In a vector tracking loop (VTL) architecture, non-linearities exist in discriminator functions and pseudo-range/pseudo-range rate measurement expressions. Generally, normalisation functions are used in discriminators to export the desired code phase or carrier frequency error and the extended Kalman filter is adopted to estimate receiver's states. This process could be accurate enough when the code phase or carrier frequency error approaches zero in the signal moderate environment but begins to distort due to non-linearity when the tracking errors become large in harsh situations. This finally narrows the applicable range of VTL. To overcome this issue, a square-root cubature Kalman filter (CKF)-based VTL is designed in this study. The discriminator functions are employed directly as measurements of navigation filter, and the non-linear expressions of discriminator functions in terms of the receiver's position, velocity, and time states are derived without normalisation. Then the CKF, which is competitive in high-dimensional non-linear systems, is employed in its square-root version to estimate the position, velocity, acceleration, and time states of the receiver. Comparison trial results between traditional and proposed VTL illustrate that the proposed algorithm can not only keep a superior tracking accuracy but also improves the tracking stability of VTL in <20 dB-Hz signal harsh circumstances.

中文翻译：

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GPS信号恶劣环境下基于平方根卡尔曼滤波的矢量跟踪算法。

在矢量跟踪环（VTL）架构中，鉴别函数和伪距/伪距速率测量表达式中存在非线性。通常，在鉴别器中使用归一化函数来输出所需的码相位或载波频率误差，并采用扩展的卡尔曼滤波器来估计接收器的状态。当代码相位或载波频率误差在信号适度的环境中接近零时，此过程可能足够准确，但是当在恶劣情况下跟踪误差变大时，由于非线性而开始失真。最终缩小了VTL的适用范围。为了克服这个问题，在这项研究中设计了基于平方根库尔曼滤波器（CKF）的VTL。鉴别器功能直接用作导航过滤器的测量，并根据接收器的位置，速度和时间状态区分函数的非线性表达式无需进行归一化。然后，在高维非线性系统中具有竞争力的CKF以其平方根形式被用来估计接收器的位置，速度，加速度和时间状态。传统和拟议的VTL的对比试验结果表明，所提出的算法不仅可以保持较高的跟踪精度，而且还可以提高在<20 dB-Hz信号恶劣环境下VTL的跟踪稳定性。以平方根形式使用来估计接收器的位置，速度，加速度和时间状态。传统和拟议的VTL的对比试验结果表明，所提出的算法不仅可以保持较高的跟踪精度，而且还可以改善<20 dB-Hz信号恶劣环境下VTL的跟踪稳定性。以平方根形式使用来估计接收器的位置，速度，加速度和时间状态。传统和拟议的VTL的对比试验结果表明，所提出的算法不仅可以保持较高的跟踪精度，而且还可以提高在<20 dB-Hz信号恶劣环境下VTL的跟踪稳定性。