PERFORMANCE EVALUATION OF IONOSPHERIC TEC FORECASTING MODELS USING GPS OBSERVATIONSAT DIFFERENT LATITUDES

In this paper, Holt-Winters model, ARMA model and ARIMA model in time series analysis were used to predict total electron content (TEC).Taking ionospheric grid data of quiet period and active period in different longitude and latitude provided by IGS center as sample data, the TEC data of the first 8 days were used to build four kinds of prediction models and forecast TEC values of the next 6 days, and the results were compared with the observations provided by IGS center. The prediction effects of the four models in different ionospheric environments and different longitude and latitude are emphatically analyzed. The experimental results showed that the average relative accuracy of ARMA, ARIMA and Holt-Winters models in the quiet and active ionospheric periods for the prediction of 6 days was 89.85% in the quiet period, and 88.76% in the active period. In both periods, the higher the latitude, the lower the RMS value. In addition, VTEC from IGS center value and ARMA model and ARIMA model and Holt Winters in the quiet period and active forecast VTEC values were compared, in the quiet period or active, four models of forecasting value can better reflect the spatial and temporal variation characteristics of TEC three latitude, the prediction results of the ARIMA model can better reflect the spatial and temporal variation characteristics; But compared with the active period, the prediction results of calm period are relatively good.  Corresponding author. Address: Guilin University of Technology, Guilin,541004, China. Email address: hn_liulilong@163.com. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W10, 2020 International Conference on Geomatics in the Big Data Era (ICGBD), 15–17 November 2019, Guilin, Guangxi, China This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLII-3-W10-1175-2020 | © Authors 2020. CC BY 4.0 License. 1175


INTRODUCTION
Distance from the ground, about 60~1000 km, the atmosphere is called the ionosphere, the radiation from the sun and cosmic rays and various kinds of high-energy charged particles under the action of gas molecules in the region of ionization or completely ionization, and release a lot of free electrons, in the process of satellite signal propagation these free electrons on the navigation and positioning accuracy of the deviation of several meters to tens of meters. Therefore, how to simulate and forecast the total electron content (TEC) in ionosphere and analyze the spatial and temporal distribution of ionosphere has become an important research focus. At present, there are mainly two models to predict the total electron content in the ionosphere. One is the empirical ionosphere model, such as Klobuchar (Klobuchar, 1996), Bent(Bent et al., 1975)and IRI (Patel et al.,2018).The other is to use TEC observation data for short-term prediction, such as neural network model (Chen et al.,2005), spectral analysis (Lu et al.,2014), least-squares configuration , and time series (Chen et al.,2011;Tang et al.,2013) Xi et al. (2015) used Holt-Winter model and maldives model to conduct short-term delay modeling and prediction methods in the ionospheric region of mid-latitude region. Kim et al. (2015) proved that satisfactory results can be obtained by using ARMA model to forecast ephemeris and clock correction in satellite enhanced system. Mandrikova et al. (2015) used ARIMA model to conduct short-term prediction of regional ionospheric parameters, which had a good prediction effect for the study area. Li et al. (2014) accurately simulated TEC data in ionospheric grids by using the ARIMA model of time series theory. Sivavaraprasad et al. (2017) tested the applicability of the ARIMA, ARMA and Holt-Winter addition and multiplication models to predict ionospheric TEC values under different spatial conditions in low latitudes.
Although the current prediction models have been effectively verified, more accurate and in-depth studies are needed to predict the ionospheric morphology at different latitudes. In the future, it is necessary to analyze the validity of these general time series prediction models under different ionospheric conditions. Therefore, in this paper, the global ionospheric map (GIM) provided by the international GNSS (IGS) center will be used to study and analyze the prediction accuracy of ARIMA, ARMA, Holt-Winter addition and multiplication models in different latitudes and ionospheric conditions, in the hope that the study of time series model can promote the development of the prediction of total ionospheric electron content.

Holt-Winters Exponential Smoothing Model
Holt-Winters exponential smoothing model is a prediction model based on time series data, which includes seasonless model, additive model and multiplication model. Additive model. Applicable to sequences with linear time trends and additive seasonal changes, the formula is: The multiplication model. Applicable to sequences with linear time trends and multiplicative seasonal changes, the formula is: The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W10, 2020 International Conference on Geomatics in the Big Data Era (ICGBD), 15-17 November 2019, Guilin, Guangxi, China In equations (1) and (2)

ARMA Model
Regressive and Moving Average Model is an important method for predicting time series. It is composed of auto-regressive (AR) and Moving Average (MA). The expression of ARMA model is:

ARIMA Model
Where, ∇ ‫ܫ‬ represents the ‫ܫ‬ seasonal difference of order with period as step length; is seasonal cycle; Φ is the seasonal autoregressive operator, ܴ is the order of seasonal autoregressive, and 、 、⋯、 is part of the parameters of seasonal autoregressive. Θ is the seasonal moving average operator, ‫ܯ‬ is the order of the seasonal moving average, and 、 、⋯、 is part of the parameters of the seasonal moving average.

The Data Source
In this paper, high-precision global ionospheric map (GIM) data provided by IGS center were used as sample sequences. and low latitude (5°N, 120°).

Accuracy Evaluation Index
Where, th is the ionospheric TEC value predicted by the model, is the observed ionospheric TEC value, e is the observed calendar element, is the observed calendar element.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W10, 2020 International Conference on Geomatics in the Big Data Era (ICGBD), 15-17 November 2019, Guilin, Guangxi, China   is not big, which is the largest in the low latitude, the second in the middle latitude and the least in the high latitude.

CONCLUSION
In this paper, ARIMA model, ARMA model, holt-winter addition model and multiplication model are adopted to make short-term prediction of ionospheric grid data of IGS center in quiet period and active period of different longitude and latitude, so as to analyze the prediction accuracy of different methods in different space-time environments. The analysis results are as follows: 1) use ARIMA model, ARMA model, holt-winter addition and multiplication model to make short-term prediction of total electron content in the ionosphere, and the prediction results of the four models can reach good accuracy. In the quiet ionospheric period, the average relative accuracy of ARIMA model is better than 86%, while the relative accuracy of holt-winter addition and multiplication model is roughly the same at low latitudes, and the relative accuracy of forecast value is about 91%.In the ionospheric activity period, the average relative accuracy of ARIMA model is better than 88%, and the relative accuracy of holt-winter addition and multiplication model is better than 89% and 90% respectively in middle and high latitudes.
2) in the quiet ionospheric period, the holt-winter addition The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W10, 2020 International Conference on Geomatics in the Big Data Era (ICGBD), 15-17 November 2019, Guilin, Guangxi, China model has the best prediction accuracy in mid-latitude area, the holt-winter multiplication model has the best prediction accuracy in low-latitude area, and the ARIMA model has the best prediction accuracy in high-latitude area. The ARMA model performs well in the middle latitude. The prediction effect of ARIMA model is the same in high, medium and low latitudes, and the prediction accuracy is above 85%.In the ionospheric activity period, the prediction effect of the holt-winter addition model and the multiplication model is basically the same, and its relative accuracy is better in the middle and high latitudes, but worse in the low latitudes. In terms of the relative accuracy of ARIMA model, it is better in high, medium and low latitudes, and the accuracy is better with the increase of latitudes. The ARMA model performs well in low latitudes.