A fuzzy logic technique for correcting climatological ionospheric models

This paper reports on a fuzzy logic correction technique for the IRI90 climatological ionospheric model that uses a sparse set of GPS total electron content (TEC) measurements to provide a significant model correction over the entire sub-solar equatorial bulge. Crisp inputs, represented by a sparse set of GPS measurements of ionospheric TEC, are ingested into the fuzzy correction model which is composed of a set of fuzzy membership functions and a knowledge base (fuzzy rules). The fuzzy logic estimation is an iterative procedure that begins with the uncorrected model as the zero order prediction of the shape of the subsolar equatorial bulge. The measured data (inputs) are fuzzified to account for errors in the GPS measurements of TEC, and then are mapped onto fuzzy input-membership functions. The knowledge base is then accessed, firing the appropriate rules, to produce a fuzzy output estimate of the correction. This fuzzy estimate is then defuzzified to provide a crisp output correction that modifies the shape of the zero order prediction bulge to better fit the GPS data and to produce a first order prediction. The procedure is repeated until termination criteria are satisfied. The goal of the process is to accurately reproduce the characteristic signature of the ionospheric TEC along a satellite subtrack across the sub-solar equatorial bulge. The fuzzy logic model can make large scale alterations to the model prediction without requiring an extensive measurement data set and without inducing spikes in the local vicinity of the ingested data points. In particular, the IRI90 climatological model estimates of the ionospheric TEC were adjusted using two concurrent TEC measurements at locations approximately 800 km apart along the satellite ground track. For this first test, two simulated GPS measurements were derived from TOPEX dual-frequency TEC data. The results were compared with the TOPEX TEC measurements for four ground tracks in the Pacific across the subsolar equatorial bulge. Initial results showed a model improvement to within 0.32 TECU averaged over four entire passes ( 66 latitude) when compared with the TOPEX “ground truth” measured TEC along track profiles. (1 TECU equals 1016 electrons/m2.) The mean error over the equatorial portion of the passes ( 20 latitude) was 4.65 TECU. The fuzzy correction model was run for 18 iterations, approximately full convergence. The averaging over sunlit passes provides an upper bound on the error since the spatial and temporal sampling allowed by the equatorial application include night time passes with low TEC. The residual error is dominated by the failure to match the structure of the TEC peaks north and south of the geomagnetic equator. Incorporating measured global averaged ionospheric geomagnetic index and a local solar zenith angle as inputs to the fuzzy logic may allow this error to be reduced. Fine tuning of the fuzzy logic model rules and full development of the multi-GPS station ingestion scheme can now proceed given that this first test shows that potentially the fuzzy logic correction is able to produce a correction that could satisfy the equatorial basin-scale measurement needs for GFO.