Showing papers by "John B. Moore published in 1999"

Resolution invariant surfaces for panoramic vision systems

Abstract: A family of axially symmetric mirror shapes are proposed for panoramic imaging. These shapes keep the resolution in the image invariant to changes in elevation in the scene. In other words, this family of shapes achieves solid angle pixel density invariance. An analysis of range finding using two coaxial axially symmetric resolution invariant mirrors in a coaxial pair is presented. The resolution invariance property of these mirrors mean that when the image captured is unwarped the resultant image will not suffer from variable image quality. This problem is present in unwarped images captured with any mirror shape not designed for resolution invariance. The resolution invariance of these mirrors is especially important in the case of stereo panoramic mirrors where one view of the scene is captured within the other and thus will have lower resolution. It is necessary to clearly identify two was of an object to undertake range-finding. The proposed mirror shapes will be useful for mobile robotics and machine vision. Other applications areas such as visual sensing for control of traffic lights at street intersections could be considered.

Spectrum estimation of interleaved pulse trains

Abstract: We consider signals consisting of a finite though unknown number of periodic time-interleaved pulse trains. For such signals, we present a novel approach for determining both the number of pulse trains present and the frequency of each pulse train. Our approach requires only the time of arrival data of each pulse. It is robust to noisy time of arrival data and missing pulses and, above all, is very computationally efficient. If N is the number of pulses being processed, the computation required is of the order of N log N.

Linear-quadratic optimal control with integral quadratic constraints

Abstract: We derive closed-form solutions for the linear-quadratic (LQ) optimal control problem subject to integral quadratic constraints. The optimal control is a non-linear function of the current state and the initial state. Furthermore, the optimal control is easily calculated by solving an unconstrained LQ control problem together with an optimal parameter selection problem. Gradient formulae for the cost functional of the optimal parameter selection problem is derived. Application to minimax problems is given. The method is illustrated in a numerical example.

Finite-dimensional risk-sensitive filters and smoothers for discrete-time nonlinear systems

Abstract: Finite-dimensional optimal risk-sensitive filters and smoothers are obtained for discrete-time nonlinear systems by adjusting the standard exponential of a quadratic risk-sensitive cost index to one involving the plant nonlinearity. It is seen that these filters and smoothers are the same as those for a fictitious linear plant with the exponential of squared estimation error as the corresponding risk-sensitive cost index. Such finite-dimensional filters do not exist for nonlinear systems in the case of minimum variance filtering and control.

On the estimation of interleaved pulse train phases

Abstract: Some signals are transmitted as periodic pulse trains where information is in the times of arrival of pulses. A number of pulse trains arriving over the same time interval are said to be interleaved. We propose a method for estimating the phase and fine-tuning previously obtained frequency estimates of a known number of interleaved pulse trains using an extended Kalman filter, where discontinuities in the signal model are first smoothed. The advantage of this method is its computational efficiency.

An instrumental variable approach for identification of hidden Markov models

Abstract: In this paper we derive recursive filters for both the online and off-line identification of hidden Markov models (HMMs). The identification is achieved by taking conditional mean estimates of certain summation non-linear functions of the states and measurements and using these values to estimate the parameters of the system. This instrumental variable method we propose offers the possibility of improved parameter estimation when the state of the HMM is correlated with the system noise.

A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

Abstract: This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

Multiple objective risk-sensitive control and stochastic differential games

Abstract: In this paper, we study a (minimizing) multiple-objective risk-sensitive control problem, and show the relationship between this problem, a certain stochastic differential game, and what may be regarded as a multiple-objective deterministic differential game. The limiting deterministic differential game is one in which the opponent seeks to maximize the most vulnerable member of a set of given cost functionals, while the original controller seeks to minimize the worst 'damage' that the opponent can do over this set. This forms a natural framework in which many applications can be studied.

Risk-sensitive filters for identification of hidden Markov models

Abstract: We derive risk-sensitive filters which can be used for both online and off-line identification of hidden Markov models. The identification is achieved by taking risk-sensitive conditional mean estimates of the number of state transitions (jumps) and occupation times and then using these values to estimate the parameters of the system. Furthermore, we demonstrate that the risk-sensitive filters approach the existing asymptotically optimal (risk-neutral) filters in the limit of the risk-sensitive parameter.