scholarly journals Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 558 ◽  
Author(s):  
Hao Ma ◽  
Jian Pan ◽  
Lei Lv ◽  
Guanghui Xu ◽  
Feng Ding ◽  
...  
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Original System ◽  
Parameter Estimates ◽  
Recursive Algorithms ◽  
Parameter Vector ◽  
Identification Problems ◽  
Hierarchical Identification ◽  
Output Error ◽  
Parameter Identification Problems

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

scholarly journals The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jiling Ding
Keyword(s):  
Least Squares ◽  
Identification Problem ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
Input Output ◽  
Iterative Identification ◽  
Hierarchical Identification ◽  
Output Error ◽  
Gradient Based ◽  
Simulation Results

This paper considers the identification problem of multi-input-output-error autoregressive systems. A hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm are presented by using the hierarchical identification principle. A gradient based iterative (GI) algorithm and a least squares based iterative (LSI) algorithm are presented for comparison. The simulation results indicate that the H-LSI algorithm can obtain more accurate parameter estimates than the LSI algorithm, and the H-GI algorithm converges faster than the GI algorithm.

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.

Time Domain Method for Parameter System Identification

1990 ◽  
Vol 112 (3) ◽  
pp. 281-287 ◽  
Author(s):  
A. Hac ◽  
P. D. Spanos
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Degree Of Freedom ◽  
Parameter Estimates ◽  
Noisy Environment ◽  
Adaptive Kalman Filter ◽  
System Parameters ◽  
System Equation ◽  
Two Degree Of Freedom ◽  
Low Computational Cost

In this paper a method of parameter identification for a multi-degree-of-freedom structural system in a noisy environment is presented. The method involves an iterative procedure in which initial parameter estimates are obtained by relying on a least squares kind of approximation. This estimate is used in an adaptive Kalman filter to obtain an improved estimate of the system state. The improved estimate is then utilized in the least squares approximation to produce refined estimates of the system parameters. The iteration is repeated until it converges within an acceptable margin. The parameter errors are compensated during filtering by adding pseudonoise to the system equation; the noise itensity is updated in each iteration. Results of a simulation study conducted for a two-degree-of-freedom system indicate that the method can yield, for a relatively low computational cost, reliable estimates of system parameters, even when the data record is short.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

From acoustic to elastic inverse extended Born modeling: a first insight in the marine environment

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Milad Farshad ◽  
Hervé Chauris
Keyword(s):  
Least Squares ◽  
Marine Environment ◽  
Computational Cost ◽  
Physical Parameters ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Physical Density ◽  
Acoustic Approximation

Elastic least-squares reverse time migration is the state-of-the-art linear imaging technique to retrieve high-resolution quantitative subsurface images. A successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we extend the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density, P- and S-wave impedance models. We restrict the extension to marine environment, with the recording of pressure waves at the receiver positions. Firstly, we replace the acoustic Green's functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first illustrate the consequences of acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then we demonstrate that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.

Initialization of Identification of Fractional Model by Output-Error Technique

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Abir Khadhraoui ◽  
Khaled Jelassi ◽  
Jean-Claude Trigeassou ◽  
Pierre Melchior
Keyword(s):  
Numerical Simulation ◽  
Least Squares ◽  
Fractional Order ◽  
Fractional Integration ◽  
New Approach ◽  
Fractional Model ◽  
Output Error

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

SYSTOLIC ALGORITHMS FOR RECURSIVE TOTAL LEAST SQUARES PARAMETER ESTIMATION AND MIXED RLS/RTLS PROBLEMS

1993 ◽  
Vol 04 (01) ◽  
pp. 55-68 ◽  
Author(s):  
MARC MOONEN
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Total Least Squares ◽  
Parallel Architectures ◽  
Least Squares Estimation ◽  
Recursive Least Squares ◽  
Recursive Algorithms ◽  
Least Squares Problems ◽  
Linearly Constrained ◽  
Systolic Algorithms

Total least squares parameter estimation is an alternative to least squares estimation though much less used in practice, partly due to the absence of efficient recursive algorithms or parallel architectures. Here it is shown how previously developed systolic algorithms/architectures for recursive least squares estimation can be used for recursive total least squares problems. Unconstrained as well as linearly constrained and "mixed RLS/RTLS" problems are considered.

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