Lattice Im plication Homom orphism inIm plication Filter Spaces

ＩｍｐｌｉｃａｔｉｏｎｆｉｌｔｅｒｓｄｅｒｉｖｅｆｒｏｍＭｏｄｕｓＰｏｅｎｅｓＲｕｌｅｉｎｌｏｇｉｃ．Ｉｔｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｔｏｓｔｕｄｙｌａｔｔｉｃｅｉｍｐｌｉｃａｔｉｏｎａｌｇｅｂｒａｓａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｌａｔｔｉｃｅ－ｖａｌｕｅｄｌｏｇｉｃｓｙｓｔｅｍ．Ｉｎｏｒｄｅｒｔｏｉｎ－ｖｅｓｔｉｎｇａｔｅｌａｔｔｉｃｅｉｍｐｌｉｃａｔｉｏｎａｌｇｅｂｒａｓｆｒｏｍｔｈｅｖｉｅｗｏｆａｎａｌｙｓｉｓ，ｉｍｐｌｉｃａｔｉｏｎｆｉｌｔｅｒｓｐａｃｅｈａｓｂｅｅｎｅｓｔａｂ…     

Optimal finite-dimensional solution for a class of nonlinear observation problems

The filtering problem in a differential system with linear dynamics and observations described by an implicit equation linear in the state is solved in finite-dimensional recursive form. The original problem is posed as a deterministic fixed-interval optimization problem (FIOP) on a finite time interval. No stochastic concepts are used. Via Pontryagin's principle, the FIOP is converted into a linear, two-point boundary-value problem. The boundary-value problem is separated by using a linear Riccati transformation into two initial-value problems which give the equations for the optimal filter and filter gain. The optimal filter is linear in the state, but nonlinear with respect to the observation. Stability of the filter is considered on the basis of a related properly linear system. Three filtering examples are given.     

Markov chain approximations to filtering equations for reflecting diffusion processes

Herein, we consider direct Markov chain approximations to the Duncan–Mortensen–Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion signals with symmetrizable generators. Our Markov chains are constructed by employing a wide band observation noise approximation, dividing the signal state space into cells, and utilizing an empirical measure process estimation. The upshot of our approximation is an efficient, effective algorithm for implementing such filtering problems. We prove that our approximations converge to the desired conditional distribution of the signal given the observation. Moreover, we use simulations to compare computational efficiency of this new method to the previously developed branching particle filter and interacting particle filter methods. This Markov chain method is demonstrated to outperform the two-particle filter methods on our simulated test problem, which is motivated by the fish farming industry.     

Filtering and Control with Information Increasing

In this paper, we consider a filtering problem where the observation filtration is enlarged with a future information. In the linear case, we obtain the filter equations and study the associated linear regulator problem.     

Malliavin calculus with time dependent coefficients and application to nonlinear filtering

Summary In this paper, we prove, using Malliavin calculus, that under a local Hörmander condition the solution of a stochastic differential equation with time depending coefficients admits aC density with respect to Lebesgue measure. An application of this result to nonlinear filtering is developed in this paper to prove the existence of aC density for the filter associated with a correlated system whose observation is one dimensional with unbounded coefficients.     

Martindale quotients of Jordan algebras

In this paper we introduce Martindale quotients of Jordan algebras over arbitrary rings of scalars with respect to denominator filters of ideals. For any denominatored algebra, we show the existence of maximal Martindale quotients naturally containing all Martindale quotients of the algebra with respect to the given denominator filter.     

A Note on Closed Degrees of Difficulty of the Medvedev Lattice

We consider some nonprincipal filters of the Medvedev lattice. We prove that the filter generated by the nonzero closed degrees of difficulty is not principal and we compare this filter, with respect to inclusion, with some other filters of the lattice. All the filters considered in this paper are disjoint from the prime ideal generated by the dense degrees of difficulty. Mathematics Subject Classification: 03D30.     

Martingale measures and partially observable diffusions

In this paper, we solve the problem of existence of an optimal control based on partial observations in the general case where the observation process depends on the control. The method of solution is based on the use of relaxed controls and martingales measures: we associate a martingale problem with the filter and we prove that this problem is equivalent to the initial one     

Approximate filter for a two-dimensional nonlinear diffusion observed in a correlated low noise channel

The purpose of this article is to study a nonlinear filtering problem when the signal is a two-dimensional process from which only the second component is noisy and when only its first (and unnoisy) component is observed in a correlated low noise channel. We propose an approximate finite-dimensional filter and we prove that the filtering error converges to zero. The order of magnitude of the error between the approximate filter and the optimal filter, as the observation noise vanishes, is computed.     

