Optimal segmentation of random processes

Segmentation of a nonstationary process consists in assuming piecewise stationarity and in detecting the instants of change. We consider the case where all the data is available at the same time and perform a global segmentation instead of a sequential procedure. We build a change process and define arbitrarily its prior distribution. This allows us to propose the MAP estimate as well as some minimum contrast estimate as a solution. One of the interests of the method is its ability to give the best solution, according to the resolution level required by the user, that is, to the prior distribution chosen. The method can address a wide class of parametric and nonparametric models. Simulations and applications to real data are proposed     

Optimal automatic control of multistage production processes

Today's high-tech industries produce complicated products involving many processing steps. The usual approach of modeling and controlling each of these steps in isolation is re-evaluated. This work develops a data model of synchronized observations collected from several stages of a multistage manufacturing process, and proposes an across-stage automatic control scheme for adjusting nonstationary process drifts. The proposed controller applies dynamic programming tools to optimize multiple goals specified for individual process stages and possible mismatch between stages. Several examples and simulation studies demonstrate that the proposed method is a valuable tool for improving semiconductor manufacturing quality.     

Fast identification of autoregressive signals from noisy observations

The purpose of this brief is to derive, from the previously developed least-squares (LS) based method, a faster convergent approach to identification of noisy autoregressive (AR) stochastic signals. The feature of the new algorithm is that in its bias correction procedure, it makes use of more autocovariance samples to estimate the variance of the additive corrupting noise which determines the noise-induced bias in the LS estimates of the AR parameters. Since more accurate estimates of this corrupting noise variance can be attained at earlier stages of the iterative process, the proposed algorithm can achieve a faster rate of convergence. Simulation results are included that illustrate the good performances of the proposed algorithm.     

Optimal functional expansion for estimation from counting observations

A systematic method to develop approximate nonlinear estimators is presented, in the form of a functional series, for the signal that modulates the rate of a counting process. The estimators are optimal for the given structure and approach the minimum variance (MV) estimator when the approximation order increases. Two kinds of functional series, the iterated integral (II) series and the Fourier-Charlier (FC) series, are used. Product-to-sum formulas for the II and FC functionals are derived. By using the formulas, the MV estimate is projected onto the Hilbert subspaces of the II and the FC series driven by the counting observations with the given index set. The projection results in a Wiener-Hopf type equation for the II kernels and a system of linear algebraic equations for the FC coefficients. The FC series estimator consists of finitely many single Wiener integrals of the counting observations and a nonlinear postprocessor. The nonlinear postprocessor, however, is not memoryless.     

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (D) are derived. The approach used is based on the {em a posteriori} probability of a nonobservable event expressed in terms of the {em a priori} probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed is considered. It is shown that the MMSE estimates ale linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.     

Optimal identification of discrete-time systems from impulseresponse data

An optimal method (OM) for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented. The multidimensional nonlinear fitting error minimization problem has been theoretically decoupled into two subproblems of reduced computational complexities. The proposed approach is applicable for identifying rational models with arbitrary numbers of poles and zeros. The nonlinear denominator subproblem possesses weighted-quadratic structure which is utilized to formulate an efficient iterative minimization algorithm. The optimal numerator is found noniteratively with a linear least-squares approach that utilizes the optimized denominator. Both the decoupled subcriteria of OM posses global optimality properties. The Steiglitz-McBride (1960, SM) method is also decoupled for arbitrary numbers of poles and zeros (DSM-G). It is demonstrated that the denominator subproblem of DSM-G is theoretically optimal. For another existing decoupled SM method (DSM-J), it has been shown that only the numerator is theoretically optimal     

Optimal linear estimation with uncertain observations (Corresp.)

Nahi [2] considered the optimal linear estimation with uncertain observations. In his model, the binary random variables characterizing uncertainty of signals in the observation were statistically independent. This correspondence considers the same model but with the binary random variables correlated.     

Self-adjusting orthogonal digital filter for identification of unknown processes

A digital filter with independent adjustable parameters which may be used for online identification of linear or nonlinear unknown processes is described. Algorithms for constructing the components of the filter and computing the optimum values of the adjustable parameters are given.     

Fast recursive basis function estimators for identification oftime-varying processes

When system parameters vary rapidly with time, the weighted least squares filters are not capable of following the changes satisfactorily; some more elaborate estimation schemes, based on the method of basis functions, have to be used instead. The basis function estimators have increased tracking capabilities but are computationally very demanding. The paper introduces a new class of adaptive filters, based on the concept of postfiltering, which have improved parameter tracking capabilities that are typical of the basis function algorithms but, at the same time, have pretty low computational requirements, which is typical of the weighted least squares algorithms     

A closed-form identification of multichannel moving average processes by ESPRIT

In this paper, a closed-form identification of possibly nonminimum phase multichannel moving average (MA) processes is derived by exploiting the eigenstructures of the observation cumulant matrices using the ESPRIT algorithm. The proposed approach allows the combination of statistics of different orders for better performance and offers reduced computation complexity when compared with existing iterative approaches. Simulations are also presented to demonstrate the performance of the proposed algorithm.This work was supported in part by the National Science Foundation under Contract NCR-932183, and by the Office of Naval Research under Contract N00014-91-J-1461.     

