A surveyor hiking in a dense forest canyon is trying to establish a highly precise 3D position (Latitude, Longitude, and Elevation) using a handheld GPS receiver. The receiver connects to only 3 satellites.

Explain why the receiver cannot calculate a precise 3D position and determine the minimum number of satellites required to establish a fully resolved 3D fix while correcting for receiver clock bias.

Two survey teams are using identical RTK GPS equipment to establish control points.

Explain which team will achieve higher positional accuracy and justify the answer using the concept of Geometric Dilution of Precision (GDOP).

A GPS receiver records the time it takes for a signal to travel from Satellite SV14 to the receiver's antenna. The measured travel time ($\Delta t$) is $0.068542$ seconds. Assume the speed of light ($c$) in a vacuum is exactly $299,792,458 \text{ m/s}$.

Calculate the basic pseudorange (distance) from the satellite to the receiver, ignoring atmospheric delays and clock biases.

In a simplified 1D GPS scenario, a receiver measures a pseudorange to a satellite directly overhead as $20,500,000 \text{ m}$. The true, known distance to the satellite (calculated via ephemeris data) is exactly $20,499,850 \text{ m}$. The speed of light ($c$) is $299,792,458 \text{ m/s}$.

Calculate the magnitude of the receiver's clock bias ($t_b$) in seconds, and determine whether the receiver's clock is running fast or slow compared to GPS time.

A surveyor calculates a GPS position fix. The estimated User Equivalent Range Error (UERE) caused by satellite orbit, atmospheric delay, and receiver noise is $\pm 4.5 \text{ m}$.

Calculate the estimated positional error ($\text{Error}_{3D}$) for two different epochs: