Recursive Maximum Likelihood Estimation Method for Parameter Identification - MATLAB Source Code

The MATLAB source code for parameter identification using Recursive Maximum Likelihood Estimation can be implemented through the following steps: 1. First, input the known parameter values into the model. This initialization step typically involves setting up system matrices and initial parameter estimates using MATLAB's matrix operations. 2. Then, through a recursive approach, attempt to find the optimal parameter combination. The recursive implementation uses iterative updates where each new data point refines the parameter estimates, often employing Kalman filter-like equations for efficient computation. 3. In each recursive step, calculate the likelihood function and maximize it. This involves computing the innovation sequence and updating the parameter estimates using gradient ascent or Newton-Raphson methods, implemented through matrix operations and optimization functions. 4. Repeat the above steps until the optimal parameter combination is found. The iteration continues until convergence criteria are met, monitored through parameter change thresholds or likelihood improvement metrics. When implementing this algorithm, the following points require attention: - Data Preprocessing: Input data needs preprocessing to ensure it meets model requirements. This includes normalization, outlier removal, and ensuring stationarity using MATLAB's data filtering and statistical functions. - Algorithm Parameters: Certain algorithm parameters must be configured, such as iteration count, convergence threshold, and learning rates, to control the algorithm's convergence speed and accuracy. These are typically defined as configurable constants at the beginning of the MATLAB script. - Result Analysis: The results obtained from the algorithm need thorough analysis to evaluate effectiveness and reliability. This involves computing confidence intervals, performing residual analysis, and validating against test datasets using MATLAB's statistical toolbox. Therefore, the MATLAB source code for recursive maximum likelihood estimation parameter identification can be implemented following these steps, with careful attention to the above considerations for robust and efficient performance.