GPS Filtering

When available, GPS can provide a drift-free global position measurement.

Since these measurements are produced in a global frame, it is necessary to have a global to local frame transformation to utilize these measurements in a localization system.

Local Frame Initialization

Online Calibration

GPS Error Model

The GPS error model used is

\begin{align} \begin{bmatrix} \phi_m \\ \lambda_m \\ h_m \end{bmatrix} = \begin{bmatrix} \phi \\ \lambda \\ h \end{bmatrix} + \begin{bmatrix} n_\phi \\ n_\lambda \\ n_h \end{bmatrix} \end{align}

where

• \(\phi_m\) is the measured latitude,
• \(\lambda_m\) is the measured longitude,
• \(h_m\) is the measured altitude,
• \(\phi\) is the true latitude,
• \(\lambda\) is the true longitude,
• \(h\) is the true altitude, and
• \(n_\phi\), \(n_\lambda\), and \(n_h\) are Gaussian, white noise processes