JNTU B.Tech IV GLOBAL POSITIONING SYSTEM Previous Question Paper (September - 2022 - R16)

Trilateration is a geometric technique used to determine the unknown position of a point by measuring its distance from multiple known reference points. In the context of GPS, the reference points are satellites with precisely known orbital positions. By measuring the signal propagation time from at least four satellites, the receiver calculates its distance from each, forming spheres of radius equal to the measured range.

The position estimation process follows these steps:

1. Each satellite broadcasts its position and a precise timestamp. The receiver calculates the signal travel time by comparing the timestamp with its local clock, determining the pseudo-range.
2. A single satellite defines a sphere of possible locations. Two satellites intersect to form a circle. Three satellites intersect at two points, one of which is typically on the Earth's surface.
3. Because the receiver's clock is not perfectly synchronized with the highly accurate atomic clocks on the satellites, there is a clock bias. This creates a fourth unknown variable.
4. To solve for the four unknowns (latitude, longitude, altitude, and receiver clock bias), a minimum of four satellites is required. The system of equations is represented as:

Where ρ_i is the pseudo-range to the i-th satellite, (x_i, y_i, z_i) are satellite coordinates, (x, y, z) is the receiver position, c is the speed of light, and Δt is the receiver clock bias.

GPS time is essential because the fundamental principle of GPS is based on the precise measurement of signal travel time. Since radio signals travel at the speed of light (approximately 3x10^8 m/s), an error of even one microsecond in timing results in a positioning error of roughly 300 meters.

GPS time is maintained by atomic clocks on board the satellites and at the ground control segment, providing a continuous, stable time scale that is independent of the rotation of the Earth. It is necessary to synchronize the receiver's local clock with the satellite system time to accurately resolve the pseudo-range equations. Without a common, highly accurate time reference, the synchronization between the satellite constellation and the user equipment would fail, rendering the trilateration process impossible.