相关论文: Topological Kalman Filtering on Cell Complexes

The internal state of a dynamical system, a set of variables that defines its evolving configuration, is often hidden and cannot be fully measured, posing a central challenge for real-time monitoring and control. While observers are…

Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…

Providing a metric of uncertainty alongside a state estimate is often crucial when tracking a dynamical system. Classic state estimators, such as the Kalman filter (KF), provide a time-dependent uncertainty measure from knowledge of the…

Latent variable models have become instrumental in computational neuroscience for reasoning about neural computation. This has fostered the development of powerful offline algorithms for extracting latent neural trajectories from neural…

This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter…

We consider two nonlinear state estimation problems in a setting where an extended Kalman filter receives measurements from two sets of sensors via two channels (2C). In the stochastic-2C problem, the channels drop measurements…

A crucial challenge in decentralized systems is state estimation in the presence of unknown inputs, particularly within heterogeneous sensor networks with dynamic topologies. While numerous consensus algorithms have been introduced, they…

Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only…

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

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…

Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from…

This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure"…

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…

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…

Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random…

Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…

Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…

Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear…

We consider the problem of distributed Kalman filtering for sensor networks in the case there are constraints in data transmission and there is model uncertainty. More precisely, we propose two distributed filtering strategies with…