Showing papers by "John B. Moore published in 1975"
TL;DR: In this paper, the necessary and sufficient conditions for a pth-order observer to observe linear functions of the states of a linear dynamical system were studied, where the conditions are a set of multivariable polynomial equations which must be satisfied for some variable set in order for a Pth-ncder observer to exist.
Abstract: This paper studies the necessary and sufficient conditions for a pth-order observer to observe linear functions of the states of a linear dynamical system. The conditions are a set of multivariable polynomial equations which must be satisfied for some variable set in order for a pth-ncder observer to exist. It is possible to test for the existence of such a variable set in a finite number of steps via decision methods and thereby to construct an observer with the aid of polynomial factorization. To minimize the computational effort, the necessary and sufficient conditions are expressed in terms of the minimum number of variables.
69 citations
01 Jan 1975
TL;DR: In this article, a theory of optimal nonlinear estimation from sampled data signals where the a posteriori probability densities are approximated by Gaussian sums is adapted for application to phase and frequency estimation in high noise.
Abstract: In this paper, a theory of optimal nonlinear estimation from sampled data signals where the a posteriori probability densities are approximated by Gaussian sums is adapted for application to phase and frequency estimation in high noise. The nonlinear estimators (demodulators) require parallel processing of the received signal. In the limit as the number of parallel processors becomes infinite the FM demodulators become optimum in a minimum mean square error sense and the PM demodulators become optimum in some well defined sense. For the clearly suboptimal case of one processor, the demodulators can be readily simplified to the familiar phase-locked loop. On the other hand, for the intermediate case, significant extension of the phaselocked loop threshold is achieved where (say) six parallel processors are involved.
27 citations
TL;DR: Using this approach new estimators are derived which require less computational effort and have less limitations than previous adaptive estimators using parallel processing techniques described in the literature.
13 citations
01 Dec 1975
TL;DR: In this paper, the performance of Bayesian maximum a posteriori (MAP) decision methods for dynamic system identification is investigated, and it is shown that for the true parameter value in a prescribed region the corresponding a posterior-i probability converges exponentially (mean square) to 1.
Abstract: The performance of Bayesian maximum a posteriori (MAP) decision methods for dynamic system identification is investigated. By examining a finite set of a posteriori probabilities a decision is made as to which of several possible regions of the parameter space the true parameter value lies. It is shown that for the true parameter value in a prescribed region the corresponding a posteriori probability converges exponentially (mean square) to 1. The analysis is based on the asymptotic per sample formula for the Kullback information function, which is derived in this paper. We believe that the properties of Bayesian MAP decision methods discussed in this paper make them useful for application in dynamic system identification in conjunction with standard techniques such as the maximum likelihood (ML) method.
8 citations
TL;DR: In this paper, two equivalent sets of necessary and sufficient conditions for the existence of an asymptotically stable partial realization are developed, expressed as multi-variable polynomial equations.
4 citations
TL;DR: In this article, the phase space of a motion is discretized into a space of states and probabilities are assigned to sample paths in the state space so as to coincide with the ones assigned by a finite Markov chain.
Abstract: If the phase space X of a motion $x_{n + 1} = f(x_n )$ is discretized into a space of states $X_1 , \cdots ,X_N $, then probabilities can be assigned to sample paths in the state space so as to coincide with the ones assigned by a finite Markov chain. Theorems 1 and 2 show how the assignment of such probabilities rests on the properties of $f( \cdot )$ and on the construction of the states. Theorems 3 and 4 extend these results to the case in which $x_{n + 1} = f(x_n ,\omega )$, $\omega \in \Omega $ being a random event. Theorems 5 and 6 indicate certain applications relating to stochastic systems in which a decision-maker applies some control action which is fully or partially determined by the observed state of the system.
3 citations
TL;DR: In this article, the computational advantages of processing vector measurement data one component at a time (termed sequential processing) in adaptive estimation schemes involving banks of Kalman filters is investigated.
Abstract: The computational advantages of processing vector measurement data one component at a time (termed sequential processing) in adaptive estimation schemes involving banks of Kalman filters is investigated.
2 citations