Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias

Abstract

The accuracy of the timing group delay (TGD) transmitted in the broadcast ephemeris is an important factor that affects the service performance of a GNSS system. In this contribution, an apparent bias is found by comparing the orbit and clock difference using half-year data of the BeiDou navigation satellite system (BDS) broadcast ephemeris and precise post-processed products. The bias differs at each satellite on each frequency and shows a general systematic difference between BDS-2 and BDS-3. We attribute this to the satellite-dependent TGD bias of the BDS broadcast ephemeris, which is subsequently calibrated. Moreover, to calibrate the bias independently, a network solution strategy is proposed based on 87 globally distributed multi-GNSS experiment (MGEX) stations spanning 25 weeks. The estimated bias shows good agreement with the values observed from the orbit and clock comparison. For the validation of the bias, we compared the signal-in-space range error (SISRE) performance with and without the TGD bias correction. The results show that the SISRE of the BDS improved from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m in the B1I, B3I, and B1I/B3I frequencies. For BDS-3, the SISRE is well within 0.50 m after the bias correction. To further validate the bias, a week’s data were collected at 97 globally distributed MGEX stations. When the TGD bias is corrected, the root mean square (RMS) of single point positioning (SPP) can be improved by 5.6, 8.4, and 21.6% in the B1I, B3I, and B1I/B3I frequencies. Meanwhile, the SISRE and SPP assessment results also indicate that the TGD bias should be corrected by each satellite rather than only corrected between BDS-2 and BDS-3.

Analysis and Assessment of BDS-2 and BDS-3 Broadcast Ephemeris: Accuracy, the Datum of Broadcast Clocks and Its Impact on Single Point Positioning

“…Therefore, dD Broadcast will absorb the datum of TGD when TGD correction is performed to convert the original clock offsets to the clock offsets with a certain equipment group delay. Previous studies have shown that the TGD of BDS-2 and BDS-3 are also calculated by two information processing centers [12] and the inconsistency of the TGD datum for BDS-2 and BDS-3 resulted from different solution conditions will cause the inconsistency of the datum of satellite clock offsets between BDS-2 and BDS-3.…”

“…The estimated vector E1 in the IF SPP model includes receiver 3D position increments and the receiver clock offsets can be expressed as: E1 = x δt r IF (12) where δt r IF = δt r + IF b P + dD. If the differences exist between BDS-2 and BDS-3 in the receiver IF UCDs and the datum of satellite clock offsets, the BDS-2 and BDS-3 receiver clock offsets are inconsistent.…”

“…In order to reduce the impact of the inconsistency of the datum of broadcast clock offsets on the assessment of BDS-2 and BDS-3 signal-in-space accuracy and SPP, Zhang and Wang [12] attribute this bias to satellite-dependent TGD bias of the BDS broadcast ephemeris, and estimate TGD bias to weaken this impact. Even if TGD bias is used to correct this inconsistency, its residuals will still affect signal-in-space accuracy and SPP.…”

“…Only Wang and Li found a datum deviation of 3.8 ns between BDS-2 and BDS-3 by comparing the differential code bias (DCB) and time group delay (TGD) of BDS-3 satellites [10]. Zhang and Wang further attributed this inconsistency to satellite-dependent TGD bias of the BDS broadcast ephemeris, and corrected this inconsistency by calculating TGD bias [11,12]. Although the corrections of TGD bias can weaken the impact of the inconsistency of the datum of satellite clock offsets on the assessment of BDS-2 and BDS-3 signal-in-space accuracy, the inter-system bias (ISB) between BDS-2 and BDS-3 is affected by both the datum of satellite clock offsets and receiver pseudorange bias [13][14][15][16].…”

A Time-Varying Chaotic Multitone Communication Method Based on OFDM for Low Detection Probability of Eavesdroppers

“…This method employs the variable satellite timing information V to represent the variable m and the mapping relationship can be expressed as f (V ) = m, where m 1 < m < m 2 , m 1 ≥ 0, m 2 ≤ n and m ∈ R + . When the distance between the transmitter and the receiver is d ab , to avoid the error caused by the transmission time delay of electromagnetic wave [13], the minimum interval between different V is limited as ∆V d ab /c ignoring the internal signal processing time. Where c is the propagation rate of the electromagnetic wave in the air, which is generally defaulted As shown in FIGURE.1, for the same AFS, let…”