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摘要:
为了克服钟差和卫星位置误差对脉冲星方位误差估计的影响，设计了两步卡尔曼滤波（TSKF）算法。首先，介绍了脉冲星方位误差估计的传统模型，并通过分析和仿真验证了钟差、卫星位置误差以及2种误差同时存在时会使脉冲星方位误差估计结果产生较大偏差。其次，在传统的估计模型中加入了钟差和卫星位置误差，并将钟差和钟差变化率增广为新的状态量，从而推导出包含2种误差的新模型，并证明了该模型的完全可观测性；根据该模型并按照两步卡尔曼滤波原理，得到了TSKF算法的步骤。最后，通过仿真表明：在钟差和卫星位置误差同时影响下，传统脉冲星方位误差估计算法偏差较大且发散；TSKF算法则能够有效隔离2种误差的影响，使赤经和赤纬误差估计达到0.2 mas之内的精度。
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关键词:
- 方位误差 /
- 时钟钟差 /
- 卫星位置误差 /
- 增广状态 /
- 两步卡尔曼滤波(TSKF)
Abstract:A Two-Step Kalman Filter (TSKF) algorithm is designed to overcome the influence of clock error and satellite position error on pulsar position error estimation. First, the traditional model of pulsar position error estimation is introduced, and it is confirmed by analysis that the clock error, satellite position error, and both errors will have serious impact on the estimation. Second, the clock error and satellite position error are added to the traditional estimation model, and the clock error and its rate of change are expanded to a new state quantity, thereby deducing a new model of pulsar position error estimation containing these two errors. And its observability is proved through theoretical analysis. Then the update equation of the TSKF algorithm is written combined with the new model and based on the two-step Kalman filter principle. Finally, simulations show that the TSKF algorithm can effectively isolate the influences of the two errors and make the estimation accuracy kept within 0.2 mas while the traditional pulsar position error estimation algorithm has a large deviation and divergence of the right ascension and declination errors under the influence of the two errors.
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图 4 未修正卫星位置误差的估计结果
Figure 4. Estimation results with uncorrected satellite position errors
表 1 脉冲星B0531+21参数
Table 1. Parameters of pulsar B0531+21
参数 数值 赤经/(°) 83.63 赤纬/(°) 22.01 距离/kpc 2.0 P/ms 33.4 W/ms 1.7 Fx/(ph·cm－2·s－1) 1.54 pf/% 70 注：kpc为秒差距，是天文学中使用的距离单位；ph·cm－2·s－1为宇宙背景噪声单位。 
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表 2 卫星轨道参数
Table 2. Parameters of satellite orbit
参数 数值 半长轴/km 7 460 离心率 4.55×10-16 轨道倾角/(°) 25 近地点幅角/(°) 45 升交点赤经/(°) 0 初始真近地点/(°) 30 起始时间 2015-07-01T12：00：00
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表 3 条件设置
Table 3. Condition setup
钟差/(μs) 卫星位置误差/km 0 (0.1, 0.1, 0.1) 1 (0, 0, 0) 1 (0.1，-0.1，0.1) 2 (0.1, 0.1, 0.1) 2 (0.2，-0.2, 0.2) 2 (0.5, 0.5, 0.5) 5 (0.1, 0.1, 0.1) 5 (0.2，-0.2, 0.2)
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表 4 仿真结果
Table 4. Simulation results
赤经估计偏差/mas 赤纬估计偏差/mas 0.050 0.043 0.061 0.047 0.150 0.065 0.150 0.072 0.172 0.110 0.221 0.150 0.182 0.143
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