پيش‌ بيني كوتاه‌ مدت سري زماني تغييرات طول روز با روش SSA+ARMA

Short-term Prediction of the LOD Time-series using a Combined SSA+ARMA Method

پارامترهاي دوران زمين نقش بسيار مهمي در مسائل مربوط به ژئودزي فضايي مانند تعيين دقيق مدار ماهواره‌ها، نجوم ژئودزي، ناوبري فضايي و همچنين مطالعه‌ي پديده‌هاي ژئوفيزيكي دارند. سري‌هاي زماني اين پارامترها داراي رفتارهاي تناوبي و تصادفي مي‌باشند لذا روش‌هاي متنوع آناليز سري‌هاي زماني با دقت‌هاي متفاوت از گذشته تاكنون مورد بررسي قرار گرفته است. يكي از مهم‌ترين نيازهاي پيش‌بيني براي اين پارامترها، پيش‌بيني‌هاي كوتاه‌مدت آن‌هاست زيرا باتوجه به پيچيدگي‌هاي پردازش، به‌صورت لحظه‌اي در اختيار كاربران قرار ندارند.‌ در ميان پيش‌بيني‌ سري‌هاي زماني اين پارامتر‌ها، پيش‌بيني مولفه‌ي LOD بشدت چالش برانگيز است زيرا عوامل مختلف ژئوفيزيكي بر روي ساختار اين سري زماني اثر مي‌گذارند. در اين تحقيق به پيش‌بيني‌هاي 10 روزه پارامتر LOD، به‌وسيله‌ي تركيب روش غير پارامتريك SSA و مدل پيش‌بيني ARMA پرداخته شده است. اين پيش‌بيني‌ها با استفاده از سري‌هاي زماني IERS 14 C04 در بين سال‌هاي 2010 تا 2011 ميلادي صورت پذيرفته است. سري‌هاي زماني مذكور در وب‌سايت IERS در دسترس‌اند. نتايج با 8 روش ديگر مقايسه شده و مورد ارزيابي قرار گرفته است. نتايج نشان مي‌دهد كه روش ارائه شده، براي پيش‌بيني تمام روزها، دقت بهتري نسبت به اين 8 روش دارد. ميزان بهبود دقت براي روزهاي 5ام و 10ام به‌ترتيب 1/60 و 1/84 برابر مي‌باشد.

The Earth Orientation parameters (EOP) including the Length of Day (LOD) are vital to widely used applications of Satellite Geodesy. The precise satellite positioning and navigation and the Earth system monitoring satellites are a few applications with a near real time request for the EOP values. Data gathering from a globally distributed co-located geodetic sensors and processing the collected data for estimation of the parameters are time demanding tasks which makes delayed access to a real-time processed values unavoidable. Consequently, accurate prediction of the EOP parameters time-series has been defined as a highly demanding task in geodesy. Many different techniques have already been employed either for short- or long-term prediction of the time-series. However, the implemented methods for short-term prediction of the EOP temporal changes is in central focus of the research centers and institutes due to its applications in the Earth Centered inertial (ECI) and the Earth Centered Earth Fixed (ECEF) reference frames. Moreover, combined methods with the ability of simultaneous functional and stochastic behavior modeling of the time-series are more interested due to their functionality for one-step accurate prediction. For instance, the Least squares auto regressive (LS+AR) is the most recent published article for the LOD forecasting. In this paper, we will address an innovative approach for complicated and challenging time-series prediction. The proposed methodology consists of the Singular Spectrum Analysis (SSA) combined with the Auto Regressive Moving Average (ARMA) enabling to model the functional and stochastic constituents respectively. For more precise forecasting, the proposed method is equipped with two pre analysis statistical tests in order to detect and identify any possible outliers. Moreover, the Fast Fourier transform (FFT) is employed to give a first guess of the possible periodic pattern of the data with its later application in the SSA appropriate window length selection. The SSA setup consists of the lag-covariance matrix computation, Eigen value and Eigen vector decomposition of the lag-covariance matrix, the Eigen values clustering and the component reconstruction. Trend and offset removal before utilizing the SSA method and its restoration after performing perdition is also worth mentioning. Selection an optimal number of deterministic components plays a key role in effective implementation of the SSA approach which is fully explained in the methodology part of the paper. The stochastic behavior of LOD signal is characterized using the ARMA technique whose successful implementation is highly depend on the right selection of the Moving Average (MA) and Auto Regressive (AR) orders. The Akaike information criterion (AIC) as an estimator of prediction error as the well-known order selection criteria is used. Moreover, the Mean Absolute Error (MAE) is computed and different prediction scenarios are compared. The suggested approach has dominantly outperformed eight already published method. Publicly available LOD data from International Earth Reference System (IERS) is used for the method evaluation and numerical comparison. Daily LOD data for the years of 2005-2009 is used for model training while the year 2010 is taken for validation. A ten-day interval prediction during the whole year of 2011 is considered for evaluation. On average, accuracy improvement rate is about 1.6 and 1.84 for the 5th and 10th ahead day of prediction.