Stochastic Recursive Extended Least Squreas (RELS) of a dynamic syste
Updated 9 Jul 2016

% This function is made by Ahmed ElTahan
This function is intended to estimate the parameters of a dynamic
system of unknown parameters using the Recursive Extended Least Squares Method (RELS).
After an experiment, we get the inputs, the outputs of the system.
The experiment is operated with sample time Ts seconds.

The model is given by A(z) y(t) = B(z)sys u(t) + C(z) eps(t)
which can be written in
z^(-d) B(z) C(z)
y(t) = ------------------- u + ------------ e = L*u + M*e
A(z) A(z)
-- y : output of the system.
-- u : control action (input to the system).
-- e : color guassian noise (noise with non zero mean).
-- Asys = 1 + a_1 z^-1 + a_2 z^-2 + ... + a_na z^(-na). [denominator polynomail]
-- Bsys = b_0 + b_1 z^-1 + b_2 z^-2 + ... + b_nb z^(-nb). [numerator polynomail]
-- C = 1 + c_1 z^-1 + c_2 z^-2 + ... + c_nc z^(-nc). [noise characteristics]
-- d : delay in the system.
A and C are monic polynomials. (in output estimation of the stochastic
system as C is monic, we add e(t) to the estimation i.e. not starting from c1*e(t-1))

Function inputs
u : input to the system in column vector form
y : input of the system in column vector form
na : order of the denominator polynomail
nb : order of the numerator polynomail
nc : order of the characteristics of the noise (usually <=2 for max)
d : number represents the delay between the input and the output

Function Output
Theta_final : final estimated parameters.
Gz_estm : pulse (discrete) transfer function of the estimated parameters
1 figure for the history of the parameters that are being estimated
2 figure to validate the estimated parameters on the given output
using the instantaneous estimated parameters.
3 figure to plot the input versus time.

Note: the noise added shall not to be with a magnitude close to the
system output, it should be smaller, this is in simulation such as
here or the algorithm will go crazy that can't distinguish between
the main and the noisy signal (This can be measured in practical
case finding noise to signal ratio).

An example is added to illustrate how to use the funcrtion

Cite As

Ahmed ElTahan (2024). Ahmed-ElTahan/Stochastic-Recursive-Extended-Least-Squreas-RELS (https://github.com/Ahmed-ElTahan/Stochastic-Recursive-Extended-Least-Squreas-RELS), GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2014a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Find more on Simulation, Tuning, and Visualization in Help Center and MATLAB Answers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Versions that use the GitHub default branch cannot be downloaded

Version Published Release Notes


To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.