Abstruct -This paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single m o h g observation platform. The process is inherently nonlinear and exbibits unusual obsenability properties that are geometrydependent. A maximum likelihood estimate W E ) of the target motion analysis solution is developed and its performance analyzed. A comparison is drawn between the lMLE and two previously reported methods, a nonlinear modified-instrumental variable estimate (MW) and the pseudolinear estimate (PIX). Both the MIV and PLE are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the -%LE. The limits on performance that can be expected from processing bearing data are detailed. Specifically, for long range-to-baseline geometries, approximate expressions for the Cramer-Rao bound are derived. Extension of the results to the practical filters approximately predicts numerically observed behavior.For less restrictive geometries, bounds are presented. Incorporation of a target speed constraint on the MLE results in a transition to a lower dimensional problem as noise level and range increases. Monte Carlo experimental results are presented and the improvements realized by the MLE techniques are evident.
An efficient algorithm that can properly identify the targets to immunize or quarantine for preventing an epidemic in a population without knowing the global structural information is of obvious importance. Typically, a population is characterized by its community structure and the heterogeneity in the weak ties among nodes bridging over communities. We propose and study an effective algorithm that searches for bridge hubs, which are bridge nodes with a larger number of weak ties, as immunizing targets based on the idea of referencing to an expanding friendship circle as a self-avoiding walk proceeds. Applying the algorithm to simulated networks and empirical networks constructed from social network data of five US universities, we show that the algorithm is more effective than other existing local algorithms for a given immunization coverage, with a reduced final epidemic ratio, lower peak prevalence and fewer nodes that need to be visited before identifying the target nodes. The effectiveness stems from the breaking up of community networks by successful searches on target nodes with more weak ties. The effectiveness remains robust even when errors exist in the structure of the networks.
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