相关论文: The equation of optimal filtering, Kalman's filter…
In this paper, we study the problem of estimating a Markov chain $X$(signal) from its noisy partial information $Y$, when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
This paper is concerned with a generalized Kalman-Bucy filtering model and corresponding robust problem under model uncertainty. We find that this robust problem is equivalent to considering an estimate problem under some sublinear…
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…
Many practical settings call for the reconstruction of temporal signals from corrupted or missing data. Classic examples include decoding, tracking, signal enhancement and denoising. Since the reconstructed signals are ultimately viewed by…
Time-continuous non-anticipating quantum processes of nondemolition measurements are introduced as the dynamical realizations of the causal quasi-measurements, which are described in this paper by the adapted operator-valued probability…
We consider the problem of pointwise estimation of multi-dimensional signals $s$, from noisy observations $(y_\tau)$ on the regular grid $\bZd$. Our focus is on the adaptive estimation in the case when the signal can be well recovered using…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
Measurements of a scalar linear Gauss-Markov process are sent over a fading channel. The fading channel is modeled as independent and identically distributed random variables with known realization at the receiver. The optimal estimator at…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by…
In this paper, state and noise covariance estimation problems for linear system with unknown multiplicative noise are considered. The measurement likelihood is modelled as a mixture of two Gaussian distributions and a Student's t…
This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization…
We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian…
The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We present a system of equations that describe the flow of…
The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
We consider a statistical problem of detection of a signal with unknown energy in a multi-channel system, observed in a Gaussian noise. We assume that the signal can appear in the $k$-th channel with a known small prior probability…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…