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Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows…
We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the…
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error…
This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…
Normal priors with unknown variance (NUV) have long been known to promote sparsity and to blend well with parameter learning by expectation maximization (EM). In this paper, we advocate this approach for linear state space models for…
Machine learning is actively being explored for its potential to design, validate, and even hybridize with near-term quantum devices. A central question is whether neural networks can provide a tractable representation of a given quantum…
We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear…
State estimation is a fundamental requirement in robotics, where the accurate determination of a robot's state is essential for stable operation despite inherent process disturbances and sensor noise. Traditionally, this is achieved through…
This paper considers the simultaneous state and unknown input estimation for continuous-discrete stochastic systems. Two types of approaches (with and without modeling of unknown inputs) which can address this issue are investigated. A…
Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSM), which allow a range of statistical distributions to inform innovations and…
This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
Speech enhancement in the time-frequency domain is often performed by estimating a multiplicative mask to extract clean speech. However, most neural network-based methods perform point estimation, i.e., their output consists of a single…
In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…
This proposed work introduces a data-assimilation-assisted approach to train neural networks, aimed at effectively reducing epistemic uncertainty in state estimates of separated flows. This method, referred to as model-consistent training,…
For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte…
When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…
The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of…
In this paper, we propose a new model reduction technique for linear stochastic systems that builds upon knowledge filtering and utilizes optimal Kalman filtering techniques. This new technique will reduce the dimension of the noise…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…