1,720,989 research outputs found
Optimal linear finite-dimensional filtering for vector bilinear stochastic differential systems
No full textA way to build up the optimal linear filter for a bilinear stochastic differential system is here presented. The method uses a new representation of the vector bilinear noisy terms as wide-sense Wiener processes. The considered system evolves in a finite-dimensional vector space. The optimal linear filter has the structure a finite-dimensional Kalman-Bucy scheme
Suboptimal solutions for the cubic sensor problem
No full textIn this paper we present a way to define a suboptimal filter for the so called cubic sensor problem. In particular, we propose the optimal quadratic filter which results to be in the form of a Kalman-Bucy filter evolving in a suitably defined augmented state space
Model reference adaptive expectations in Markov-switching economies
No full textThis paper offers a theory of model reference adaptive beliefs as a selection device in Markov-switching
economies under equilibrium indeterminacy. Consistent with the classical rational choice paradigm, our
theory requires that endogenous expectations be replaced with a general-measurable function of the observable
states of the model, to be determined optimally. This forecasting function is derived as the
regime-independent feedback control minimizing the mean-square deviation of the equilibrium path
from the corresponding perfect-foresight state motion (the reference model). We show that model reference
adaptive expectations always generate a rational expectations equilibrium, irrespective of the presence
of nonlinearities and/or imperfect information. Under equilibrium indeterminacy, this forecasting
mechanism enforces the unique mean-square stable solution producing nearly perfect-foresight dynamics
An Approximation Theory for Optimal Filtering of Linear Discrete Time Non-Gaussian Systems
No full textA new suboptimal approach to the filtering problem for bilinear stochastic differential systems
No full textThe aim of this paper is to present a new approach to the filtering problem for the class of bilinear stochastic multivariable systems, consisting in searching for suboptimal state-estimates instead of the conditional statistics. As a rst result, a finite-dimensional optimal linear filter for the considered class of systems is defined. Then, the more general problem of designing polynomial finite-dimensional filters is considered. The equations of a finite-dimensional filter are given, producing a state-estimate which is optimal in a class of polynomial transformations of the measurements with arbitrarily fixed degree. Numerical simulations show the effectiveness of the proposed filter
Optimal filtering for degenerate nonlinear diffusions
No full textThe optimal filtering problem for a nonlinear stochastic system with a non-elliptic diffusion term is studied. Under a more general geometric assumption involving the system reachability, (which includes the strong elliptic case), a Zakai-like equation is derived, and the existence and unicity of the solution is proved. This equation results to be satisfied by a suitably defined unnormalized conditional probability density, from which the optimal state-estimate can be easily derive
Filtering and Parameter Estimation for a Class of Hidden Markov Models with Application to Bubble-Counting in Microfluidics
No full textMotivated by a practical problem, in this work we investigate the problem of simultaneous estimation of state and parameters of an Hidden Markov Model with a particular structure. The motivating application is the problem of automatic counting of bubbles or droplets flowing into a microfluidic channel, where the noisy output of a photodiode has to be processed in order to detect the transit of bubbles. The goal is achieved through the recursive computation of a pseudo-max-likelihood estimate
Polynomial filtering of discrete-time stochastic linear systems with multiplicative state noise
No full textIn this paper, the problem of finding an optimal polynomial state estimate for the class of stochastic Linear models with a multiplicative state noise term is studied. For such models, a technique of state augmentation is used, leading to the definition of a general polynomial filter, The theory is developed for time-varying systems with nonstationary and non-Gaussian noises. Moreover, the steady-state polynomial filter for stationary systems is also studied, Numerical simulations show the high performances of the proposed method with respect to the classical Linear filtering techniques
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