Hierarchical least squares identification for feedback nonlinear equation-error systems

2020 ◽  
Vol 357 (5) ◽  
pp. 2958-2977 ◽  
Author(s):  
Feng Ding ◽  
Ximei Liu ◽  
Tasawar Hayat
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Equation Error

Advances in System Identification Using Fractional Models

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Rachid Malti ◽  
Stephane Victor ◽  
Alain Oustaloup
Keyword(s):  
System Identification ◽  
Least Squares ◽  
Prior Knowledge ◽  
Time Domain ◽  
Simultaneous Estimation ◽  
Thermal System ◽  
Fractional Model ◽  
Output Error ◽  
Equation Error ◽  
Fractional Models

This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error- and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model coefficients and differentiation orders using nonlinear programing. As an example, a thermal system is identified using a fractional model and is compared to a rational one.

A least‐squares approach to depth determination from gravity data

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 357-360 ◽  
Author(s):  
O. P. Gupta
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Data ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Random Errors ◽  
Depth Determination ◽  
Vertical Fault ◽  
Horizontal Cylinders ◽  
Least Squares Approach

The present paper deals with a numerical approach to determine the depth of a buried structure from the residual anomaly. The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of the form [Formula: see text]. Formulas have been derived for a sphere, vertical and horizontal cylinders, and for a vertical fault (thin plate approximation). The procedure is applied to synthetic data with and without random errors. Finally, a field example is presented in which the depth to a fault is estimated at 3.8 km and verified from drilling results.

On: “A least‐squares approach to depth determination from gravity data” by O.P. Gupta (GEOPHYSICS, 48, 357–360, March 1983)

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 376-377 ◽  
Author(s):  
El‐Sayed M. Abdelrahman
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Anomaly ◽  
Gravity Data ◽  
Residual Gravity ◽  
Depth Determination ◽  
Residual Gravity Anomaly ◽  
Least Squares Approach

In the article by Gupta, the problem of depth determination of a buried structure from the residual gravity anomaly has been transformed into a problem of finding the solution of a nonlinear equation of the form f(z) = 0. Gupta begins his formulation of the problem with equation (1) from Mettleton (1942) Eq. (1) [Formula: see text]

scholarly journals Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 609 ◽  
Author(s):  
Lijuan Wan ◽  
Ximei Liu ◽  
Feng Ding ◽  
Chunping Chen
Keyword(s):  
Least Squares ◽  
Moving Average ◽  
Identification Problem ◽  
Autoregressive Moving Average ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
Hierarchical Identification ◽  
Iterative Search ◽  
Time Varying Parameters ◽  
Equation Error

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.

Sign in / Sign up

Export Citation Format

Share Document