Search

The authors study an optimal searcher path problem of the following type. A team of searchers tries to find an immobile target on a unit network (in a unit network, all edges are of unit length). The target is located at some point on this network, and its location probability distribution is known to the searcher team. Searchers move along the edges on the network at a constant speed. When one searcher passes the target location, detection happens and the search ends. The objective is to find paths for this team of searchers to minimize the expected search time. A linear binary programming model is built to find the optimal search strategy. Computational experiments are conducted to test the capability of this model, and to analyze how searcher team size and target distribution might affect the search time. Analytical results are given for a special problem scenario: one searcher searching for a uniformly distributed target on a tree. We prove that, any depth-first search path is optimal for a given searcher start point, and the best start point is one of the leaf nodes.

As the traditional imaging dead zone, how to achieve high angular resolution in forward-looking region is always a big challenge in radar imaging field. In recent years, many approaches are proposed to solve this problem. However, most of the proposed forward-looking imaging approaches fail to work in the complex sea-surface situation. In this study, a Bayesian deconvolution method aimed at the sea-surface target is presented, which relies on the convolution model between the target distribution and the antenna pattern of scanning radar. In view of the situation of sea surface, Rayleigh distribution is adopted to describe the statistical property of sea-surface clutter, and lognormal distribution is employed to represent the prior distribution of sea-surface target. Then, the optimisation theory is utilised to obtain the iterative estimated solution. The simulation results are given to verify the superior performance of the presented method.

Abundance estimates of out-migrating sockeye salmon Oncorhynchus nerka smolts are used to prepare preseason forecasts of adult returns and to set escapement goals. Here we describe a method for estimating smolt flux and abundance that uses side-looking sonar. This method more efficiently covers the river cross section and is logistically easier to deploy than up-looking sonar systems. To account for the skewed vertical distribution of smolts, we used a recently developed model for correcting echo integration bias associated with nonuniform target distribution. The correction is based on adjusting the integrated beam pattern for a given distribution of targets relative to the transverse cross section of the beam. We compared the results with estimates derived from video data and modeled the effect of three vertical distributions of smolts and three transducer pitch angles. The model estimated correction factors that ranged from 0.6 to 2.6. Correction factors were greater than 1 (which indicates ne...

We consider the Gibbs sampler as a tool for generating an absolutely continuous probability measure ≥ on Rd. When an appropriate irreducibility condition is satisfied, the Gibbs Markov chain (Xn;n ≥ 0) converges in total variation to its target distribution ≥. Sufficient conditions for geometric convergence have been given by various authors. Here we illustrate, by means of simple examples, how slow the convergence can be. In particular, we show that given a sequence of positive numbers decreasing to zero, say (bn;n ≥ 1), one can construct an absolutely continuous probability measure ≥ on Rd which is such that the total variation distance between ≥ and the distribution of Xn, converges to 0 at a rate slower than that of the sequence (bn;n ≥ 1). This can even be done in such a way that ≥ is the uniform distribution over a bounded connected open subset of Rd. Our results extend to hit-and-run samplers with direction distributions having supports with symmetric gaps. Nous considerons l'echantillonneur de Gibbs comme outil pour engendrer une loi absolument continue sur Rd, disons ≥. Lorsqu'une certaine condition d'irreductibilite est satisfaite, la chaǐne de Markov (Xn;n ≥ 0) associee a l'echantillonneur de Gibbs converge en variation totale vers sa loi cible ≥. Plusieurs auteurs ont donne des conditions suffisantes pour assurer que le taux de convergence soit geometrique. Dans le present travail, nous illustrons, au moyen d'exemples simples, la lenteur avec laquelle cette convergence peut avoir lieu. En particulier, nous montrons que pour toute suite de nombres positifs (bn;n ≥ 1) qui converge vers 0, il existe dans Rd un ensemble ouvert, borne et connexe, disons G, qui est tel que si ≥ est la loi uniforme sur G, et si (Xn;n ≥ 0) est la chaǐne de Markov associee a l'echantillonneur de Gibbs pour ≥, alors la distribution de Xn converge vers 0 plus lentement que la suite (bn;n ≥ 1). Nos resultats se generalised a l'echantillonneur hit-and-run lorsque celui-ci possede une distribution de direction avec un trou symetrique.

This article investigates the problem of planning an optimal layered search for a stationary target. A search is layered if it assigns each point in the search space an integer number of glimpses or looks. General necessary and sufficient conditions and an existence theorem are obtained. The special case in which the initial target distribution is bivariate normal is considered in detail