## 1 Introduction
In response to the above problems, this paper draws on the ideas of innovation [14] and square root filtering [15] on the basis of cubature Kalman filtering to estimate the covariance of measurement noise in real time. At the same time, in the filtering process, the recursive update is directly performed in the form of the square root of the covariance matrix to reduce the computational complexity and to ensure the nonnegative definiteness of the covariance matrix, which effectively avoids the divergence of the filter. This article mainly solves the tracking problem of high dynamic weak signals. In order to adapt to the Doppler frequency shift of the carrier signal in a high dynamic environment, the traditional receiver needs to increase the loop bandwidth, and the increase in the bandwidth will introduce noise interference. On the contrary, if the bandwidth is not increased, the carrier Doppler frequency shift is likely to exceed the tracking range of the loop. Therefore, the loop bandwidth can only be chosen as a compromise. In order to improve the accuracy of signal tracking, this article no longer uses the traditional scalar tracking loop but uses a vector tracking loop to make full use of the information correlation between each channel. The navigation filter in the loop tracks the carrier and the C/A code while performing navigation calculations on parameters such as position, speed, and clock error. Secondly, under high dynamic conditions, the carrier signal frequency, the first and second derivatives of the frequency, and other parameters not only change rapidly but also have strong nonlinearity [16]. In this case, the navigation filter needs to have a strong nonlinear filtering performance. For this, this paper uses the cubature Kalman filter algorithm based on the spherical radial criterion and combines the algorithm with the square root filter and the innovation covariance idea to propose an adaptive square root cubature Kalman filter algorithm, which realizes real-time adjustment of the measurement noise covariance matrix according to changes in the environment so that the tracking loop can always keep the signal locked even in the challenging environment of high dynamic and weak signal, and the RMS frequency estimation error, position error, and velocity error can be maintained at a better level. This paper is organized as follows: Section 2 gives the operating mechanism of the vector tracking loop, the process equation, and the measurement equation of the loop in high dynamics. Through the analysis of the specific form of the measurement equation, the nonlinear relationship between the measurements and the states is given. In this nonlinear relationship, an adaptive square root cubature Kalman filter algorithm is proposed for estimating position, velocity, acceleration, and other parameters as accurately as possible, as well as for real-time processing of measurement noise items. Section 3 gives the specific design and implementation process of the ASRCKF algorithm. Section 4 uses the navigation signal simulator to generate the navigation signals needed for the experiment and verifies the proposed algorithm in the Beidou vector software receiver. Section 5 gives a summary of the whole paper.