scholarly journals Efficient Iterative Algorithms for a Class of Nonlinear Systems using the Block Matrix Inversion and Hierarchical Principle

2021 ◽  
Author(s):  
Siyu Liu ◽  
Feng Ding ◽  
Erfu Yang
Keyword(s):  
Computational Efficiency ◽  
Space Form ◽  
Iterative Algorithms ◽  
Matrix Decomposition ◽  
Estimation Algorithm ◽  
Identification Problem ◽  
Block Matrix ◽  
State Estimator ◽  
Iterative Estimation ◽  
Hierarchical Identification

Abstract This paper is concerned with the identification of the bilinear systems in the state-space form. The parameters to be identified of the considered system are coupled with the unknown states, which makes the identification problem difficult. To deal with the trouble, the iterative estimation theory is considered to derive the joint parameter and state estimation algorithm. Specifically, a moving data window least squares-based iterative (MDW-LSI) algorithm is derived to estimate the parameters by using the window data. Then, the unknown states are estimated by a bilinear state estimator. Moreover, for the purpose of improving the computational efficiency, a matrix decomposition-based MDW-LSI algorithm and a hierarchical MDW-LSI algorithm are developed according to the block matrix and the hierarchical identification principle. Finally, the computational efficiency is discussed and the numerical simulation is employed to test the proposed approaches.

scholarly journals Robust and Fast State Estimation for Poorly-Observable Low Voltage Distribution Networks Based on the Kalman Filter Algorithm

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4457 ◽  
Author(s):  
Antončič ◽  
Papič ◽  
Blažič
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Low Voltage ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Estimation Algorithm ◽  
Distribution Networks ◽  
Voltage Distribution ◽  
State Estimator

This paper presents a novel approach for the state estimation of poorly-observable low voltage distribution networks, characterized by intermittent and erroneous measurements. The developed state estimation algorithm is based on the Extended Kalman filter, where we have modified the execution of the filtering process. Namely, we have fixed the Kalman gain and Jacobian matrices to constant matrices; their values change only after a larger disturbance in the network. This allows for a fast and robust estimation of the network state. The performance of the proposed state-estimation algorithm is validated by means of simulations of an actual low-voltage network with actual field measurement data. Two different cases are presented. The results of the developed state estimator are compared to a classical estimator based on the weighted least squares method. The comparison shows that the developed state estimator outperforms the classical one in terms of calculation speed and, in case of spurious measurements errors, also in terms of accuracy.

scholarly journals Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3302
Author(s):  
Naveed Ishtiaq Chaudhary ◽  
Muhammad Asif Zahoor Raja ◽  
Zeshan Aslam Khan ◽  
Khalid Mehmood Cheema ◽  
Ahmad H. Milyani
Keyword(s):  
Parameter Estimation ◽  
Gradient Descent ◽  
Identification Problem ◽  
Descent Method ◽  
Estimation Accuracy ◽  
Gradient Descent Method ◽  
Hierarchical Identification ◽  
System A ◽  
Nonlinear Autoregressive ◽  
Fractional Orders

Recently, a quasi-fractional order gradient descent (QFGD) algorithm was proposed and successfully applied to solve system identification problem. The QFGD suffers from the overparameterization problem and results in estimating the redundant parameters instead of identifying only the actual parameters of the system. This study develops a novel hierarchical QFDS (HQFGD) algorithm by introducing the concepts of hierarchical identification principle and key term separation idea. The proposed HQFGD is effectively applied to solve the parameter estimation problem of input nonlinear autoregressive with exogeneous noise (INARX) system. A detailed investigation about the performance of HQFGD is conducted under different disturbance conditions considering different fractional orders and learning rate variations. The simulation results validate the better performance of the HQFGD over the standard counterpart in terms of estimation accuracy, convergence speed and robustness.

An Improved Triangle Centroid Localization Algorithm Based on PIT Criterion

2020 ◽  
Author(s):  
Mao Li ◽  
Feng Jiang ◽  
Cong Pei
Keyword(s):  
Response Speed ◽  
Estimation Algorithm ◽  
Localization Algorithm ◽  
Iterative Estimation ◽  
Localization Accuracy ◽  
Experimental Platform ◽  
Surrounding Environment ◽  
Intersection Points ◽  
Simulation Results ◽  
Communication Distance

Abstract Considering that the traditional triangle centroid localization algorithm based on RSSI is susceptible to surrounding environment, this paper improves the algorithm from two aspects of positioning accuracy and response speed also proposes an improved triangle centroid localization algorithm based on PIT criterion. Combined with actual positioning situation, the algorithm treats the calculated coordinates of the intersection points as the new beacon nodes. Thus, the area of triangle in the intersection region is reduced. Repeat positioning process until the predicted position of node is outside the triangle according to the PIT criterion. Compared with traditional triangle centroid localization algorithm, it showed from the simulation results that the improved triangle centroid localization algorithm can increase the localization accuracy up to 5 times based on the guaranteed response time when communication distance is 15 ~ 30 m, and this algorithm has higher localization accuracy and faster response speed than centroid iterative estimation algorithm in larger communication range. In additions, the experimental platform is built to verify that the proposed algorithm can effectively reduce the positioning error.

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