Normalized fractional adaptive methods for nonlinear control autoregressive systems

Chaudhary, Naveed Ishtiaq; Khan, Zeshan Aslam; Zubair, Syed; Raja, Muhammad Asif Zahoor; Dedović, Nebojša

doi:10.1016/j.apm.2018.09.028

Cited by 44 publications

(22 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The rise in standard deviation of measurement noise results in exponential decay in the accuracy of both algorithms for each case of the passive tracking problem and vice versa. In future, one may investigate the fractional adaptive filtering algorithms [ 50 , 51 , 52 , 53 ] for achieving better state estimation results in an underwater noisy medium, which is still a challenging research domain and has a wide capability for progress and expansion.…”

Section: Discussionmentioning

confidence: 99%

Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

Ali

Chen

et al. 2019

Entropy

Self Cite

View full text Add to dashboard Cite

In this paper, an application of spherical radial cubature Bayesian filtering and smoothing algorithms is presented to solve a typical underwater bearings only passive target tracking problem effectively. Generally, passive target tracking problems in the ocean environment are represented with the state-space model having linear system dynamics merged with nonlinear passive measurements, and the system is analyzed with nonlinear filtering algorithms. In the present scheme, an application of spherical radial cubature Bayesian filtering and smoothing is efficiently investigated for accurate state estimation of a far-field moving target in complex ocean environments. The nonlinear model of a Kalman filter based on a Spherical Radial Cubature Kalman Filter (SRCKF) and discrete-time Kalman smoother known as a Spherical Radial Cubature Rauch–Tung–Striebel (SRCRTS) smoother are applied for tracking the semi-curved and curved trajectory of a moving object. The worth of spherical radial cubature Bayesian filtering and smoothing algorithms is validated by comparing with a conventional Unscented Kalman Filter (UKF) and an Unscented Rauch–Tung–Striebel (URTS) smoother. Performance analysis of these techniques is performed for white Gaussian measured noise variations, which is a significant factor in passive target tracking, while the Bearings Only Tracking (BOT) technology is used for modeling of a passive target tracking framework. Simulations based experiments are executed for obtaining least Root Mean Square Error (RMSE) among a true and estimated position of a moving target at every time instant in Cartesian coordinates. Numerical results endorsed the validation of SRCKF and SRCRTS smoothers with better convergence and accuracy rates than that of UKF and URTS for each scenario of passive target tracking problem.

show abstract

Section: Discussionmentioning

confidence: 99%

Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

Ali

Chen

et al. 2019

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…Wellknown kernel adaptive filtering algorithms are kernel least mean square (KLMS) [9][10][11][12], kernel normalized least mean square (KNLMS), kernel affine projection algorithms (KAPA) [13,14], and kernel recursive least squares (KRLS) [15]. In this context, it is worth citing fractional adaptive signal processing [16][17][18][19][20] as these modern filtering algorithms outperform their counterparts in terms of accuracy and convergence, for example in active noise control systems.…”

Section: Related Workmentioning

confidence: 99%

Anisotropic Gaussian kernel adaptive filtering by Lie-group dictionary learning

et al. 2020

View full text Add to dashboard Cite

The present paper proposes a novel kernel adaptive filtering algorithm, where each Gaussian kernel is parameterized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of scalar width parameter. In fact, different from conventional kernel adaptive systems, the proposed filter is structured as a superposition of non-isotropic Gaussian kernels, whose non-isotropy makes the filter more flexible. The adaptation algorithm will search for optimal parameters in a wider parameter space. This generalization brings the need of special treatment of parameters that have a geometric structure. In fact, the main contribution of this paper is to establish update rules for precision matrices on the Lie group of SPD matrices in order to ensure their symmetry and positive-definiteness. The parameters of this filter are adapted on the basis of a leastsquares criterion to minimize the filtering error, together with an ℓ 1-type regularization criterion to avoid overfitting and to prevent the increase of dimensionality of the dictionary. Experimental results confirm the validity of the proposed method.

show abstract

“…A class of fractional adaptive signal processing algorithms for nonlinear system identification have been proposed using the multidirectional step‐size strategy, the step‐size was adjusted according to the status of the active noise control system for faster convergence . In addition, the fractional calculus‐based adaptive algorithms can be applied in various physics and engineering problems . The fractional least mean square adaptive algorithm uses the concept of the fractional order gradient in addition to the standard integer order gradient calculation in the recursive parameter update mechanism of optimization.…”

Section: Introductionmentioning

confidence: 99%

“…9 In addition, the fractional calculus-based adaptive algorithms can be applied in various physics and engineering problems. [10][11][12] The fractional least mean square adaptive algorithm uses the concept of the fractional order gradient in addition to the standard integer order gradient calculation in the recursive parameter update mechanism of optimization. Stochastic optimization solvers based on the artificial intelligence look promising, and the identification methods for nonlinear systems based on the artificial intelligence algorithm 13,14 will be taken as a potential research direction and can be used to study parameter identification methods of dynamical stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

Liu

Ding

Hayat

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary The combined iterative parameter and state estimation problem is considered for bilinear state‐space systems with moving average noise in this paper. There are the product terms of state variables and control variables in bilinear systems, which makes it difficult for the parameter and state estimation. By designing a bilinear state estimator based on the Kalman filtering, the states are estimated using the input‐output data. Furthermore, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. A state estimator‐based MDW gradient‐based iterative (MDW‐GI) algorithm is proposed to estimate the unknown states and parameters jointly. Moreover, given the extended gradient‐based iterative (EGI) algorithm as a comparison, the MDW‐GI algorithm can reduce the impact of noise to parameter estimation and improve the parameter estimation accuracy. The numerical simulation examples validate the effectiveness of the proposed algorithm.

show abstract

Normalized fractional adaptive methods for nonlinear control autoregressive systems

Cited by 44 publications

References 60 publications

Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

Anisotropic Gaussian kernel adaptive filtering by Lie-group dictionary learning

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

Contact Info

Product

Resources

About