相关论文: UltimateKalman: Flexible Kalman Filtering and Smoo…

We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…

Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The…

We describe an application of the Invariant Extended Kalman Filter (IEKF) design methodology to the scan matching SLAM problem. We review the theoretical foundations of the IEKF and its practical interest of guaranteeing robustness to poor…

The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control…

Nonlinear Kalman Filters are powerful and widely-used techniques when trying to estimate the hidden state of a stochastic nonlinear dynamic system. In this paper, we extend the Smart Sampling Kalman Filter (S2KF) with a new point symmetric…

In this paper, stochastic optimal control problems in continuous time and space are considered. In recent years, such problems have received renewed attention from the lens of reinforcement learning (RL) which is also one of our motivation.…

The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…

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…

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…

We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…

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…

A Schmidt filter is a modification of the Kalman filter that allows to append system parameters as states and considers their uncertainty effect in the filtering process without attempting to estimate such parameters. The states that are…

We introduce a computationally efficient variant of the model-based ensemble Kalman filter (EnKF). We propose two changes to the original formulation. First, we phrase the setup in terms of precision matrices instead of covariance matrices,…

State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…

We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least…

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…

Model Predictive Control (MPC) represents nowadays one of the main methods employed for process control in industry. Its strong suits comprise a simple algorithm based on a straightforward formulation and the flexibility to deal with…

Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…

In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…