Related papers: An Elementary Introduction to Kalman Filtering

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers…

The problem of faulty sensor detection is investigated in large sensor networks where the sensor faults are sparse and time-varying, such as those caused by attacks launched by an adversary. Group testing and the Kalman filter are designed…

The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…

We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a…

State estimation is critical to control systems, especially when the states cannot be directly measured. This paper presents an approximate optimal filter, which enables to use policy iteration technique to obtain the steady-state gain in…

This paper is on learning the Kalman gain by policy optimization method. Firstly, we reformulate the finite-horizon Kalman filter as a policy optimization problem of the dual system. Secondly, we obtain the global linear convergence of…

This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…

State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when…

Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

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…

In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using…

This paper introduces a novel approach to detect and address faulty or corrupted external sensors in the context of inertial navigation by leveraging a switching Kalman Filter combined with parameter augmentation. Instead of discarding the…

Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…

This paper studies the problem of developing computationally efficient solutions for steering the distribution of the state of a stochastic, linear dynamical system between two boundary Gaussian distributions in the presence of…

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…

We consider a general form of the sensor scheduling problem for state estimation of linear dynamical systems, which involves selecting sensors that minimize the trace of the Kalman filter error covariance (weighted by a positive…

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…

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…

Simultaneous Input and State Estimation (SISE) enables the reconstruction of unknown inputs and internal states in dynamical systems, with applications in fault detection, robotics, and control. While various methods exist for linear…