RESEARCH COMMUNICATIONS CURRENT SCIENCE, VOL. 89, NO. 7, 10 OCTOBER 2005 1245 *For correspondence. (e-mail: ad_sarma@yahoo.com) Modelling of foF 2 using neural networks at an equatorial anomaly station A. D. Sarma 1, * and T. Madhu 2 1 Research and Training Unit for Navigational Electronics, Osmania University, Hyderabad 500 007, India 2 ECE Department, SRKR Engineering College, Chinna-Amiram, Bhimavaram 534 204, India The critical frequency of the F 2 -layer (foF 2 ) is an impor- tant parameter in estimating the total electron content (TEC) of the ionosphere, which is necessary for predi- cting the ionospheric time delay in GPS applications. The foF 2 data from Ahmedabad, which is in the equa- torial anomaly region, are modelled using a multilayer neural network trained with back-propagation algo- rithm. The IRI-2001 model together with this neural network model can be used for predicting/forecasting of the foF 2 parameter within the Indian subcontinent. The foF 2 values thus predicted can be used to estimate the critical TEC parameter. Keywords: Back-propagation, GPS, ionosphere, navi- gation, neural network. THE introduction of GPS has led to a major improvement in the worldwide navigation facilities. The positional accu- racy of GPS is limited by the precision in measuring the atmospheric time delays. Precise ionospheric and tropo- spheric time delay estimation is needed for achieving bet- ter accuracy in position fixing, satellite navigation and geodesy. While the refractive index of vacuum is unity for electromagnetic waves (radio waves), the presence of free electrons in the terrestrial ionosphere decreases the refractive index significantly below unity and thus increases the phase velocity of propagation. Since group velocity and phase velocity are inversely related, the group velocity of radio waves (which constitute the GPS signal) decreases and its value is considerably reduced below the free space velocity of propagation. For example, 1 total electron content unit (TECU) of 10 16 el/m 2 at GPS L 1 frequency (1.575 GHz) causes a delay of 0.54 ns. As the troposphere is a non- dispersive medium for frequencies up to 15 GHz, stan- dard models are available to accurately measure the time delay error. But as the ionosphere is an ever-changing medium, it is difficult to model it. Various electron den- sity models such as Bent and International Reference Ionosphere (IRI-2001) have been developed to estimate the TEC. However, these models are not effective in low lati- tude and anomaly region TEC modelling. Further, the ionosphere over India is known for its large temporal and spatial variability. The dominant variability is diurnal due to the large variation in incident solar radiation. This is true of all low latitude stations 1 . It is reported that the maxi- mum ionization occurs at around 1500 h local time in India 2 . As there is no suitable and dedicated TEC model avail- able for the Indian subcontinent (6–38°N), as a first step, it is proposed to model the foF 2 values using multilayered neural networks (MNNs). The neural network model can be used as a subroutine in IRI-2001 to increase the predic- tion accuracy of the model in the equatorial anomaly region. Earlier, Wintoft and Cander 3 used time-delay feed-forward neural networks with back-propagation to predict the hourly values of foF 2 at a single station. Also, Lamming and Cander 4 used the monthly median values of foF 2 along with month, local time and solar sunspot number (ssn) in predicting the foF 2 values at Poitiers station. However, no significant contribution is reported from the Indian research- ers in modelling the ionospheric parameters using MNNs. Hence, in this communication modelling of the Ahmeda- bad station foF 2 data over the solar cycle 20 (October 1964 to June 1976) is attempted using an MNN trained with back-propagation algorithm. As the Ahmedabad station (23.01°N, 72.60°E) is at the equatorial anomaly crest, day-to-day variations of the ionosphere are large, and model- ling of the ionospheric parameters at this station assumes significance. This model can be extended to other stations also. National Physical Laboratory (NPL), New Delhi collects ionospheric data from Delhi, Ahmedabad, Haringhata, Mumbai, Hyderabad, Tiruchirapalli, Kodaikanal and Thumba stations spread all over India. Here, the monthly median values of ionosonde foF 2 data of Ahmedabad station are used for modelling. The solar cycle comprised of 141 months. A few missing data values are replaced with those generated using the NPL-derived coefficients 5 . The data were arranged sequentially, month-wise, in four columns for use in the developed program. The four columns denote month, local time, SSN and ionosonde foF 2 data respecti- vely. Multilayered feed-forward neural networks became well known as a neural model after Rumelhart developed a learning algorithm called backwards error propagation or x 2 x 3 x 4 W 22 W 44 W 33 W 1 1 Output Layer nodes Hidden Layer nodes Input Layer nodes Input 1 2 3 4 1 2 8 1 Output X1 [W 1 ] X 2 [W 2 ] X 3 (y) Figure 1. Multilayer feed-forward neural network with input/output and one hidden layer.