Random Sequence Generation Programs with System Identification Algorithms

This article presents comprehensive MATLAB implementations for system identification and signal generation algorithms. 【1】Random Sequence Generation Program: Implements probabilistic distribution functions (uniform, normal, etc.) using MATLAB's rand() and randn() functions with seed control for reproducible results. 【2】White Noise Generation Program: Creates zero-mean, constant-variance white noise sequences through Gaussian random number generation with variance normalization techniques. 【3】M-Sequence Generation Program: Generates maximum-length sequences using linear feedback shift registers (LFSR) with primitive polynomials for optimal autocorrelation properties in system identification. 【4】One-Step Least Squares Identification for Second-Order Systems: Implements batch matrix operations (pinv() function) to directly compute system parameters from input-output data matrices. 【5】Practical Pressure System Least Squares Identification: Incorporates real-world sensor data preprocessing before applying standard least squares estimation for industrial pressure systems. 【6】Recursive Least Squares Identification Program: Utilizes iterative matrix updates (RLS algorithm) with forgetting factors for efficient real-time parameter estimation with large datasets. 【7】Augmented Least Squares Identification Program: Extends standard least squares to handle uncontrollable systems through state augmentation and observability matrix construction. 【8】Gradient-Corrected Least Squares Program: Implements gradient descent optimization with adaptive step sizes to refine parameter estimates and improve convergence accuracy. 【9】Recursive Maximum Likelihood Identification Program: Combines Kalman filtering concepts with likelihood maximization for sequential parameter estimation under Gaussian assumptions. 【10】Bayes Identification Program: Applies Bayesian inference with prior distributions and posterior updates using conjugate priors for probabilistic parameter estimation. 【11】Modified Neural Network MBP Algorithm for Noisy System Identification: Employs multi-layer perceptrons with backpropagation enhancements for robust parameter estimation in high-noise environments. 【12】Multi-dimensional Nonlinear Function Identification MATLAB Program: Uses neural networks or polynomial basis expansions with regularization for complex nonlinear mapping identification. 【13】Fuzzy Neural Network Decoupling MATLAB Program: Implements hybrid fuzzy logic and neural networks with time-scale separation techniques for multi-rate system decoupling. 【14】F-test Method Partial Program: Calculates F-statistics from residual sums of squares to test model significance and validate parameter estimates against null hypotheses.