the standard deviation of ranging measurement error to the standard deviation of computed position error

clear all

close all

x1 = -30e3; % coordinates of ref station 1

y1 = 0;

x2 = 20e3; % coordinates of ref station 2

y2 = 0;

xu_true = 10e3; % true x coordinate of user

yu_true = 20e3; % true y coordinate of user [FOR CASE 2 THIS IS 5e3]

R1true = sqrt( (xu_true-x1)^2 + (yu_true-y1)^2);

R2true = sqrt( (xu_true-x2)^2 + (yu_true-y2)^2);

rng_std = 10; % standard deviation of the ranging measurement error

for i = 1:5000,

R1meas = R1true + rng_std*randn;

R2meas = R2true + rng_std*randn;

xu = 5e3; % initializing the initial guess of the user position

yu = 5e3;

delta_pos = [999999; 999999];

while norm(delta_pos) > 1e-3,

R1 = sqrt((xu-x1)^2+(xu-y1)^2) % top equation on slide 4 but use xu for x and yu for y;

% This is the computed distance from ref station 1 to the

% guessed user position

H(1,1) = (xu-x1)/R1 % (1,1) element of bottom right 2x2 matix on slide 4

H(1,2) = (yu-y1)/R1 % (1,2) element of bottom right 2x2 matix on slide 4

R2 = sqrt((xu-x2)^2+(yu-y2)^2) % similar as above

H(2,1) = (xu-x2)/R2

H(2,2) = (yu-y2)/R2

deltaR = [1600;100]; % this is a 2x1 vector consisting of the range

% measurements minus the ranges calculated from the

% ref stations to the guessed user position

delta_pos =[44.7;-22.5] % final equation on slide 4 (or use ordinary least

% squares; i.e., eqns 9 or 10 on page 2 of the

% Mod04 linearization handout)

xu = xu + delta_pos(1);

yu = yu + delta_pos(2);

end

xu_err(i) = xu - xu_true;

yu_err(i) = yu - yu_true;

horz_err(i) = sqrt(xu_err(i)^2 + yu_err(i)^2);

end

plot(xu_err,yu_err,'.')

ylabel('y error [m]')

xlabel('x error [m]')

axis equal

Htru(1,1) = (xu_true-x1)/R1true;

Htru(1,2) = (yu_true-y1)/R1true;

Htru(2,1) = (xu_true-x2)/R2true;

Htru(2,2) = (yu_true-y2)/R2true;

G = [1 0;1 0];

XDOP = 0.9

YDOP = 2.55

HDOP = 1.41

theoretical_x_err_std = 1414

sim_x_err_std = std(xu_err)

theoretical_y_err_std = 10;

sim_y_err_std = std(yu_err)

theoretical_h_err_std = 10^4;

sim_horz_err_std = sqrt( sim_x_err_std^2 + sim_y_err_std^2 );

Why i can not get my plot? When i run the program still running with out stop in the command windows, when i select pause stop and i have values in the workspace and in the command windows but the quit debugging show red(first time) im a new guys learning matlab but now im confuse. Any one can help me what is wrong with the program and guide me to the correct path?? thanks in advance.

Answer 1

[Abhishek Kumar]

Having studied your code, there seems to be a logical error in "while loop":

>>while norm(delta_pos) > 1e-3

compares "norm(delta_pos)" but delta_pos is hard coded with a fixed value within loop:

>>deltaR = [1600;100]; % this is a 2x1 vector consisting of the range

>> % measurements minus the ranges calculated from the

>> % ref stations to the guessed user position

>>delta_pos =[44.7;-22.5] % final equation on slide 4 (or use ordinary least

This results in an infinite loop. You need to correct this error, other than that, you can use "figure" container to hold the "plot":

>>figure;

>>plot(xu_err,yu_err,'.');

>>ylabel('y error [m]');

>>xlabel('x error [m]');

You can learn about "figure" by using following link:

https://www.mathworks.com/help/matlab/ref/figure.html