Related papers: Uniform observability of hidden Markov models and …
This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…
The nonlinear filtering equation is said to be stable if it ``forgets'' the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…
We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a…
This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS.We show that…
It is known that Kalman-Bucy filter is stable with respect to initial conditions under the conditions of uniform complete controllability and uniform complete observability (Bishop et. al 2017, Ocone et. al 1996). In this paper, we prove…
We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
The nonlinear filter associated with the discrete time signal-observation model $(X_k,Y_k)$ is known to forget its initial condition as $k\to\infty$ regardless of the observation structure when the signal possesses sufficiently strong…
The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability,…
Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to incorrect initial condition is derived in the case of slowly…
In this paper, we introduce the concept of observability of targeted state variables for systems that may not be fully observable. For their estimation, we introduce and exemplify a deep filter, which is a neural network specifically…
We consider a hidden Markov model with multiplicative noise emerging from studies of software reliability. We show the stability of the optimal filter with respect to general initial conditions in the total variation- and $L^p$-norm and…
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…
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides…
We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…