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摘要: 建立了舰船相关坐标系与舰载GNSS天线相关坐标系, 构建了GNSS卫星与倾斜天线的空间位置关系模型; 基于理论分析与动、静态试验, 给出了舰船摇摆条件下GNSS信号的多路径效应随接收机天线倾斜角的变化规律。研究结果表明: 当舰载天线受横纵摇影响连续处于摇晃倾斜姿态时, 卫星信号多路径效应的变化与天线倾斜方向、天线倾角和卫星相对高度角的差有关; 卫星位于天线倾斜方向时, 相对高度角大于天线倾角的卫星信号多路径效应不受天线姿态变化的影响, 小于天线倾角的卫星信号多路径效应随天线倾角的增大而增大, 且逐渐趋于稳定; 卫星位于背对天线倾斜方向时, 相对高度角大于天线倾角的卫星信号多路径效应随天线倾角增大而缓慢增大, 小于天线倾角的卫星信号多路径效应随天线倾角增大而显著增大, 甚至部分卫星信号完全失锁; 卫星处于倾斜天线天顶方位时, 其多路径效应不受天线倾斜角影响。可见, 根据舰船不同姿态确定各颗GNSS观测卫星信号置信度, 可为海上动态精密定位与测量的误差修正问题提供解决方向。Abstract: The ship related coordinate system and ship-based GNSS antenna correlation coordinate system were established, and the spatial position relationship model between the GNSS satellite and tilt antenna was constructed. Based on theoretical analysis and dynamic and static experiments, the variation rules of multipath effect of GNSS signal with the tilt angle of receiver antenna under ship swing condition were given. Analysis result shows that when the ship-based antenna is continuously at the swaying and tilting position by the roll and pitch effect, the variation of multipath effect of satellite signal is related to the antenna tilt direction, antenna tilt angle and the difference of satellite relative height angle. When the satellite faces the antenna tilted direction, the multipath effect of satellite signal with a relative height angle greater than the antenna tilt angle is not affected by the antenna attitude change. The multipath effect of satellite signal with a relative height angle smaller than the antenna tilt angle increases as the antenna tilt angle increases, and gradually becomes stable. When the satellite is in the opposite tilted direction of antenna, the multipath effect of satellite signal whose relative height angle is greater than the antenna tilt angle increases slowly with the increase of antenna tilt angle. While the multipath effect of satellite signal whose relative height angle is smaller than the antenna tilt angle increases significantly with the increase of antenna tilt angle, and even some satellite signals are completely unlocked. When the satellite is at the zenith position of inclined antenna, its multipath effect is not affected by the antenna tilt angle. Therefore, determining the signal confidence of each GNSS observation satellite according to the different attitudes of the ship can provide a solution for the error correction problem of dynamic precision positioning and measurement at sea.
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图 7 位于天线倾斜方向的卫星多路径效应偏差角度序列
Figure 7. Deviation angle series of multipath effects of satellites facing antenna tilt direction
图 8 xR > 0且E-γ < 0时试验站D观测卫星的多路径效应综合指标
Figure 8. Multipath effect composite indicators of observation satellites at test station D when xR > 0 and E-γ < 0
图 9 位于背对天线倾斜方向的卫星多路径效应偏差角度序列
Figure 9. Deviation angle series of multipath effects of satellites in tilt back azimuth of antenna
图 10 xR < 0且E-γ < 0时试验站D观测卫星的多路径效应综合指标
Figure 10. Multipath effect composite indicators of observation satellites of test station D when xR < 0 and E-γ < 0
图 11 轨迹穿过yRORzR面的卫星多路径效应偏差角度序列
Figure 11. Deviation angle series of multipath effects of satellites passing through plane yRORzR
表 1 相关坐标系框架
Table 1. Frameworks of relevant coordinate systems
坐标框架 坐标原点 z轴 x轴 y轴 接收机天线坐标系OAxAyAzA 天线几何中心(OA) 沿天线垂直对称轴指向天顶方向(zA) 与z轴垂直指向天线倾斜方向(xA) 与x轴、z轴构成右手坐标系(yA) 接收机天线水平坐标系ORxRyRzR 天线几何中心(OR) 垂直于水平面指向天顶方向(zR) OAxAyAzA坐标系的xA轴在水平面上的投影(xR) 与x轴、z轴构成右手坐标系(yR) 站心坐标系OLxLyLzL 天线几何中心(OL) 垂直于水平面指向天顶方向(zL) 与z轴垂直指向北极(xL) 与x轴、z轴构成左手坐标系(yL) 地心地固坐标系OExEyEzE 地球质心(OE) 指向国际地球自转服务系统定义的参考极方向(zE) 指向国际地球自转服务系统定义的参考子午面和赤道的交点(xE) 与x轴、z轴构成右手坐标系(yE) 大地坐标系 坐标用纬度B、经度L和大地高程H表示 
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表 2 倾斜天线与卫星的相对位置对信号的影响
Table 2. Effects of relative position of tilted antenna and satellite on signal
倾斜天线与卫星的相对位置 对信号的影响 相对方位 相对高度角 直射信号 多路径信号 xR > 0 E-γ > 0 正常接收 扼流圈削弱 E-γ < 0 正常接收 正常接收 xR≤0 E-γ > 0 正常接收 扼流圈削弱 E-γ < 0 扼流圈削弱 扼流圈削弱
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表 3 试验参数
Table 3. Experimental parameters
接收机型号 中海达iRTK2 采样间隔/s 1 截止高度角/ (°) 15 天线方位角/ (°) 125 天线倾角范围/ (°) 0~70 天线倾角间隔/ (°) 10 卫星信号 GPS、BDS、GLONASS 观测历元 每个倾角观测历元为300个
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