Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter

Kulikova, Maria V.; Kulikov, G. Yu.

doi:10.1016/j.apnum.2021.08.013

Cited by 6 publications

(2 citation statements)

References 51 publications

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“…The matrix of innovation has the following characteristics. 27,28 1. The mean of the matrix of innovation is zero; 2. the covariance is consistent with the theoretical covariance calculated by the Kalman filter; 3. the matrices of innovation at different times are not correlated.…”

Section: Chi-square Hypothesis Test Conditionmentioning

confidence: 99%

Adaptive fading Kalman depth estimation with chi-square hypothesis testing for Geiger-mode avalanche photo diode LIDAR

et al. 2023

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.The operation of a Geiger-mode avalanche photo diode (GM-APD) LIDAR is severely disturbed by background noise, which makes it challenging to rapidly and accurately estimate the target depth. Therefore, we propose an adaptive fading Kalman depth estimation technique based on chi-square hypothesis testing for GM-APD LIDARs. First, by analyzing the consistency of the echo photon distribution between adjacent pixels of the GM-APD, the pixels are fused to rapidly obtain the echo data of the target surface, thereby accelerating the depth estimation process. Second, we design a chi-square hypothesis test condition based on the statistical characteristics of the innovation vector, which can help evaluate whether the fading factor is introduced at the current moment, promote the convergence of the algorithm, and reduce the depth estimation time. Third, we propose a fading memory index weighted method to adaptively adjust the weight of the observed values to accurately estimate the innovation matrix covariance and determine the optimal fading factor. We demonstrate the effectiveness of the proposed algorithm through simulations and experiments. The results show that the proposed algorithm can rapidly and accurately estimate the target depth in the presence of strong background noise.

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Section: Chi-square Hypothesis Test Conditionmentioning

confidence: 99%

Adaptive fading Kalman depth estimation with chi-square hypothesis testing for Geiger-mode avalanche photo diode LIDAR

et al. 2023

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“…Parameter estimation methods based on SVD factorization have also been developed for a class of nonlinear stochastic systems. SVD-based extended [11], cubature [12], and extended-cubature [13] Kalman filters were proposed for state estimation in continuousdiscrete nonlinear stochastic systems. Advanced square-root cubature Kalman filters, which are based on the SVD factorization and sequential processing, were suggested in [14].…”

Section: Introductionmentioning

confidence: 99%

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

Tsyganov,

Tsyganova

2024

Mathematics

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This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known.

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A structural response reconstruction method based on a continuous-discrete state space model

Chen,

Peng

2023

J Mech Sci Technol

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Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter

Cited by 6 publications

References 51 publications

Adaptive fading Kalman depth estimation with chi-square hypothesis testing for Geiger-mode avalanche photo diode LIDAR

Adaptive fading Kalman depth estimation with chi-square hypothesis testing for Geiger-mode avalanche photo diode LIDAR

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

A structural response reconstruction method based on a continuous-discrete state space model

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