Variable Altitude Cognizant Slepian Functions

We present an approach to calculate potential fields on a planet’s surface from regionally confined gradient data at spacecraft altitude, such as measurements of magnetic fields or gravitational acceleration. Our method uses altitude cognizant Slepian functions with a reference radial position that varies as a function of longitude and latitude. This is an evolution from previous altitude cognizant Slepian functions which use a fixed reference radial position. We demonstrate the advantage of these variable altitude cognizant Slepian functions over the fixed altitude cognizant Slepian functions and the classical Slepian functions using numerical tests.