What are the main challenges and solutions for modeling GPS errors in geodetic surveys?

1 Sources of GPS errors

GPS errors can be classified into four categories: satellite, propagation, receiver, and multipath. Satellite errors are caused by the orbit, clock, and antenna of the GPS satellites. Propagation errors are caused by the refraction, ionization, and scintillation of the GPS signals as they travel through the atmosphere. Receiver errors are caused by the noise, bias, and drift of the GPS receivers and antennas. Multipath errors are caused by the reflection, diffraction, and scattering of the GPS signals by nearby objects.

2 Modeling GPS errors

Modeling GPS errors is the process of estimating and correcting the effects of the errors on the geodetic data. There are two main approaches to modeling GPS errors: empirical and stochastic. Empirical models use mathematical formulas or tables to describe the expected behavior of the errors based on physical principles or observations. Stochastic models use statistical methods to describe the random variation of the errors based on their probability distribution and covariance.

3 Empirical models

Empirical models are useful for reducing the systematic errors that have a known or predictable pattern. For example, satellite errors can be reduced by using the broadcast or precise ephemeris and clock corrections provided by the GPS service providers or other agencies. Propagation errors can be reduced by using the standard or modified atmospheric models that account for the pressure, temperature, humidity, and ionospheric conditions along the signal path. Receiver errors can be reduced by using the antenna phase center corrections that account for the offset and variation of the receiver antenna.

4 Stochastic models

Stochastic models are useful for reducing the random errors that have an unknown or unpredictable pattern. For example, multipath errors can be reduced by using the elevation-dependent weighting or filtering techniques that assign lower weights or higher variances to the signals with lower elevation angles or longer path lengths. Stochastic models can also be used to estimate the residual errors that are not accounted for by the empirical models. For example, the least-squares adjustment or the Kalman filter can be used to estimate the unknown parameters and error terms of the geodetic data.