Unscented Kalman filter and control on $$\mathsf {TSE(3)}$$ with application to spacecraft dynamics

Mangiacapra, Gennaro; Wittal, Matthew; Capello, Elisa; Nazari, Morad

doi:10.1007/s11071-022-07293-x

Cited by 16 publications

(5 citation statements)

References 57 publications

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“…Theorem 1. Suppose that each particle A i (t) on the Lorentz group SO(1, 1) is parametrized by equation (26). Then, the closed-loop system (13) and ( 15) is equivalent to…”

Section: Resultsmentioning

confidence: 99%

“…For autonomous spacecraft rendezvous and docking, the control on the special Euclidean group SE(3) is investigated. 25,26 The Lorentz group is a Lie group of symmetries of the Minkowski spacetime in special relativity. Many physics laws, equations, and theories, e.g., Maxwell's field equations in the theory of electromagnetism, 27,28 the Dirac equation in the theory of the electron, 29,30 and the Standard Model of particle physics, 31,32 respect the Lorentz symmetry.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rendezvous control for a double-integrator multi-particle system on Lorentz group SO (1,1)

2023

Preprint

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multi-particle system under a proximity-based communication topology on the Lorentz group SO(1,1). With the help of the Riemannian manifold structure on the Lorentz group SO(1,1), we design a rendezvous controller for particles by using the covariant derivative, parallel transport, and Riemannian logarithm map on SO(1,1). We further show that the proposed controller can guarantee that the distance between each particle converges to zero and maintain the connectivity of the communication topology if the initial network is connected. Several numerical simulations are provided to verify and illustrate the theoretical results.

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“…Theorem 1. Suppose that each particle A i (t) on the Lorentz group SO(1, 1) is parametrized by equation (26). Then, the closed-loop system (13) and ( 15) is equivalent to…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rendezvous control for a double-integrator multi-particle system on Lorentz group SO (1,1)

2023

Preprint

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“…Given their ability to dynamically assimilate new data and provide updated estimates, they are especially valuable for engineering applications that experience rapid changes or require continuous monitoring [17,18]. The Unscented Kalman Filter (UKF) stands out as one of the most robust Bayesian filters [19][20][21] because of its ability to capture nonlinearities in the system without resorting to linear approximations or iterative methods, which makes it particularly appealing for complex dynamical systems [22,23]. The UKF is often preferred for its accuracy and efficiency in many real-world applications [24,25].…”

Section: Introductionmentioning

confidence: 99%

Physics-Aware Tuning of Unscented Kalman Filter:Statistical Framework for Solving Inverse Problems Involving Nonlinear Dynamical Systems and Missing Data

Ghorbani,

Dollon,

Gosselin

2024

Preprint

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The performance of the Unscented Kalman Filter (UKF) strongly depends on the proper choice of measurement and process uncertainty matrices, as well as on the scaling parameter of the unscented transform. To avoid cumbersome trial-and-error manual settings in finding the optimal hyperparameters, we introduce a hands-off meta-optimization framework, which incorporates a nonlinear mesh adaptive direct search optimization algorithm in an offline outer loop, paired with a physics-aware loss function. The novelty of this approach is twofold. First, a physics-aware loss function is used to optimize the UKF hyperparameters. It minimizes the physical discrepancy induced by the data-driven correction of the prior states during filtering. Notably, sensor data are not directly incorporated into the calculation of the loss function, which expedites the tuning of the filter in weakly informative data scenarios, especially when the underlying physics is well understood. Second, UKF relaxation is embedded in the optimization to make the measurement and process noise covariance matrices adaptive, which greatly reduces the dimension of the optimization space while remaining very general with respect to the structure of the matrices. We demonstrate the effectiveness of the proposed framework, as the cornerstone of a future digital twin technology combining data- and physics-based models, through various classical problems in solid mechanics, rotating machinery, civil engineering, and fluid-solid interaction.

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“…In recent years, the application of multi-sensor systems has gained widespread attention in the fields of signal and processing, robot localization and navigation, multi-target tracking, and navigation and guidance systems [ 1 , 2 , 3 ]. Due to the problem of network latency or limited data communication capability of sensor systems, the packet dropout and noise coupling of measurement data are inevitable [ 4 ].…”

Section: Introductionmentioning

confidence: 99%

Sequential Fusion Filter for State Estimation of Nonlinear Multi-Sensor Systems with Cross-Correlated Noise and Packet Dropout Compensation

Tan

Wang

et al. 2023

Sensors

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This paper is concerned with the problem of state estimation for nonlinear multi-sensor systems with cross-correlated noise and packet loss compensation. In this case, the cross-correlated noise is modeled by the synchronous correlation of the observation noise of each sensor, and the observation noise of each sensor is correlated with the process noise at the previous moment. Meanwhile, in the process of state estimation, since the measurement data may be transmitted in an unreliable network, data packet dropout will inevitably occur, leading to a reduction in estimation accuracy. To address this undesirable situation, this paper proposes a state estimation method for nonlinear multi-sensor systems with cross-correlated noise and packet dropout compensation based on a sequential fusion framework. Firstly, a prediction compensation mechanism and a strategy based on observation noise estimation are used to update the measurement data while avoiding the noise decorrelation step. Secondly, a design step for a sequential fusion state estimation filter is derived based on an innovation analysis method. Then, a numerical implementation of the sequential fusion state estimator is given based on the third-degree spherical-radial cubature rule. Finally, the univariate nonstationary growth model (UNGM) is combined with simulation to verify the effectiveness and feasibility of the proposed algorithm.

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Unscented Kalman filter and control on $$\mathsf {TSE(3)}$$ with application to spacecraft dynamics

Cited by 16 publications

References 57 publications

Rendezvous control for a double-integrator multi-particle system on Lorentz group SO (1,1)

Rendezvous control for a double-integrator multi-particle system on Lorentz group SO (1,1)

Physics-Aware Tuning of Unscented Kalman Filter:Statistical Framework for Solving Inverse Problems Involving Nonlinear Dynamical Systems and Missing Data

Sequential Fusion Filter for State Estimation of Nonlinear Multi-Sensor Systems with Cross-Correlated Noise and Packet Dropout Compensation

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