GNSS Array-Based Ionospheric Spatial Gradient Monitoring: Precision and Integrity Analyses

Integrity monitoring and reliable detection of the ionospheric spatial gradient is of importance for various fields including total electron content modeling, radio communication and radar, and differential GNSS applications such as landing, departure and surface operations at an airport. In this contribution, we investigate the precision and the integrity of the ionospheric spatial gradient estimation upon the double-differenced (DD) array-based GNSS model of observations. Closed-form expressions for the variance matrix of the ionospheric spatial gradient and the corresponding uniformly most powerful invariant (UMPI) minimal detectable biases (MDBs) are provided for different scenarios, through which we assess the importance of several contributing factors. The closed-form expressions will show that the precision of the ionospheric spatial gradient estimator and its detectability are independent of our choice for the reference receiver and the reference satellite when forming the DD equations. In this contribution it will be shown how the precision of the estimated ionospheric spatial gradient and its MDB depend on and benefit from the number of receivers, number of satellites, number of frequencies, and the size and geometry of the array.