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第 39 卷 第 4 期 董阁等： 利用频域 β-warping 变换的浅海目标航向估计方法 511
航向，再利用渐近无偏最小二乘方法对目标航向进 of waveguide invariant and heading angle[J]. Technical
行估计。数值仿真和实验数据处理结果表明，在浅 Acoustics, 2012, 31(6): 559–565.
[9] 余赟, 袁延艺, 刘雄厚. 利用波导不变量进行运动单线阵的无
海水平不变波导远场条件下，对于单一静止的观测
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平台，该方法无需目标保持匀速直线运动，对直航运 Yu Yun, Yuan Yanyi, Liu Xionghou. Passive ranging
动的目标均可以进行可靠地航向估计。同时，该方 and velocity estimation using a moving hydrophone ar-
法航向估计性能与观测时间内的平均方位变化率 ray based on the waveguide invariant[J]. Acta Acustica,
2017, 42(6): 661–668.
密切相关。复杂浅海环境下的方法的适用性是下一 [10] 戚聿波, 周士弘, 张仁和, 等. 一种基于 β-warping 变换算子的
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致谢 感谢参加实验的全体人员，他们的辛勤工作 warping operator[J]. Acta Physica Sinica, 2015, 64(7):
为本文的科学研究提供了宝贵的实验数据。 074301.
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