Abstract
The parameter estimation problem of the ARX model is studied in this paper. First, some traditional identification algorithms are briefly introduced, and then a new parameter estimation algorithm—the modified momentum gradient descent algorithm—is developed. Two gradient directions with their corresponding step sizes are derived in each iteration. Compared with the traditional parameter identification algorithms, the modified momentum gradient descent algorithm has a faster convergence rate. A simulation example shows that the proposed algorithm is effective.
Highlights
Complexity modified momentum gradient descent algorithm, which has a quicker convergence rate and no root calculation
E remainder of this paper is organized as follows
When θt is close to the true value, the calculated step size would be imprecise, which will cause the error to fluctuate. erefore, the steepest descent algorithm is inefficient
Summary
Complexity modified momentum gradient descent algorithm, which has a quicker convergence rate and no root calculation. To obtain the minimum value of J(θ), let the iteration function be As a special case of the MI-SG algorithm, when two sets of input-output data are performed in each iteration, we term it as two-innovation stochastic gradient (TI-SG) algorithm.
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