Describe the standard GNSS measurement model used in navigation filters.

• A. Pseudorange (and sometimes carrier phase) measurements modeled as true range plus receiver and satellite clock biases, ionospheric/tropospheric delays, multipath, and measurement noise; linearized for EKF with line-of-sight geometry.
• B. Only pseudorange without biases
• C. Only velocity measurements from Doppler
• D. Attitude measurements

Answer: (A)

The main idea is that a GNSS pseudorange measurement is modeled as the true geometric distance between the receiver and a satellite, plus clock biases and various delays and errors, with randomness treated as noise. Specifically, observed pseudorange equals the geometric range (the straight-line distance from the receiver’s position to the satellite’s known position) plus the receiver clock bias (the receiver’s time offset) minus the satellite clock bias, plus ionospheric and tropospheric delays, plus multipath effects and measurement noise. This reflects the reality that both the receiver and the satellite clocks are imperfect and that signals travel through the atmosphere and can reflect off surfaces.

Because the geometric range depends nonlinearly on the receiver’s position and the satellite’s position, the measurement model is nonlinear and is linearized for use in navigation filters like the Extended Kalman Filter. Each satellite contributes a row to the measurement Jacobian, with partial derivatives equal to the line-of-sight direction from the receiver to that satellite; this line-of-sight geometry is what links the measurements to the unknown state (typically receiver position and receiver clock bias, and sometimes clock drift or biases for satellites).

Delays are treated with physical models or mitigations: ionospheric delay is frequency-dependent and is often reduced by dual-frequency measurements or modeled as part of the state; tropospheric delay is modeled with a zenith delay and a mapping function to convert it to the satellite’s elevation angle; multipath and measurement noise are treated as stochastic errors, usually assumed Gaussian in the filter framework. Carrier-phase measurements can also be included for higher precision, with ambiguities handled separately.

This combination—pseudorange as true range plus clock biases, atmospheric delays, multipath, and noise, with a nonlinear relationship to the receiver state that’s linearized for EKF usage—constitutes the standard GNSS measurement model used in navigation filters.