Related papers: Likelihood Gradient Evaluation Using Square-Root C…
The Kalman filter operates by storing a Gaussian description of the state estimate in the form of a mean and covariance. Instead of storing and manipulating the covariance matrix directly, a square-root Kalman filter only forms and updates…
This paper suggests a few novel Cholesky-based square-root algorithms for the maximum correntropy criterion Kalman filtering. In contrast to the previously obtained results, new algorithms are developed in the so-called {\it condensed} form…
In recursive state estimation, numerical error can play a major role in an algorithm's overall performance and reliability. Roundoff errors due to finite precision arithmetic can violate theoretical guarantees, leading to asymmetric and…
The maximum likelihood estimates of an ARMA model can be obtained by the Kalman filter based on the state-space representation of the model. This paper presents an algorithm for computing gradient of the log-likelihood by an extending the…
Square-root Kalman filters propagate state covariances in Cholesky-factor form for numerical stability, and are a natural target for gradient-based parameter learning in state-space models. Their core operation, triangularization of a…
Recent developments in the realm of state estimation of stochastic dynamic systems in the presence of non-Gaussian noise have induced a new methodology called the maximum correntropy filtering. The filters designed under the maximum…
The state-space model and the Kalman filter provide us with unified and computationaly efficient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the…
This paper addresses the numerical aspects of adaptive filtering (AF) techniques for simultaneous state and parameters estimation arising in the design of dynamic positioning systems in many areas of research. The AF schemes consist of a…
In this article, square-root formulations of the statistical linear regression filter and smoother are developed. Crucially, the method uses QR decompositions rather than Cholesky downdates. This makes the method inherently more numerically…
In this paper we provide novel closed-form expressions enabling differentiation of any scalar function of the Kalman filter's outputs with respect to all its tuning parameters and to the measurements. The approach differs from the previous…
Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave…
The state-of-the-art tensor network Kalman filter lifts the curse of dimensionality for high-dimensional recursive estimation problems. However, the required rounding operation can cause filter divergence due to the loss of positive…
This paper continues the research devoted to the design of numerically stable square-root implementations for the maximum correntropy criterion Kalman filtering (MCC-KF). In contrast to the previously obtained results, here we reveal the…
Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally…
A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…
This paper continues our research devoted to an accurate nonlinear Bayesian filters' design. Our solution implies numerical methods for solving ordinary differential equations (ODE) when propagating the mean and error covariance of the…
A stable square-root approach has been recently proposed for the unscented Kalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as for the mixed-type methods consisting of the extended Kalman filter (EKF) time update…
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
We propose KOALA++, a scalable Kalman-based optimization algorithm that explicitly models structured gradient uncertainty in neural network training. Unlike second-order methods, which rely on expensive second order gradient calculation,…