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The widely-used Extended Kalman Filter (EKF) provides a straightforward recipe to estimate the mean and covariance of the state given all past measurements in a causal and recursive fashion. For a wide variety of applications, the EKF is…

This paper introduces a Gaussian Bayesian Network-based Extended Kalman Filter (GBN-EKF) for non-linear state estimators on stiff and ill-conditioned continuous-discrete stochastic systems, with a further analysis on systems with…

We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into…

This article introduces a new algorithm for nonlinear state estimation based on deterministic sigma point and EKF linearized framework for priori mean and covariance respectively. This method reduces the computation cost of UKF about 50%…

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central fusion…

This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information…

The Distributed Adaptive Signal Fusion (DASF) framework is a meta-algorithm for computing data-driven spatial filters in a distributed sensing platform with limited bandwidth and computational resources, such as a wireless sensor network.…

Optimization problems on the Stiefel manifold, ranging from principal component analysis to enhancing neural network robustness, are ubiquitous in machine learning. The Landing algorithm avoids computationally expensive retraction…

Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter…

Displacement plays a crucial role in structural health monitoring (SHM) and damage detection of structural systems subjected to dynamic loads. However, due to the inconvenience associated with the direct measurement of displacement during…

In this paper, we describe a general algorithmic framework for solving linear signal or feature fusion optimization problems in a distributed setting, for example in a wireless sensor network (WSN). These problems require linearly combining…

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here we explore another promising solution in which diffusion models are used to…

This paper addresses the synthesis of an optimal fixed-gain distributed observer for discrete-time linear systems over wireless sensor networks. The proposed approach targets the steady-state estimation regime and computes fixed observer…

Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as…

A novel method for distributed estimation of the frequency of power systems is introduced based on the cooperation between multiple measurement nodes. The proposed distributed widely linear complex Kalman filter (D-ACKF) and the distributed…

In this paper, we propose a joint time-frequency splitting (TFS) strategy for a multiuser orthogonal frequency division multiplexing (OFDM) system with simultaneous wireless information and power transfer (SWIPT). In TFS, the time sharing…

Distributed Kalman filter approaches based on the maximum correntropy criterion have recently demonstrated superior state estimation performance to that of conventional distributed Kalman filters for wireless sensor networks in the presence…

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…

Invariant Extended Kalman Filter (IEKF) has been successfully applied in Visual-inertial Odometry (VIO) as an advanced achievement of Kalman filter, showing great potential in sensor fusion. In this paper, we propose partial IEKF (PIEKF),…

This paper addresses the issues of unmanned aerial vehicle (UAV) indoor navigation, specifically in areas where GPS and magnetometer sensor measurements are unavailable or unreliable. The proposed solution is to use an error state extended…