Terrain Referenced Navigation Using a Multilayer Radial Basis Function-Based Extreme Learning Machine

Algorithm 1

Proposed ML-RBF-ELM algorithm.

(1) Prepare a training set where is the input data with the normalized longitude and latitude and is the normalized terrain height in the DEM

(2) Set the activation function of the 1st hidden layer, , by equation (2) and assign the center and width of the RBF by K-means clustering

(3) Calculate the 1st hidden layer output matrix by equation (3)

(4) Calculate the output weight matrix of the 1st hidden layer, where

(5) Calculate the new input data of the 2nd hidden layer:

(6) Set the activation function of the 2nd hidden layer, , by equation (2) and assign the center and width of the RBF by K-means clustering

(7) Calculate the 2nd hidden layer output matrix by equation (3)

(8) Calculate the output weight matrix of the 2nd hidden layer, where

(9) Calculate the new input data of the 3rd hidden layer:

(10) Set the activation function of the 3rd hidden layer, , by equation (2) and assign the center and width of the RBF by K-means clustering

(11) Calculate the 3rd hidden layer output matrix by equation (3)

(12) Calculate the output weight matrix of the 3rd hidden layer,

(13) Compute and verify the regression results,