You are involved in the search for a lost passenger plane. It appears that the p

Question

You are involved in the search for a lost passenger plane. It appears that the plane has been redirected and its modern location reporting systems have been disabled. You discover that your company's geostationary satellite received signals transmitted from an unidentified aircraft that may be the missing plane. These signals only tell you the distance of the craft from the satellite, but you realize that frequency shifts in the signals should also contain information on the aircraft's speed away from or towards the satellite. Here are the data you received. Note that the distance from satellite quoted is the ground distance, that is, the distance between the satellite's position projected down to the earth's surface and the plane's position projected down to the surface. You assume that the frequency shifts are corrected to relate to the ground speed of the plane relative to the ground location of the satellite at ON, 59degree E. Your job is to identify possible latitudes and longitudes where the plane ran out of fuel. The plane you are seeking has a range of 10 000 km after 1800 UTC. You will need to integrate the distance along the path you find, and use a zero finding algorithm, such as the Newton Raphson method, to find the position along the extrapolated path where the plane may have stopped. You should assume the plane was traveling at around 800 kmh. Useful facts: The Doppler shift in frequency is measured around the satellite carrier frequency of 1375 MHz. The Doppler shift can be written as delta f/fc = u/c where u is the speed of the plane directly towards the satellite location. A shift of one degree of latitude is about 111 km distance. The length of one degree of longitude depends on the latitude at which it is traversed. The size of one degree of longitude can be written in km approximately as delta long = 111cos phi where phi is the latitude. If you need to integrate a distance along the plane's projected track, you can integrate the derivative to get an arc length using: S = integral ds = integral 1 + (dy/dx)2 dx are the distances in the north-south and east-west directions, respectively.

Explanation / Answer

I = imread('image.bmp'); %I is logical 300x300 image. Acc = zeros(100,100,100,100); for i = 1:300 for j = 1:300 if I(i,j)==1 for x0 = 3:3:300 for y0 = 3:3:300 for a = 3:3:300 b = abs(j-y0)/sqrt(1-((i-x0)^2) / (a^2)); b1=floor(b/3); if b1==0 b1=1; end a1=ceil(a/3); Acc(x0/3,y0/3,a1,b1) = Acc(x0/3,y0/3,a1,b1)+1; end end end end end end

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