Related papers: Fitting a Kalman Smoother to Data
In Kalman filtering, unknown inputs are often estimated by augmenting the state vector, which introduces reliance on fictitious input models. In contrast, minimum-variance unbiased methods estimate inputs and states separately, avoiding…
The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. However, when these…
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…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
The augmented, iterated Kalman smoother is applied to system identification for inverse problems in evolutionary differential equations. In the augmented smoother, the unknown, time-dependent coefficients are included in the state vector,…
This report provides a brief historical evolution of the concepts in the Kalman filtering theory since ancient times to the present. A brief description of the filter equations its aesthetics, beauty, truth, fascinating perspectives and…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
The immersion and the interaction are the important features of the driving simulator. To improve these characteristics, this paper proposes a low-cost and mark-less driver head tracking framework based on the head pose estimation model,…
Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…
Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking…
In this paper, we focus on batch state estimation for linear systems. This problem is important in applications such as environmental field estimation, robotic navigation, and target tracking. Its difficulty lies on that limited operational…
This paper solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion which avoids linearized approximations altogether. Based on creating virtual synthetic measurements, the algorithm uses a linear time-…
UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and…
Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…
Kalman smoothers reconstruct the state of a dynamical system starting from noisy output samples. While the classical estimator relies on quadratic penalization of process deviations and measurement errors, extensions that exploit Piecewise…