Related papers: Nonlinear State Estimation using Gaussian Integral
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…
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman…
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…
This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…
A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and…
In this paper, we study the problem of estimating the state of a dynamic state-space system where the output is subject to quantization. We compare some classical approaches and a new development in the literature to obtain the filtering…
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter,…
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 deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF)…
The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We…
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…
In this paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear…