An improved prediction method for BDS-3 SISA parameters and the preliminary performance evaluation

Abstract The ephemeris accuracy parameters broadcast in the ephemeris messages are commonly utilized as an alarm threshold for the signal-in-space ranging errors (SISRE) of the Global Navigation Satellite System (GNSS). Accurately predicting the orbit and clock errors of broadcast ephemeris, and converting the prediction errors into broadcast ephemeris accuracy parameters using a robust model, is important for the integrity service of GNSS. The BeiDou Navigation Satellite System (BDS-3) broadcasts four ephemeris accuracy parameters, namely <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>SIS</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>A</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>oe</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>SIS</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>A</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>ocb</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>SIS</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>A</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>oc1</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>SIS</mml:mtext> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>A</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>oc2</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , to represent the standard deviations of the satellite orbit and clock prediction errors in the broadcast ephemeris. The probability that the broadcast ephemeris SISRE exceeds 4.42 times the signal-in-space accuracy (SISA) without triggering an alarm in time is expected to be less than 1 × 10 −5 . In addition to accurately enveloping the broadcast ephemeris SISRE, SISA should also reduce the over-envelopment margin over SISRE to accurately express the system service accuracy. Thus, an accurate prediction of orbit and clock errors in the broadcast ephemeris is crucial for calculating the SISA. An orbit and clock error prediction method based on the Long Short-Term Memory (LSTM) neural network is proposed in this study. This method uses historical satellite orbit and clock errors, derived from the difference between precise and broadcast ephemeris, to train an LSTM neural network. The trained LSTM model is then used to predict the orbit and clock errors for the next 24 h. The predicted errors are used to calculate the corresponding SISA for the broadcast ephemeris. The results indicate that the 24 h accuracies of the predicted orbit and clock errors are less than 0.06 m and 0.25 m, respectively. The calculated SISA can completely envelop the actual broadcast ephemeris SISRE, achieving 100% coverage while also decreasing the over-envelopment margin by 80%. Furthermore, the horizontal protection level and vertical protection level calculated using the corresponding SISA are reduced by approximately 14%, meeting the integrity requirements set by the International Civil Aviation Organization for Approach with Vertical Guidance I. The proposed method enhances the timeliness of SISA parameter calculation and the integrity and availability of the BDS-3 service, serving as a crucial reference value for safety critical applications such as civil aviation services.