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This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

The input-parameter-state estimation capabilities of a novel unscented Kalman filter is examined herein on both linear and nonlinear systems. The unknown input is estimated in two stages within each time step. Firstly, the predicted dynamic…

Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which…

Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only…

We propose to use the ensemble Kalman smoother (EnKS) as linear least squares solver in the Gauss-Newton method for the large nonlinear least squares in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble…

The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…

Smoothing is a specialized form of Bayesian inference for state-space models that characterizes the posterior distribution of a collection of states given an associated sequence of observations. Ramgraber et al. (2023) proposes a general…

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the…

Gauss-Newton methods and their stochastic version have been widely used in machine learning and signal processing. Their nonsmooth counterparts, modified Gauss-Newton or prox-linear algorithms, can lead to contrasting outcomes when compared…

We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…

Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear…

Stochastic models in biomolecular contexts can have a state-dependent process noise covariance. The choice of the process noise covariance is an important parameter in the design of a Kalman Filter for state estimation and the theoretical…

Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…

Many filters have been proposed in recent decades for the nonlinear state estimation problem. The linearization-based extended Kalman filter (EKF) is widely applied to nonlinear industrial systems. As EKF is limited in accuracy and…

This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are available. While gradient-free methods have been developed for…

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…

This work highlights the duality between state estimation methods and model predictive control. A predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear time-horizon…

In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…