Design of RLS Wiener fixed-lag smoother using covariance information in linear discrete stochastic systems

In this paper, we propose a new design for the recursive least-squares (RLS) Wiener fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. It is assumed that the signal is observed with additive white observation noise. The signal is uncorrelated with the observation noise. The estimators require knowledge of the system matrix, the observation matrix and the variance of the state vector. These quantities can be obtained from the auto-covariance function of the signal. In the estimation algorithms, moreover, the variance of the observation noise is assumed to be known, as a priori information.     

Risk Sensitive Filtering with Poisson Process Observations

In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter. Accepted 23 July 1999     

Stability-enhancing control of a coupled transport–diffusion system with Dirichlet actuation and Dirichlet measurement

We investigate the problem of enhancing the stability of a coupled transport–diffusion system with Dirichlet actuation and Dirichlet measurement. In the recent paper [H. Sano, Neumann boundary control of a coupled transport–diffusion system with boundary observation, J. Math. Anal. Appl. 377 (2011) 807–816], we treated the stabilization problem for the case with Neumann actuation and Dirichlet measurement, where the variable transformation of the state is performed by using the fractional power of an unbounded operator. However, we cannot use the similar transformation for the case with Dirichlet actuation and Dirichlet measurement, since it brings an ill-posed expression of the system. So, we use an algebraic approach for the formulation of the system. In this paper, it is shown that a reduced-order model with a finite-dimensional state variable is controllable and observable. The fact enables us to construct a finite-dimensional stability-enhancing controller for the original infinite-dimensional system by using a residual mode filter (RMF) approach. The novelty of this paper is the structure that the controller contains the dynamics with respect to the control variable. As a result, the state vector of the resulting closed-loop system includes the control variable as its entry.     

Center,Centroid, Extended Centroid,and Quotients of Jordan Systems

In this article we prove that the extended centroid of a nondegenerate Jordan system is isomorphic to the centroid (and to the center in the case of Jordan algebras) of its maximal Martindale-like system of quotients with respect to the filter of all essential ideals.     

Convolution kernels implementation of cardinalized probability hypothesis density filter

The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.     

Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems

An unscented filtering algorithm is derived for a class of nonlinear discrete-time stochastic systems using noisy observations which can be randomly delayed by one or two sample times. The update and the possible delays (of one and two sampling times) of any observation are modelled by using three Bernoulli random variables such that only one of them takes the value one. The algorithm performs in two-steps, prediction and update, and it uses a scaled unscented transformation to approximate the conditional mean and covariance of the state and observation at each time. The performance of the proposed filter is shown in a simulation example which uses a growth model with randomly delayed observations; in this example, the proposed filter is compared with the extended one obtained by linearizing the state and the observation equations and, also, with the unscented Kalman filter. A clear superiority of the proposed filter over the others is inferred.     

基于分数布朗运动的非线性滤波

本文研究一类由Host指数为1/2相似文献   

On the ill conditioning of locating transmission zeros in least squares ARMA filtering

The algorithms of Levinson-Schur and Nevanlinna-Pick are briefly reviewed. Both produce least squares predictive filters. By minimizing the least squares error with respect to the interpolation points of the Nevanlinna-Pick algorithm we find the transmission zeros of an ARMA filter. It is shown by some simple examples that this is an ill conditioned problem.     

Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises

We investigate the optimal filtering problem in the simplest Gaussian linear system driven by fractional Brownian motions. At first we extend to this setting the Kalman–Bucy filtering equations which are well-known in the specific case of usual Brownian motions. Closed form Volterra type integral equations are derived both for the mean of the optimal filter and the variance of the filtering error. Then the asymptotic stability of the filter is analyzed. It is shown that the variance of the filtering error converges to a finite limit as the observation time tends to infinity. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the optimal design of the output transformation for discrete-time linear systems

The optimization of the output matrix for a discrete-time, single-output, linear stochastic system is approached from two different points of view. Firstly, we investigate the problem of minimizing the steady-state filter error variance with respect to a time-invariant output matrix subject to a norm constraint. Secondly, we propose a filter algorithm in which the output matrix at timek is chosen so as to maximize the difference at timek+1 between the variance of the prediction error and that of the a posteriori error. For this filter, boundedness of the covariance and asymptotic stability are investigated. Several numerical experiments are reported: they give information about the limiting behavior of the sequence of output matrices generated by the algorithm and the corresponding error covariance. They also enable us to make a comparison with the results obtained by solving the former problem.This work was supported by the Italian Ministry of Education (MPI 40%), Rome, Italy.