Our newly proposed approach to extended object tracking (EOT) using extension deformation is simple and effective. This approach assumes that the extension of an object is deformed from an ellipsoidal reference extension, which unfortunately restricts its use for complex extensions. To overcome this weakness, this paper proposes that the current object extension be modeled as deformed from the one...
Evaluating the performance of multi-target tracking with respect to tracks rather than unlabeled estimated points is important and challenging. Existing approaches assume exact knowledge of the ground truth. However, this is far from the reality. This paper proposes a method to deal with the case of unknown ground truth by measuring the difference between mock tracks and the assumed targets in the...
Emission source localization and sensor registration using received signal strength (RSS) measurements is investigated. Previous studies for RSS localization assume that the sensors receiving signals are bias free, which is not the case in practice. This issue is taken into consideration in this paper for the localization problem. To avoid non-convexity of the global optimization problem for the traditional...
This paper presents an approach to fault detection, identification, and state estimation (FDISE) for a dynamic system with abrupt total or partial failures. FDISE includes both decision and estimation and they are highly coupled. Decision includes fault detection and identification (FDI), while estimation is for failure magnitude and system state. Correct FDI benefits estimation and accurate estimation...
This paper deals with some fundamental problems of the constrained dynamic system, especially where dynamics and constraint are not congruous. First, we introduce a concept of compatibility of the system dynamics and constraint. It divides all constrained systems into three classes: incompatible (0% compatible), (partially) compatible, and congruous (100% compatible). We argue convincingly that the...
Performance evaluation and ranking based on multiple performance metrics are required in many fields. These metrics have commonality since they evaluate the same thing despite in different aspects. If the performance is deemed good in all metrics, the overall performance is indeed good. In view of this, making full use of this commonality should be good for ranking and evaluation. Voting theory deals...
Multi-target tracking (MTT) has been an important and challenging area of research in the past several decades. A number of algorithms for MTT have been proposed and related performance evaluation (PE) is also gaining more attention. However, these PE methods assume exact knowledge of the ground truth, which is far from the reality. In this paper we deal with the PE of MTT without knowing ground truth...
This paper presents a new approach based on extension deformation for extended object tracking (EOT). In this approach, the extension of an object is assumed to be deformed from a reference extension by moving some control points in the latter to those in the former. That is, the properties of an extension can be fully captured by the control points, given the reference extension. Thus, modeling and...
For extended-object/group-target tracking (EOT/GTT), the random-matrix approach is appealing. This approach assumes that the measurements are linear in the state and in the noise with its covariance being a random matrix to represent the object extension or the target group. In practice, however, the measurements are nonlinear in the state and noise. This paper proposes a random-matrix approach for...
This paper presents a follow-up and improvement of our previous work on conflict detection and resolution (CDR) for unmanned aircraft “sense-and-avoid” (SA) applications. More specifically, we propose an extension of our previous model predictive control formulation and algorithm that takes into account costs incurred by possible deviation from the desired destination so that the optimized solution...
Performance evaluation of tracking methods includes methods of relative and absolute performance. Absolute tracking performance is the robust end result presented to a user which determines the product solution for real world analysis. However, to achieve robust performance, the tracking method is subject to the sensor data, filtering performance, and associated models, which requires relative performance...
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