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By utilizing measurements of the so-called pseudo range between an object and each of several earth orbiting GPS satellites, the object can be very accurately located in space. A general description of GPS can be found in the article, which you should read thoroughly, and in the detailed Web site. Additional technical information can be found in and other articles in. Using your knowledge of the nonlinear least-squares problem you will solve the problem of locating an object given GPS pseudo range data. A self-contained technical development, sufficient for you to perform this task, can be found in the appendix to this assignment and in the class lecture supplement on gradient descent GPS algorithms. Signals are sent from earth orbiting satellites to a receiver located on the surface of the earth. In principle, utilizing timing information and knowledge of the satellite orbit, the true range (the receiver-to-satellite distance) to each satellite can be measured. In practice the range measurement is error full due to a systematic error caused by an inaccurate receiver clock (to keep the cost of commercial GPS units low) and random errors due to atmospheric distortion, communication channel noise, sensor noise, etc. The error full range measurement is known as a pseudo range in order to distinguish it from the unknown true range (see the Appendix below). Because of the speed of light; the non-relativistic speeds of the satellites and receiver; and the close proximity of the satellites and object, it is assumed that during the time period needed to collect all the pseudo range information the satellites and receiver are motionless.
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