利用GNSS所得的差分斜路徑總電子含量對BURSTT進行電離層延遲的校準

Abstract

電離層是地球大氣層中包含電離介質（即等離子體）的區域。當無線電訊號從訊號源傳播至地面接收機時，電離層會造成時間上的傳播延遲。這種電離層時延取決於訊號穿過電離層傳播路徑上的總電子含量（TEC），即斜路徑總電子含量（STEC）。 臺灣宇宙電波爆廣角監測實驗（BURSTT）是一台電波望遠鏡，旨在透過位於臺灣北部福山的主站與包括臺灣中部南投站在內的多個支站之間構成的特長基線干涉儀（VLBI）技術，對類快速電波爆（FRB）事件進行探測並對其宿主(星系)實現精確的定位。由於主站天線與支站天線同時追蹤同一電波脈衝，脈衝到達各站的時間差會受到電離層的影響；因此，必須對該時間差進行校準，以實現對其宿主的精確定位。 本研究利用位於福山的 BURSTT 主站和位於南投的支站所觀測到的全球衛星導航系統（GNSS）接收儀數據（分別為 t02 和 t09 資料集），對 2026 年 4 月 19 日（世界協調時間，UT）的一個電波脈衝其對兩站之間傳播所受的電離層延遲進行校準，而該電離層延遲由該脈衝對兩站之間的斜路徑總電子含量的差（dSTEC）來表示；首先，我們從 t02 和 t09 資料集的雙頻 GNSS 觀測值中提取了TEC的虛擬距離觀測量（prTEC）和TEC的載波相位觀測量（phTEC）。隨後，利用 2026 年 4 月 9 日至 5 月 26 日（UT）期間夜間且高度角不低於 65° 的 GNSS 衛星所觀測的prTEC 數據集，解出兩個站間的每日接收儀差分延遲（DCB）。結果顯示，各 GNSS 衛星群的接收儀DCB 均呈現不規則且顯著的逐日變化，平均標準差（σ）為 2.588 TEC.U，這反映了 prTEC 測量值本身雜訊大的特性。 為了獲取精確且絕對的STEC值，我們採用了兩種方法以雜訊小但存在相對量的phTEC來平滑雜訊大但絕對的prTEC：第一種方法是計算phTEC與prTEC之差的加權平均值；第二種方法則通過測試一組整數值將其代入phTEC的週波未定值項，並評估相對量平滑結果與prTEC之間的卡方（χ²）統計量，來確定週波未定值。由於兩種方法的結果一致，我們採用第一種（加權平均）方法進行相對量平滑，隨後校正每日接收儀DCB，從而獲得兩站之間的dSTEC。 我們透過估算GNSS衛星E06和G14其與2026年4月19日（UT）且仰角≥60°時的dSTEC，並將其與同時期同仰的實際GNSS觀測值進行對比，來評估電離層延遲校準的性能。每顆衛星的dSTEC估算值取自角距離 θ≤45° 或 θ≤30° 範圍內的鄰近GNSS衛星的dSTEC平均值。結果顯示，衛星E06和G14的估算值與相應的GNSS觀測值相比，分別存在約1 TEC.U和2 TEC.U的偏差；這表明該dSTEC估算方法尚需改進，以將偏差降低至0.1 TEC.U水平。 dSTEC的估算值 與 GNSS 測量值之間存在顯著偏差，這主要源自於每日接收儀DCB的顯著變化、prTEC雜訊對相對量平滑過程的強烈影響，以及週波未定值搜尋間隔相對較窄。針對 dSTEC 估算方法的改進應包括：利用雙頻（甚至三頻）的 phTEC 和 prTEC 觀測量建立 Melbourne–Wübbena 組合，以實現更精確的確定衛星特定週波未定值；同時，利用相對量平滑處理後的高精度 prTEC 觀測量來解出每日接收儀DCB。

The ionosphere is the region of the terrestrial atmosphere that contains an ionised medium, or plasma. It introduces a time delay into the propagation of a radio signal travelling from a radio source to a ground-based receiver. This ionospheric delay depends on the total electron content (TEC) along the signal’s propagation path through the ionosphere, referred to as the slant TEC (STEC). The Bustling Universe Radio Survey Telescope in Taiwan (BURSTT) is a software radio telescope designed to detect fast radio burst (FRB)-like events with accurate localization, using very long baseline interferometry (VLBI) between a main station at Fushan and multiple outrigger stations, including one at Nantou. Because the main array and the outrigger stations track the same radio pulse simultaneously, the time delay between the pulse’s arrival at different stations is affected by the ionosphere; this delay must therefore be calibrated to achieve accurate localization of the source. In this thesis, we calibrate the ionospheric delay—parametrized by the differential STEC (dSTEC)—of a radio pulse travelling between the BURSTT main station at Fushan and the outrigger station at Nantou on 19 April 2026 UT, using Global Navigation Satellite System (GNSS) receiver data observed at Fushan (the t02 dataset) and at Nantou (the t09 dataset). We first extract pseudorange-derived TEC (prTEC) and phase-derived TEC (phTEC) measurements from dual-frequency GNSS observations in both the t02 and t09 datasets. We then solve for the daily differential receiver Differential Code Bias (DCB) between the two stations by applying the prTEC dataset to GNSS satellite tracks observed at elevations ≥65° and at night, over the period from 9 April to 26 May 2026 UT. The results reveal an irregular and substantial day-to-day variation in the differential receiver DCB across all GNSS constellations, with an average standard deviation σ of 2.588 TEC.U, reflecting the inherently noisy nature of prTEC. Two approaches for reconciling the precise but ambiguous phTEC with the unambiguous prTEC are applied to obtain precise, absolute STEC values: the first computes the weighted average of the difference between phTEC and prTEC, while the second performs phase-ambiguity fixing by testing a set of integer values for the phase-ambiguity term and evaluating the chi-square (χ²) statistic between the phase-levelled results and prTEC. As both methods yield identical results, we adopt the first (weighted-average) approach for phase levelling, followed by correction for the daily differential receiver DCB to obtain the differential STEC (dSTEC) between the two stations. We evaluate the performance of the ionospheric delay calibration by estimating the dSTEC for GNSS satellites E06 and G14 and comparing these estimates with their own GNSS measurements at elevations ≥60° on 19 April 2026 UT. The dSTEC of each satellite is estimated as the average dSTEC of nearby GNSS satellites within an angular distance of θ ≤45° or θ ≤30°. We find that satellites E06 and G14 show offsets of roughly 1 TEC.U and 2 TEC.U, respectively, relative to their corresponding GNSS measurements, indicating that the dSTEC-estimation method requires further improvement to reduce this offset to the sub-TEC.U level. This large offset between the estimated dSTEC and the GNSS measurements arises from substantial variation in the daily differential receiver DCB, the strong dependence of phase levelling on prTEC, and the relatively narrow spacing of the ambiguity search. Improvements to the dSTEC-estimation method should include applying the Melbourne–Wübbena combination of phTEC and prTEC across two (or even three) frequencies for more accurate, satellite-specific phase-ambiguity fixing, as well as solving for the daily differential receiver DCB using the precise, post-phase-levelling prTEC dataset.