Questions: GNSS Satellite Positioning (GPS and Related Systems)

Question 1

Why does a GNSS receiver need signals from at least four satellites to find a 3D position?

• A. One satellite is needed for each of the four cardinal directions
• B. There are four unknowns: three position coordinates and the error in the receiver's clock
• C. Each satellite can see only one quarter of Earth
• D. Four signals are needed to cancel out the effect of the ionosphere

Answer: (B)

Distances come from signal travel times, so a clock error of even a millionth of a second shifts every distance by about 300 m. The receiver's cheap clock adds a fourth unknown, which requires a fourth measurement.

Question 2

Signal travel time is used to compute distance. If a timing error of 1 microsecond (10⁻⁶ s) went uncorrected, about how large would the distance error be?

Model answer: About 300 m, because radio signals travel at about 3 × 10⁸ m/s, and 3 × 10⁸ m/s × 10⁻⁶ s = 300 m.

This calculation shows why GNSS satellites carry atomic clocks and why receivers must solve for their own clock error.

Question 3

Differential GNSS improves accuracy by using a base station at a precisely known location to measure current errors and send corrections to nearby receivers.

• T. True
• F. False

Answer: True

Many error sources, such as signal delays in the ionosphere and small orbit and clock errors, are nearly the same for receivers close to each other. A base station that knows its true position can measure these errors and broadcast corrections. Real-time kinematic (RTK) methods that also track the carrier wave can reach centimeter-level accuracy.

Question 4

A surveyor's GNSS position in a narrow city street between tall buildings is much worse than in an open field. What is the most likely cause?

• A. The satellites move more slowly over cities
• B. Buildings block some satellites and reflect signals (multipath), and the remaining satellites are bunched in a poor geometry
• C. City air is too dense for radio waves
• D. GNSS does not work below 100 m elevation

Answer: (B)

Blocked signals reduce the number of usable satellites, and reflections make some signals travel a longer path. When the visible satellites are close together in the sky, small distance errors cause larger position errors; this effect is measured by dilution of precision (DOP).