Solving 4 equations with 4 unknowns.

hello everyone!

i have been trying to solve 4 equations with 4 unknowns but the result the code has been producing each time is a structure with values of 4 variables all equal to 0. Shown below is the code and the error.

% velocity of EM signal propagation %
c = 3e8;       % meters per second %
% assuming errors for reference station %
Ir = 10e-9;   % Ionospheric error, seconds %
Tr = 1.5e-9;  % Tropospheric error, sedconds %
Er = 12e-9;   % Ephemeris error, seconds %
Mr = 1e-9;    % Multipath error, seconds %
Rr = 1e-9;    % Reciever's noise, seconds %
Dr = 0.5e-9;  % Dilution of precsion, seconds %

%total error in reference station's pseudorange%
Tr = c*(Ir + Tr + Er + Mr + Rr + Dr);
% Assumed pseudoranges of the satellites 1,2,3 and 4 from the user U %
Ru1 = 222; 
Ru2 = 234;
Ru3 = 246;
Ru4 = 258;

syms x 
syms y
syms z
syms t
equation1 = Ru1 - ((((S1(1,1) - x)^2 + (S1(1,2) - y)^2 + (S1(1,3) -z)^2)^0.5) + c*t + Tr);
equation2 = Ru2 - ((((S2(1,1) - x)^2 + (S2(1,2) - y)^2 + (S2(1,3) -z)^2)^0.5) + c*t + Tr); 
equation3 = Ru3 - ((((S3(1,1) - x)^2 + (S3(1,2) - y)^2 + (S3(1,3) -z)^2)^0.5) + c*t + Tr); 
equation4 = Ru4 - ((((S4(1,1) - x)^2 + (S4(1,2) - y)^2 + (S4(1,3) -z)^2)^0.5) + c*t + Tr);

sol = solve(equation1,equation2,equation3,equation4);

thank y'all for your inputs in advance.

Answer 1

[Nikhil Sonavane]

Can you share S1, S2 and S3 matrices which you are using?

[Walter Roberson]

They just happen to be completely visible in the image of the IDE:

S1 = [118, 118, 117];
S2 = [130, 130, 130];
S3 = [140, 140, 140];
S4 = [152, 152, 152];

Answer 2

[Nikhil Sonavane]

You can refer to the Tips section of the documention of solve function. It states that "If solve cannot find a solution and ReturnConditions is true, solve returns an empty solution with a warning. If no solutions exist, solve returns an empty solution without a warning". I would suggest you check if your system of equations have a solution.

[Walter Roberson]

Maple is not finding any solution. I am working on some step-by-step work in Maple that just might find a solution.