Sensor management using an active sensing approach

Kreucher, Chris; Kastella, Keith; Hero, Alfred O.

doi:10.1016/j.sigpro.2004.11.004

Cited by 148 publications

(119 citation statements)

References 33 publications

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“…When λ tends to 1, by l'Hospital's rule, H λ converges to the Shannon entropy that will thus be denoted by continuity H 1 = H. The Rényi entropy is widely used, not only in physics (e.g. statistical mechanics, physics of turbulence, cosmology, see [10,11,12] and references therein), but in various other areas such as in signal processing (time scale analysis, decision problems, machine learning, see [4,13,14,15] and references therein), or image processing (image matching, image registration see [16,17] and references therein). …”

Section: The Rényi Entropy Uncertainty Relationmentioning

confidence: 99%

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

Zozor

Vignat

2007

Physica A: Statistical Mechanics and its Applications

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In this paper we revisit the Bialynicki-Birula & Mycielski uncertainty principle [1] and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Rényi entropies. We recall that in both Shannon and Rényi cases, and for a given dimension n, the only case of equality occurs for Gaussian random vectors. We show that as n grows, however, the bound is also asymptotically attained in the cases of n-dimensional Student-t and Student-r distributions. A complete analytical study is performed in a special case of a Student-t distribution. We also show numerically that this effect exists for the particular case of a n-dimensional Cauchy variable, whatever the Rényi entropy considered, extending the results of Abe [2] and illustrating the analytical asymptotic study of the student-t case. In the Student-r case, we show numerically that the same behavior occurs for uniformly distributed vectors. These particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a "Gaussianization" of the vector when the dimension increases.

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Section: The Rényi Entropy Uncertainty Relationmentioning

confidence: 99%

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

Zozor

Vignat

2007

Physica A: Statistical Mechanics and its Applications

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“…The joint PMF of a particular sensor may be obtained by means of estimation algorithms (e.g., [27,30]), or by learning algorithms using wavelets or mixtures of Gaussians [16,35]. In this paper, we adopt the method presented in [36,37], in which the PMF is learned from data and represented by a Bayesian network (BN) model.…”

Section: Bayesian Network Approach To Sensor Modelingmentioning

confidence: 99%

“…Several informationtheoretic functions have been proposed for this purpose. Cross entropy was used in [28] to solve a multisensor-multitarget assignment problem, and in [29,30] to manage agile sensors with Gaussian models for target detection and classification. Entropy and the Mahalanobis distance measure were used in [27] for sensor selection in ad-hoc sensor networks.…”

Section: Measurement Information Valuementioning

confidence: 99%

“…As shown in this subsection, the expected entropy reduction (EER) can be used to represent the value of information, V, in terms of the joint PMF P(y i , M i ) known from the sensor model (Section 3.2). Other information-theoretic functions can be similarly applied, as shown in Section 4.2, to construct information roadmaps for other sensor applications, e.g., [27,28,30]. Entropy reduction is formulated in terms of conditional entropy, which can be used to represent the uncertainty in a discrete and random variable Y, given the value of another discrete and random variable Z , based on their joint and conditional PMFs,…”

Section: Measurement Information Valuementioning

confidence: 99%

“…While robot path planning typically aims to optimize a deterministic additive function such as Eucledian distance, sensor planning aims to optimize a stochastic sensing objective that is not necessarily additive. Another basic difficulty in sensor planning is that, although the measurements ultimately determine the sensor performance, they cannot be factored into the planning problem because the sensor's position must be planned prior to obtaining the sensor's measurements [27][28][29][30][31]. Recently, several authors have shown that this difficulty can be overcome by an approach known as information-driven sensor planning, which uses information theoretic functions to estimate the measurements' value prior to deploying the sensor [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Information Roadmap Method for Robotic Sensor Path Planning

Zhang

Ferrari

Qian

2009

J Intell Robot Syst

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A new probabilistic roadmap method is presented for planning the path of a robotic sensor deployed in order to classify multiple fixed targets located in an obstacle-populated workspace. Existing roadmap methods have been successful at planning a robot path for the purpose of moving from an initial to a final configuration in a workspace by a minimum distance. But they are not directly applicable to robots whose primary objective is to gather target information with an on-board sensor. In this paper, a novel information roadmap method is developed in which obstacles, targets, sensor's platform and field-of-view are represented as closed and bounded subsets of an Euclidean workspace. The information roadmap is sampled from a normalized information theoretic function that favors samples with a high expected value of information in configuration space. The method is applied to a landmine classification problem to plan the path of a robotic ground-penetrating radar, based on prior remote measurements and other geospatial data. Experiments show that paths obtained from the information roadmap exhibit a classification efficiency several times higher than that of existing search strategies. Also, the information roadmap can be used to deploy non-overpass capable robots that must avoid targets as well as obstacles.

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