Minimal Detectable Biases of GPS observations for a weighted ionosphere

The theory and application of statistical quality control is well established in precise positioning, navigation and geodesy. Quality control is made up of several contributing factors, one of which is internal reliability. Internal reliability describes the ability to find biases in observational data and is represented by the Minimal Detectable Bias (MDB). The MDB provides a diagnostic tool to infer the strength with which positioning models can be validated. In this contribution closed-form expressions will be given for the MDBs of GPS code and carrier observations for three different baseline models: the geometry-free model and two variants of the geometry-based model. These expressions apply to any number of carrier frequencies. The expressions take into account the presence of ionospheric disturbances by weighting these effects. As such, they are applicable to baselines of any length.