Recursive Algorithm for Least Squares Parameter Estimation

This text introduces a recursive algorithm for least squares parameter estimation. This algorithm computes a set of identification parameters including a1, a2, b1, and b2 through iterative updates. The parameter values obtained after algorithm execution are: a1 = -1.4981, a2 = 0.7038, b1 = 1.0476, b2 = 0.4704. The recursive implementation uses a covariance matrix update and gain calculation at each step, avoiding the need for full matrix inversion.

When implementing this algorithm, we obtain valuable information for system modeling. These parameters can optimize predictive models by minimizing the sum of squared residuals between observed and predicted values. The estimated parameters also help identify relevant factors in dynamic systems through transfer function coefficients or difference equation parameters. In code implementation, this typically involves initializing parameter vectors and covariance matrices, then updating them recursively as new data becomes available.

In summary, this algorithm provides an efficient computational method for recursive least squares estimation, enabling continuous parameter updates without reprocessing entire datasets. This approach significantly enhances our ability to understand and analyze time-varying systems through adaptive parameter tracking and real-time model refinement.