| The ionosphere is a region of partially ionized plasma in Earth's upper atmosphere distributed in layers of varying free electron density. The free electrons change the local index of refraction causing radio waves propagating in the ionosphere to be delayed and bent. Trans-ionospheric propagation of GPS radio signals transmitted from satellites provides observations, in a tomographic sense, of the electron density field by measuring the amount of delay and/or bending.; Tomographic estimation of the ionosphere is attractive for two reasons: one, the number of measurements grows as the product of the number of transmitters and receivers whereas for in situ techniques the number grows linearly in the number of sensors; two, the smoothing function of the integral operator makes the measurements most sensitive to large scale structure. A three-dimensional tomographic inversion algorithm is implemented as a real time process ingesting live measurements from a network of dual frequency GPS reference receivers.; The tomographic inversion technique is based on a state space model encompassing ionospheric parameters as well as certain measurement biases in the GPS satellite transmitters and reference receivers. Three different state space models were constructed using discrete spectra, separable lattice wavelets, and a hybrid of separable and non-separable two-dimensional wavelets.; The primary purpose of the real-time estimator is to provide an ionospheric model for correcting range delay errors on GPS measurements to differentially improve the position solution for aviation applications. Specifically, the Federal Aviation Administration is developing the Wide Area Augmentation System (WAAS) for GPS where positioning accuracy on the order of ones of meters is coupled with a six second time to alarm in the aircraft. In this application the real-time estimator ingests measurements from the GPS reference receiver network, applies the tomographic inversion to form an ionospheric model and transmits that model through a low bandwidth broadcast data link to the aircraft. Further, the estimator must provide a confidence interval for each and every correction to protect the navigation solution. Indeed this latter function is the most ambitious and critical in safety of life operations such as precision approach. |
