Error bounds for joint detection and estimation of a single object with random finite set observation (original) (raw)
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Digital Signal Processing, 2015
Joint detection and estimation (JDE) of a target refers to determining the existence of the target and estimating the state of the target, if the target exists. This paper studies the error bounds for JDE of an unresolved target-group in the presence of clutter and missed detection using the random finite set (RFS) framework. We define a meaningful distance error for JDE of the unresolved target-group by modeling the state as a Bernoulli RFS. We derive the single and multiple sensor bounds on the distance error for an unresolved target-group observation model, which is based on the concept of the continuous individual target number. Maximum a posterior (MAP) detection criteria and unbiased estimation criteria are used in deriving the bounds. Examples 1 and 2 show the variation of the bounds with the probability of detection and clutter density for single and multiple sensors. Example 3 verifies the effectiveness of the bounds by indicating the performance limitations of an unresolved target-group cardinalized probability hypothesis density (UCPHD) filter.
Joint detection and estimation of multiple objects from image observations
2010
Abstract The problem of jointly detecting multiple objects and estimating their states from image observations is formulated in a Bayesian framework by modeling the collection of states as a random finite set. Analytic characterizations of the posterior distribution of this random finite set are derived for various prior distributions under the assumption that the regions of the observation influenced by individual objects do not overlap.
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In state estimation theory, two directions are mainly followed in order to model disturbances and errors. Either uncertainties are modeled as stochastic quantities or they are characterized by their membership to a set. Both approaches have distinct advantages and disadvantages making each one inherently better suited to model different sources of estimation uncertainty. This paper is dedicated to the task of combining stochastic and set-membership estimation methods. A Kalman gain is derived that minimizes the mean squared error in the presence of both stochastic and additional unknown but bounded uncertainties, which are represented by Gaussian random variables and ellipsoidal sets, respectively. As a result, a generalization of the well-known Kalman filtering scheme is attained that reduces to the standard Kalman filter in the absence of set-membership uncertainty and that otherwise becomes the intersection of sets in case of vanishing stochastic uncertainty. The proposed concept also allows to prioritize either the minimization of the stochastic uncertainty or the minimization of the set-membership uncertainty.
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Navigation, mapping, and tracking are state estimation problems relevant to a wide range of applications. These problems have traditionally been formulated using random vectors in stochastic filtering, smoothing, or optimization-based approaches. Alternatively, the problems can be formulated using random finite sets, which offer a more robust solution in poor detection conditions (i.e., low probabilities of detection, and high clutter intensity). This paper mathematically shows that the two estimation frameworks are related, and equivalences can be determined under a set of ideal detection conditions. The findings provide important insights into some of the limitations of each approach. These are validated using simulations with varying detection statistics, along with a real experimental dataset.
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We consider a well defined joint detection and parameter estimation problem. By combining the Baysian formulation of the estimation subproblem with suitable constraints on the detection subproblem we develop optimum one-and two-step test for the joint detection/estimation case. The proposed combined strategies have the very desirable characteristic to allow for the trade-off between detection power and estimation efficiency. Our theoretical developments are then applied to the problems of retrospective changepoint detection and MIMO radar. In the former case we are interested in detecting a change in the statistics of a set of available data and provide an estimate for the time of change, while in the latter in detecting a target and estimating its location. Intense simulations demonstrate that by using the jointly optimum schemes, we can experience significant improvement in estimation quality with small sacrifice in detection power.
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We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian distribution, whose random mean is to be estimated. Forgoing the need for a fusion center, the processing is performed locally and the sensors interact with their neighbors following the consensus+innovations approach. We design the test at the individual sensors such that the performance measures, namely, error probabilities and mean-squared error, do not exceed predefined levels while the average sample number is minimized. After converting the constrained problem to an unconstrained problem and the subsequent reduction to an optimal stopping problem, we solve the latter utilizing dynamic programming. The solution is shown to be characterized by a set of non-linear Bellman equations, parametrized by cost coefficients, which are then determined by linear programming as to fulfill the performance specifications. A numerical example validates the proposed theory.
Set membership approach to the propagation of uncertain geometric information
Proceedings. 1991 IEEE International Conference on Robotics and Automation, 1991
The fusion of geometric information is of great significance in multisensorial systems, mainly in robotics applications, where multiple sensors or mobile sensor systems that change their perspective of the environment capture sparse, and sometimes partial, geometric data. These data contain some level of uncertainty and, in general, some level of redundancy. Probabilistic approaches have been used to solve the problem of fusing this information to obtain the best estimate of a given set of parameters describing a collection of geometric features and its final associated uncertainty. Nevertheless, a probabilistic description of errors is not always available and only a bound on them is known. The setmembership approach postulates that a measurement only allows us to establish an uncertainty region in the space of parameters dcscribing a geometric feature. This approach avoids the general assumptions of unbiased and independent measurements taken by the probabilistic approaches.