JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year GLOBAL POSITIONING SYSTEM Previous Question Paper (December - 2020 - R16)

Determining user position and velocity from satellite ephemeris involves processing navigation messages to compute the satellite's coordinates and then solving the navigation equations. The process is divided into two primary stages: satellite state vector calculation and user position/velocity estimation.

First, the satellite position is calculated using the broadcast ephemeris parameters (Keplerian elements). The steps are:

1. Calculate the mean motion and the mean anomaly at the time of transmission.
2. Determine the eccentric anomaly by solving Kepler's equation iteratively.
3. Calculate the true anomaly and the argument of latitude.
4. Apply corrections for second-order perturbations (inclination, argument of latitude, and radial distance).
5. Transform the coordinates from the orbital plane to the Earth-Centered, Earth-Fixed (ECEF) frame using the rotation matrices involving the longitude of the ascending node and inclination.

Second, the user position is determined using the pseudorange measurements. The fundamental observation equation is:

Where (x, y, z) is the user position, (x_s, y_s, z_s) is the satellite position, dt is the receiver clock bias, and dT is the satellite clock bias. Since there are four unknowns (x, y, z, and clock bias), at least four satellite measurements are required. These non-linear equations are typically solved using the Least Squares Estimation or Kalman Filtering by linearizing the equations around an initial guess using a Taylor series expansion.

To determine the user velocity, the Doppler shift measurements are utilized. The rate of change of the pseudorange (pseudorange rate) is related to the user velocity vector and the satellite velocity vector. By differentiating the pseudorange equation with respect to time, we obtain:

Here, ṙ is the range rate, u is the line-of-sight unit vector, v_u is the user velocity, and v_s is the satellite velocity. By measuring the Doppler shift from at least four satellites, the user velocity components (v_x, v_y, v_z) and the receiver clock drift rate can be solved using a similar linear system of equations.

The Global Positioning System (GPS) architecture is comprised of three primary segments that work in coordination to provide precise positioning, navigation, and timing services.

Space Segment: This segment consists of a constellation of at least 24 satellites orbiting the Earth in six orbital planes at an altitude of approximately 20,200 km. Each satellite transmits continuous L-band signals containing navigation data, including precise time, satellite health, and orbital parameters (ephemeris). The constellation is designed to ensure that at least four satellites are visible from any point on Earth at any time, which is the minimum requirement for 3D positioning.

Control Segment: This segment is responsible for the monitoring, maintenance, and management of the satellite constellation. It includes a Master Control Station (MCS), several monitor stations, and ground antennas located globally. The monitor stations track the satellites to collect ranging data, which is sent to the MCS. The MCS processes this data to calculate precise satellite orbits and clock corrections, which are then uploaded to the satellites via ground antennas to ensure the accuracy of the navigation messages broadcast to users.

User Segment: This segment consists of all GPS receivers and the processing software used by individuals, military, and commercial entities. A GPS receiver captures signals from multiple satellites simultaneously, measures the time of arrival of these signals to determine the distance (pseudorange) to each satellite, and solves a set of equations to calculate the user's 3D position (latitude, longitude, and altitude) and precise time. Modern receivers are integrated into various devices, including smartphones, aviation navigation systems, and surveying equipment.