A New Ionospheric Model for Single Frequency GNSS User Applications Using Klobuchar Model Driven by Auto Regressive Moving Average (SAKARMA) Method Over Indian Region

Abstract

The single-frequency users of Global Navigation Satellite System (GNSS) require an effective mathematical model that mitigate the dominant errors due to ionospheric delays. Klobuchar model approximately reduces ionospheric effect up to 50% through its coefficients in the navigation message, which is not sufficient for the GNSS single frequency users at critical applications. Hence, a new model, for Single Frequency GNSS User Applications using Klobuchar model driven by Auto Regressive Moving Average Method (SAKARMA) is proposed to forecast and enhance the precision of ionospheric delay estimations for GNSS users. The hourly VTEC maps are obtained from the Assimilated Indian Regional Vertical Total Electron Content (AIRAVAT) by the process of data assimilation using the Kalman filter exclusively for the Indian region (longitude: 65 • E to 100 • E; latitude: 5 • N to 40 • N) using 26 GPS TEC stations over Indian region. The accuracy of the SAKARMA model is investigated using the AIRAVAT maps for various Indian geographic regions during both geomagnetic quiet and disturbed conditions of September month in 2016 year. Furthermore, in order to test SAKARMA model, a dual-frequency Navigation with Indian Constellation (NavIC) receiver located at the KL Education Foundation, Guntur, India (geographic: 16.37 • N, 80.37 • E; geomagnetic: 7.44 • N, 153.75 • E) is used to collect the observations during 2-12 September 2017. Furthermore, SAKARMA model is also validated with Klobuchar model, Klobuchar-style coefficients provided by the Center for Orbit Determination in Europe (CODE) (CODKlob) Model, BeiDou System (BDS2) Model and NeQuick 2 Model over a low latitude NavIC station in forecasting the ionospheric delays. The experimental results of SAKARMA for NavIC have revealed that the MAPE for proposed SAKARMA model is 9-17% (accuracy: 83-91%), while 34-53% (accuracy: 47-66%) for the Klobuchar model. Thus, the results illustrate that the proposed SAKARMA model is capable of predicting the ionospheric delays for single frequency GNSS/NavIC users. INDEX TERMS GNSS, NavIC, ionospheric delay, Klobuchar model, auto regressive moving average (ARMA) model, SAKARMA model. The associate editor coordinating the review of this manuscript and approving it for publication was Halil Ersin Soken .

Effect of Higher-Order Ionospheric Delay on Precise Orbit Determination of GRACE-FO Based on Satellite-Borne GPS Technique

“…By comparison, it can be found that due to different frequencies of L1 and L2, the influence of the higher-order term of the ionosphere on L1 and L2 band signals is different. According to Equation (8) and Equation (11), the influence of the second-order term on L2 is about 2.11 times that on L1, and the influence of the third-order term on L2 is about 2.71 times that on L1 [41] .…”

“…Ionospheric delay is one of the main error terms in satellite-borne GPS POD technology. The variation of electron density distribution with time and space results in the complexity of ionospheric delay [10][11][12] . How to deal with ionospheric delay is an important factor to improve POD precision.…”

Efficient FPGA Implementation of a Dual-Frequency GNSS Receiver with Robust Inter-Frequency Aiding

“…In this case, the ambiguity of the RZ CL code, CL amb , cannot be solved by the bit-boundary given its extremely long code duration (1500 ms). The ionospheric delay of each channel is solved as TEC × 40.3 /c f 2 using the Klobuchar algorithm [21,22], which is a curve fitting technique that considers eight inputted Klobuchar coefficients obtained from the navigation messages. This delay was found to be proportional to the TEC and inversely proportional to a square of the carrier frequency f and speed of light c. In this model, the value of 40.3 was the so-call Klobuchar factor [20], which is computed to reduce the ionospheric root mean square range error by 57% [23].…”

“…That is to say, the amb CM is solved as "1" for the assist Equation ( 5) by the tracked bit edge. Hence, a simplified relationship of the two code phases (τ L1 , τ L2 ) is shown as: Klobuchar algorithm [21,22], which is a curve fitting technique that considers eight inputted Klobuchar coefficients obtained from the navigation messages. This delay was found to be proportional to the TEC and inversely proportional to a square of the carrier frequency f and speed of light c .…”

Study of Spatial and Temporal Variations of Ionospheric Total Electron Content in Japan, during 2014–2019 and the 2016 Kumamoto Earthquake

“…Regional ionospheric models include polynomial model (POLY), spherical cap harmonic function (SCH), auto-regressive moving average (ARMA), etc. [ 6 , 7 , 8 ]. However, different models have different performance and spatial resolutions, and their applications in different regions need to be verified by further work.…”