A MATLAB/Octave toolbox for recursive parameter estimation and system identification. This repository implements various least squares estimation methods, from basic to advanced recursive algorithms with exponential forgetting.

• Basic Least Squares Estimation (MMQ)
• Weighted Least Squares (MMQP)
• Recursive Least Squares (MMQR)
• Recursive Least Squares with Exponential Forgetting (MMQRE)
• Built-in validation and regression tools
• Suitable for real-time parameter estimation
• Compatible with both MATLAB and Octave

The basic least squares estimator.

[Theta] = MMQ(PHI, Y)

• PHI: Regressor matrix
• Y: Output vector
• Returns: Estimated parameters Theta

A weighted version of the least squares estimator.

[Theta] = MMQP(PHI, Y)

• PHI: Regressor matrix
• Y: Output vector
• Returns: Estimated parameters Theta
• Features: Implements a weighting scheme (0.6) for datasets with less than 60 samples

A recursive least squares estimator.

[THETA, Pk] = MMQR(P, Phi, Theta, y)

• P: Covariance matrix
• Phi: Current regressor vector
• Theta: Current parameter estimate
• y: Current output measurement
• Returns:
  • Updated parameters THETA
  • Updated covariance matrix Pk

An extended version of MMQR with exponential forgetting factor.

[THETA, Pk] = MMQRE(P, Phi, Theta, y, L)

• P: Covariance matrix
• Phi: Current regressor vector
• Theta: Current parameter estimate
• y: Current output measurement
• L: Forgetting factor (lambda)
• Returns:
  • Updated parameters THETA
  • Updated covariance matrix Pk

% Example data
PHI = [1 2; 3 4; 5 6];  % Regressor matrix
Y = [1; 2; 3];          % Output vector

% Estimate parameters
Theta = MMQ(PHI, Y);

% Initial setup
P = eye(2);             % Initial covariance matrix
Theta = zeros(2,1);     % Initial parameter estimate

% For each new measurement
for k = 1:N
    phi = [x1(k); x2(k)];  % Current regressor vector
    y = y(k);              % Current measurement
    
    % Update parameters
    [Theta, P] = MMQR(P, phi, Theta, y);
end

% Initial setup
P = eye(2);             % Initial covariance matrix
Theta = zeros(2,1);     % Initial parameter estimate
lambda = 0.95;          % Forgetting factor

% For each new measurement
for k = 1:N
    phi = [x1(k); x2(k)];  % Current regressor vector
    y = y(k);              % Current measurement
    
    % Update parameters with forgetting
    [Theta, P] = MMQRE(P, phi, Theta, y, lambda);
end

• The MMQP function automatically applies a weighting factor of 0.6 for datasets with less than 60 samples
• For MMQRE, the choice of the forgetting factor (lambda) is important and should be tuned based on:
  • Data velocity
  • Amount of data
  • System dynamics
• Typical values for lambda range between 0.95 and 0.99

• Henrique Perez Gomes da Silva
• hperez@unifei.edu.br
• Maid with ❤️ in UNIFEI - Federal de Itajubá :)
• Tnx to Prof. Jeremias B. Machado