Estimation in hidden Markov models via efficient importance sampling

Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a multi-dimensional parameter. We propose an importance sampling formula for efficient simulation in this context. Our approach consists of constructing a locally asymptotically normal (LAN) family of probability distributions around the default resampling rule and then minimizing the asymptotic variance within the LAN family. The solution of this minimization problem characterizes the asymptotically optimal resampling scheme, which is given by a tilting formula. The implementation of the tilting formula is facilitated by solving a Poisson equation. A few numerical examples are given to demonstrate the efficiency of the proposed importance sampling scheme.Comment: Published at http://dx.doi.org/10.3150/07--BEJ5163 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Development of a bio-inspired vision system for mobile micro-robots

In this paper, we present a new bio-inspired vision system for mobile micro-robots. The processing method takes inspiration from vision of locusts in detecting the fast approaching objects. Research suggested that locusts use wide field visual neuron called the lobula giant movement detector to respond to imminent collisions. We employed the locusts' vision mechanism to motion control of a mobile robot. The selected image processing method is implemented on a developed extension module using a low-cost and fast ARM processor. The vision module is placed on top of a micro-robot to control its trajectory and to avoid obstacles. The observed results from several performed experiments demonstrated that the developed extension module and the inspired vision system are feasible to employ as a vision module for obstacle avoidance and motion control