Author's reply to “Comments on ‘Performance evaluation of UKF-based nonlinear filtering”’

Xiong, Kai; Zhang, H. Y.; Chan, C.W.

doi:10.1016/j.automatica.2006.10.002

Cited by 48 publications

(40 citation statements)

References 1 publication

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“…4, the proposed nonaugmented GF recursively operates by combining the analytical computation in (26) with the nonlinear Gaussian integrals in (18)- (24) and (27)- (29). The heart of implementing such GF is thus transformed to compute these nonlinear integrals.…”

Section: Theorem 1 Consider the System In (1)-(2) With The Given Initmentioning

confidence: 99%

“…and then, the second equation in (26) can be also obtained by substituting (33) into the definition of the covariance term P k− j,k−l|k in (6).…”

Section: Theorem 1 Consider the System In (1)-(2) With The Given Initmentioning

confidence: 99%

“…Further, GSF provides a feasible approach to meet both accuracy and real time required in the filtering problem of nonlinear time-delay systems. However, the existing literatures concerning GSF or GF have been limited to the research on the robust filter for dealing with the model error [13], on the adaptive filter with Gaussian sum refinement and coarsening [12,14], on the numerical technologies for approximating the nonlinear integrals [15][16][17][18][19][20], on the state smoothing framework design [10,[21][22][23], on the numerical and stability analyses [24][25][26][27][28], on the constrained estimation [29][30][31], and on the colored and correlated noises [9,10]. So far, there are seldom results paying adequate research attention on designing the GSF for the nonlinear time-delay systems despite GSF has been significantly shown to be good at both accuracy and real time.…”

Section: Each Constituent Gf Essentially Acts Independentlymentioning

confidence: 99%

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Gaussian sum approximation filter for nonlinear dynamic time-delay system

Wang

Liang

2015

Nonlinear Dyn

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This paper focuses on designing Gaussian sum approximation filter for both accurately and rapidly estimating the state of a class of nonlinear dynamic time-delay systems. Firstly, a novel nonaugmented Gaussian filter (GF) is derived, whose superiority in computation efficiency is theoretically analyzed as compared to the standard augmented GF. Secondly, a nonaugmented Gaussian sum filter (GSF) is proposed to accurately capture the state estimates by a weight sum of the above-proposed GF. In GSF, each GF component is independent from the others and can be performed in a parallel manner so that GSF is conducive to high-performance computing across many compute nodes. Finally, the performance of the proposed GSF is demonstrated by a vehicle suspension system with time delay, where the GSF achieves higher accuracy than the single GF and is computationally much more efficient than the particle filter with the almost same accuracy.

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Section: Theorem 1 Consider the System In (1)-(2) With The Given Initmentioning

confidence: 99%

“…and then, the second equation in (26) can be also obtained by substituting (33) into the definition of the covariance term P k− j,k−l|k in (6).…”

Section: Theorem 1 Consider the System In (1)-(2) With The Given Initmentioning

confidence: 99%

Section: Each Constituent Gf Essentially Acts Independentlymentioning

confidence: 99%

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Gaussian sum approximation filter for nonlinear dynamic time-delay system

Wang

Liang

2015

Nonlinear Dyn

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“…3 Recursive operation of the non-augmented GF Then, according to Gaussian computation rule (see Appendix A in [42]), rearranging (34) yields (see (35)) Using the Bayesian rule [46], we have…”

Section: Non-augmented Gfmentioning

confidence: 99%

Gaussian/Gaussian‐mixture filters for non‐linear stochastic systems with delayed states

Wang

Liang

Huang

2014

IET Control Theory & Applications

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The Gaussian mixture approximation to the probability density function of the state is more appropriate than the single Gaussian approximation. A Gaussian mixture filter (GMF) is proposed for a class of non-linear discrete-time stochastic systems with the multi-state delayed case. First, a novel non-augmented filtering framework of the constituent Gaussian filter (GF) in GMF is derived, which recursively operates by analytical computation and non-linear Gaussian integrals. The implementation of such GF is thus transformed to the computation of such non-linear integrals in the proposed framework, which is solved by applying different numerical technologies for developing various variations of the non-augmented GF, for example, GF-cubature Kalman filter (CKF) based on the cubature rule. Secondly, a non-augmented GMF is discussed by a weight sum of the above proposed GF, where each GF component is independent from the others and can be performed in a parallel manner, and its corresponding weigh is updated by using the measurements according to Bayesian formula. Naturally, a variation or implementation of such GMF based on the cubature rule is the GMF-CKF. Finally, the performance of the new filters is demonstrated by a numerical example and a vehicle suspension estimation problem.

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“…The first one numerically approximates the multidimensional integrals by means of a third-degree spherical-radial cubature rule; it features good accuracy and high convergence speed, but accuracy may be reduced by model uncertainty and noise [41,42,49]. On the other hand, SCRHKF is robust against uncertainty and noise, but due to the use of a finite number of measurements, its convergence speed is slower than SCKF.…”

Section: Kalman Filtermentioning

confidence: 99%

On the Vehicle Sideslip Angle Estimation: A Literature Review of Methods, Models, and Innovations

2018

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Typical active safety systems that control the dynamics of passenger cars rely on the real-time monitoring of the vehicle sideslip angle (VSA), together with other signals such as the wheel angular velocities, steering angle, lateral acceleration, and the rate of rotation about the vertical axis, which is known as the yaw rate. The VSA (also known as the attitude or "drifting" angle) is defined as the angle between the vehicle's longitudinal axis and the direction of travel, taking the centre of gravity as a reference. It is basically a measure of the misalignment between vehicle orientation and trajectory; therefore, it is a vital piece of information enabling directional stability assessment, such as in transience following emergency manoeuvres, for instance. As explained in the introduction, the VSA is not measured directly for impracticality, and it is estimated on the basis of available measurements such as wheel velocities, linear and angular accelerations, etc. This work is intended to provide a comprehensive literature review on the VSA estimation problem. Two main estimation methods have been categorised, i.e., observer-based and neural network-based, focussing on the most effective and innovative approaches. As the first method normally relies on a vehicle model, a review of the vehicle models has been included. The advantages and limitations of each technique have been highlighted and discussed.

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Author's reply to “Comments on ‘Performance evaluation of UKF-based nonlinear filtering”’

Cited by 48 publications

References 1 publication

Gaussian sum approximation filter for nonlinear dynamic time-delay system

Gaussian sum approximation filter for nonlinear dynamic time-delay system

Gaussian/Gaussian‐mixture filters for non‐linear stochastic systems with delayed states

On the Vehicle Sideslip Angle Estimation: A Literature Review of Methods, Models, and Innovations

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