Estimation of Navigation Mark Floating Based on Fractional-Order Gradient Descent with Momentum for RBF Neural Network

Table 1

Pseudocode of FGM-RBF for navigation mark drifting estimation.

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Algorithm 1: FOGDM-RBF for AIS interpolation

Input: Navigation mark position data, meteorological and hydrological data as training samples and testing samples

Output: the estimated drifting position of testing samples

1: function FOGDM ()

2: Initialization of the neural network model;

3: Initialization of neural networks with weights;

4: it = 0;

5: while it < maxIT and the training error does not meet the learning requirements

6:   Calculate the activation function of the neural network according to equation (7);

7:  Calculate the output of neural network according to equation (10);

8:   Calculate the output error of the neural network according to equation (15);

9:    Calculate the objective function according to (16);

10:   Calculate the caputo fractional derivative of the objective function according to (22);

11:    Update the momentum coefficient according to equation (20);

12:     Update the weight of the neural network according to equation (18);

13: it = it + 1;

14: end while

15: Use the obtained neural network weights and the input testing data set, calculate the estimated drifting position of testing samples.

16: End function

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