fast_TV.m

% Program by Saurav Kumaraswami Shastri, Shrikanth Yadav, Ghanashyam B. Chakravarthi, Viraj Kumar, Divya Rao A, Vinod Agrawal.
% This program computes Total Variance (TV) employing the fast algorithm proposed in [1].
% [1] S. M. Yadav, S. K. Shastri, G. B. Chakravarthi, V. Kumar, D. R. A and V. Agrawal, "A Fast, Parallel Algorithm for Fully Overlapped Allan Variance and Total Variance for Analysis and Modelling of Noise in Inertial Sensors," in IEEE Sensors Letters. doi: 10.1109/LSENS.2018.2829799 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8345576&isnumber=7862766
clc; clear all; close all;

%% Extracting Data

file_name = 'gyro2_x.txt';
raw = fopen(file_name,'r');
A = textscan(raw,'%f ');
fclose(raw);
x = cell2mat(A(1));
x = x(1:30000);

%% Computing TV

Corr_size = 1:1:10000;
len = 30000;
N = len*3-2;
count = 4;

tic;

w = x(1:len);
xpc = zeros(N,1);
xpc(1:len-1) = flip(w(1:len-1));
xpc(len:2*len-1) = w;
xpc(2*len:end) = flip(w(2:len));

tall1 = xpc(1:end-1);
tall2 = xpc(2:end);

tv = zeros(size(Corr_size')); % stores the TV values

for n = Corr_size
    
    temp = (tall2-tall1).^2;
    
    tv(n) = sum(temp) / (2*(3*len - 2*n - 1)*n*n);
    
    tall1 = (tall1(1:end-2) + xpc(n+1:end-n-1));
    tall2 = (tall2(2:end-1) + xpc(count:end));
    
    count = count + 2;
    
end

toc;