In order to improve the interoperability within the Global Navigation Satellite System (GNSS), the International Committee on Global Navigation Satellite Systems published a joint statement in December 2019 that stated that all GNSS providers agree to monitor and broadcast the time offsets between each system timescale and the Universal Time Coordinated (UTC) or the rapid realization of UTC (UTCr). This commitment requires the study of precise prediction models for system time offsets. The prediction model of system time offsets is different from that of the atomic clock because of the control of the system timescale. The offsets between the system time of the Beidou Satellite Navigation System-3 (BDS-3) and the National Time Service Center (NTSC), called [UTC(NTSC)-BDT], have two main periods of 12 h and 24 h, according to the Fast Fourier Transform analysis. The rescaled range (R/S) analysis demonstrates that it has long memory, making it a fractal time series with a memory period of about 10.4 h. While using the fractal interpolation method to predict the [UTC(NTSC)-BDT] series, we found that the prediction error reaches its minimum value if adding disturbance on the estimated endpoint of the forecasted interval. After verifying the correlation between the estimated endpoints with the minimal interpolation error and minimal prediction error and proving the existence and uniqueness of the estimated endpoint with the minimal interpolation error, we established the endpoint-based optimal fractal interpolation prediction method. The experimental results indicate that the average prediction accuracy of the proposed prediction model is improved by 57.90% and 39.26% compared to that of a quadratic model and standard fractal prediction model, respectively. The accuracy analysis results of numerical tests indicate that the proposed prediction model can restrain the divergence of prediction error. Finally, we transform the [UTC(NTSC)-BDT] into [UTCr -BDT] using the [UTCr-UTC(NTSC)] published by the Bureau International des Poids et Mesures (BIPM) to meet the requirement of GNSS interoperability. The prediction accuracies of daily [UTCr-BDT] using the proposed prediction model are no more than 1.5 ns with uncertainty about 6 ns.

为了提高全球导航卫星系统（GNSS）的互操作性，全球导航卫星系统国际委员会于2019年12月发表了一份联合声明，指出所有GNSS提供商均同意监视和广播每个系统时标与时标之间的时差。世界标准时间（UTC）或UTC的快速实现（UTCr）。为此，需要研究系统时间偏移的精确预测模型。由于系统时标的控制，系统时间偏移量的预测模型与原子钟的预测模型不同。北斗卫星导航系统3（BDS-3）和国家时间服务中心（NTSC）的系统时间之间的偏移称为[UTC（NTSC）-BDT]，其主要时间间隔为12小时和24小时，根据快速傅立叶变换分析。重标范围（R / S）分析表明它具有较长的记忆力，使其成为具有约10.4 h记忆时间的分形时间序列。在使用分形插值方法预测[UTC（NTSC）-BDT]系列时，我们发现，如果在预测间隔的估计端点上添加干扰，则预测误差将达到其最小值。在验证了最小插值误差和最小预测误差的估计端点之间的相关性，并证明了最小插值误差的估计端点的存在性和唯一性之后，我们建立了基于端点的最优分形插值预测方法。实验结果表明，提出的预测模型的平均预测精度提高了57。与二次模型和标准分形预测模型相比分别为90％和39.26％。数值试验的精度分析结果表明，所提出的预测模型可以抑制预测误差的发散。最后，我们使用国际测绘局（BIPM）发布的[UTCr-UTC（NTSC）]将[UTC（NTSC）-BDT]转换为[UTCr -BDT]，以满足GNSS互操作性的要求。使用所提出的预测模型的每日[UTCr-BDT]的预测精度不超过1.5 ns，不确定性约为6 ns。我们使用国际测绘局（BIPM）发布的[UTCr-UTC（NTSC）]将[UTC（NTSC）-BDT]转换为[UTCr -BDT]，以满足GNSS互操作性的要求。使用所提出的预测模型的每日[UTCr-BDT]的预测精度不超过1.5 ns，不确定性约为6 ns。我们使用国际测绘局（BIPM）发布的[UTCr-UTC（NTSC）]将[UTC（NTSC）-BDT]转换为[UTCr -BDT]，以满足GNSS互操作性的要求。使用所提出的预测模型的每日[UTCr-BDT]的预测精度不超过1.5 ns，不确定性约为6 ns。