Related papers: Linear Filtering for Discrete Time Systems Driven …
In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
In many engineering applications the level of nonlinear distortions in frequency response function (FRF) measurements is quantified using specially designed periodic excitation signals called random phase multisines and periodic noise. The…
We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety…
A multivariate score-driven filter is developed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student's t distribution changes over time, we construct a robust filter…
The key advantage of using multiple microphones for speech enhancement is that spatial filtering can be used to complement the tempo-spectral processing. In a traditional setting, linear spatial filtering (beamforming) and single-channel…
We explore the diffusion process in the non-Markovian spatio-temporal noise.%the escape rate problem in the non-Markovian spatio-temporal random noise. There is a non-trivial short memory regime, i.e., the Markovian limit characterized by a…
Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…
This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization,…
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and…
We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for its law, for some time $t > 0 $, conditional on all observations up to this time $ t $. This is a general, possibly high dimensional…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric…
We study backward stochastic differential equations (BSDEs) for time-changed L\'evy noises when the time-change is independent of the L\'evy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…