Optimal reassignment-based complex nonlinear processing of vector discrete-continuous Markovian random processes

Methods of the Markovian estimation theory are applied to the synthesis of optimal and quasi-optimal algorithms that involve time-stepped reassignment of the values of the parameters of conditional a posteriori probability densities of filtered continuous processes. The algorithms are intended for nonlinear processing of a vector discrete-continuous Markovian random process whose continuous component is a vector diffusion Markovian process and whose discrete component is a two-component vector, each component of which is characterized by a simple several-position Markovian chain. It is assumed that one group of simultaneously processed signals is observed against the background of colored (time-correlated) noise, while the other group is observed in the presence of white Gaussian noise. Basic analytic relationships and the corresponding block diagram of a system for quasi-optimal complex nonlinear processing of signals typical of the GLONASS, GPS, Galileo, and QZSS satellite navigation systems and such satellite mobile-communications systems as the Globalstar system are presented.     

Collaborative linear dynamical system identification by scarce relevant/irrelevant observations

Multidimensional Systems and Signal Processing - In the current paper, linear dynamical system identification by relevant and irrelevant multi-sensor observations is presented. In common system...     

Optimal controlled ALOHA for two-way data communication in a cabletelevision network

Based on a unified analysis of both pure and slotted ALOHA systems, a new control algorithm for ALOHA systems is proposed. A feature of great practical importance is the algorithm's automatic adjustment to changes in average traffic intensity or the (finite or infinite) number of active stations in the system. In addition, the algorithm has a low-complexity implementation. Computer simulations, concentrating on the use for two-way data communication in a cable television network, have demonstrated that the practical performance of the algorithm closely approximates the theoretical optimum, even under extremely heavy traffic load conditions. Furthermore, dynamic performance simulations have shown that the algorithm assures swift recovery from overload situations     

Optimal ARMA parameter estimation based on the sample covariancesfor data with missing observations

The problem of spectral estimation through the autoregressive moving-average (ARMA) modeling of stationary processes with missing observations is considered. A class of estimators based on the sample covariances is presented, and an asymptotically optimal estimator in this class is proposed. The proposed algorithm is based on a nonlinear-least-squares fit of the sample covariances computed from the data to the true covariances of the assumed ARMA model. The statistical properties of the algorithm are explored and used to show that it is asymptotically optimal, in the sense of achieving the smallest possible asymptotic variance. The performance of the algorithm is illustrated by some numerical examples     

Surface and bulk laser-damage statistics and the identification of intrinsic breakdown processes

The experimental evidence presented confirms the existence of a statistical nature in the laser-induced intrinsic damage process both in the bulk and on the surfaces of transparent materials. A damage process determined by an electron-avalanche breakdown with statistical starting properties was found to be consistent with the data. The importance of irradiating only a small volume of the material in order to avoid studying inclusion-induced laser damage is discussed. In addition, a new procedure was developed to permit rapid identification of the occurrence of damage due to an intrinsic process.     

Optimal tradeoff circular harmonic function correlation filtermethods providing controlled in-plane rotation response

Correlation methods are becoming increasingly attractive tools for image recognition and location. This renewed interest in correlation methods is spurred by the availability of high-speed image processors and the emergence of correlation filter designs that can optimize relevant figures of merit. In this paper, a new correlation filter design method is presented that allows one to optimally tradeoff among potentially conflicting correlation output performance criteria while achieving desired correlation peak value behavior in response to in-plane rotation of input images. Such controlled in-plane rotation response is useful in image analysis and pattern recognition applications where the sensor follows a pre-arranged trajectory while imaging an object. Since this new correlation filter design is based on circular harmonic function (CHF) theory, we refer to the resulting filters as optimal tradeoff circular harmonic function (OTCHF) filters. Underlying theory, OTCHF filter design method, and illustrative numerical results are presented.     

Parameter estimation and linear system identification with randomly interrupted observations (Corresp.)

The problem of estimating the unknown parameters of linear discrete-time stochastic system models is considered for the case when the observations may contain noise alone. The interruptions in the observations are modeled as an independent stationary binary (zero or one) sequence where the probability of an interruption may not be known. The criterion for parameter estimation is chosen to be minimization of the prediction errors using linear predictors. Sufficient conditions for strong consistency of the parameter estimates are derived. It is shown by means of an example that even a few missing observations can lead to a serious degradation in the quality of the parameter estimate.     

生物细胞亚类识别多维光学传感光路优化设计

针对生物细胞原位检测和提高分类精度这一研究热点,以白细胞为主要研究对象,利用细胞光散射识别方法,根据细胞各方向散射光的特点,设计了一种多维光学传感系统,即是通过该光学系统可以检测细胞前向大小角,侧向偏振动,以及后向散射光。其中对各向光路系统构成和各个元件参数进行了优化设计,使系统的分辨率在80lp/mm时,MTF值不低...