Once the receiver has computed the range for at least ______ satellites, it processes a three-dimensional position that is accurate to about ______ meters.

Once the receiver has computed the range for at least ______ satellites, it processes a three-dimensional position that is accurate to about ______ meters.

• A. 3, 15
• B. 4, 33
• C. 5, 50
• D. 6, 100

Answer: (B)

The key idea is that you must solve for four unknowns to get a 3D position with GPS: the receiver’s x, y, z coordinates and its clock bias relative to GPS time. Each satellite measurement provides a distance (a pseudorange) that defines a sphere around the satellite’s known position. With four independent ranges from four satellites, you have four spheres that intersect in a single point, which gives both the position and the receiver’s time offset. Once you have ranges from at least four satellites, the computation yields a three-dimensional position, and for typical civilian GPS in open sky, that fix is about 33 meters accurate. More satellites and better geometry improve the accuracy, while poor geometry or errors in the measurements can make it worse.

The key idea is that you must solve for four unknowns to get a 3D position with GPS: the receiver’s x, y, z coordinates and its clock bias relative to GPS time. Each satellite measurement provides a distance (a pseudorange) that defines a sphere around the satellite’s known position. With four independent ranges from four satellites, you have four spheres that intersect in a single point, which gives both the position and the receiver’s time offset. Once you have ranges from at least four satellites, the computation yields a three-dimensional position, and for typical civilian GPS in open sky, that fix is about 33 meters accurate. More satellites and better geometry improve the accuracy, while poor geometry or errors in the measurements can make it worse.