Yasin Hassan Project 2

We are trying to find your location using four satellites.

For my formulas,b = [(x-A(1))^2+(x-B(1))^2+(x-C(1))^2-(c(t(1)-d))^2;(x-A(2))^2+(x-B(2))^2+(x-C(2))^2-(c(t(2)-d))^2;(x-A(3))^2+(x-B(3))^2+(x-C(3))^2-(c(t(3)-d))^2;(x-A(4))^2+(x-B(4))^2+(x-C(4))^2-(c(t(4)-d))^2].

Then, my dr is A=dr = [dr1/A1 dr1/B1 dr1/C1 dr1/t1;dr2/A2 dr2/B2 dr2/C2 dr2/t2;dr3/A3 dr3/B3 dr3/C3 dr3/t3;dr4/A4 dr4/B4 dr4/C4 dr4/t4].

I did this so I could use Newton's medthod, x_n=x_(n-1) - A\b;

The initial position is [0;0;6370;0]. For problem 1, I got 1.0e+003 *(-0.04177270957085,-0.01678919410654,6.37005955922333,-0.00000320156583. The true location was (x,y,z,d)=(-41.77271, -16.78919, 6370.0596, -3.201566 * 10^-3).

The true location for problem 4-6 is The true location is [0;0;6370;.0001].

For problem 4, we changed the time values by 10^-8. For one trial, I did +,-,+,- 10^-8 for the t values and found the EMF, which was 3.19175982379753. When I did -,+,-,+ 10^-8 for the t values, I got an EMF of 3.19175273487148.

For problem 5, I made the satellitles closer together by 5% and kept the same 10^-8 time rule. For one trial, I did +,-,+,- 10^-8 for the t values and found the EMF, which was 3.13866977190569e+005. When I did -,+,-,+ 10^-8 for the t values, I got an EMF of 3.22118820187518e+005.

For problem 6, I used 8 satellites. Without the 10^-8 time rule, The EMF for far sattelites I got was 0.03335640951982. For satellites 5% apart, I used the 10^-8 rule. I got an EMF of 3.58907267574255e+004 for +,-,+,-,+,-,+,- 10^-8 time values. For -,+,-,+,-,+,-,+ 10^-8 time values, I got 3.58001686478463e+004.