Square-root cubature Kalman filter-based vector tracking algorithm in GPS signal harsh environments

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.