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Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is…
One of the most common misconceptions made about the Kalman filter when applied to linear systems is that it requires an assumption that all error and noise processes are Gaussian. This misconception has frequently led to the Kalman filter…
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…
Biomolecular systems are often modeled with partially known nonlinear stochastic dynamics, making state and parameter estimation a central challenge. While Kalman filtering techniques are widely used in this setting, their performance…
Satellite dynamics and tracking remain important challenges in the context of space exploration and communication systems. Accurate state estimation is essential to maintain reliable orbital motion and system performance. This paper…
Using state-space representation, mobile object positioning problems can be described as dynamic systems, with the state representing the unknown location and the observations being the information gathered from the location sensors. For…
The real-world applications in signal processing generally involve estimating the system state or parameters in nonlinear, non-Gaussian dynamic systems. The estimation problem may get even more challenging when there are physical…
The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…
We study the problem of optimal estimation and control of linear systems using quantized measurements, with a focus on applications over sensor networks. We show that the state conditioned on a causal quantization of the measurements can be…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
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…
This paper develops a robust extended Kalman filter to estimate the rotor angles and the rotor speeds of synchronous generators of a multimachine power system. Using a batch-mode regression form, the filter processes together predicted…
The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
The Kalman filter is ubiquitous for state space models because of its desirable statistical properties, ease of implementation, and generally good performance. However, it can perform poorly in the presence of outliers, or measurements with…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
The estimation of non-Gaussian measurement noise models is a significant challenge across various fields. In practical applications, it often faces challenges due to the large number of parameters and high computational complexity. This…
Kalman Filter requires the true parameters of the model and solves optimal state estimation recursively. Expectation Maximization (EM) algorithm is applicable for estimating the parameters of the model that are not available before Kalman…