# Enhancing Real-Time Kinematic Relative Positioning for Unmanned Aerial Vehicles
## 1 Introduction
However, for a moving-baseline RTK, it is crucial to correct the measurement time difference to obtain an accurate relative position vector. Secondly, a KF-based RTK algorithm outperforms the single-epoch least-squares method [22; 23] in terms of resolving integer ambiguities by LAMBDA due to its more precise integer ambiguity estimates and corresponding covariance matrix. The KF-based RTK measurement model assumes the consistency of integer ambiguities between two consecutive epochs. Therefore, a reliable cycle slip detection method is necessary to handle these changes in carrier phase measurements. Although some GNSS receivers generate a loss of lock indicator (LLI) to report cycle slip measurements, LLI may contain incorrect information [24]. Therefore, it is not recommended to rely solely on LLI for cycle slip detection, and a robust cycle slip detection strategy for single and dual-frequency measurements is required. Moreover, for UAVs in motion, the noise level of the cycle slip test metrics can be significantly higher than that for static ground receivers. As a result, this study developed cycle slip detection thresholds for UAVs based on the test statistics of flight test data to avoid unnecessary and frequent exclusion of carrier phase measurements. Thirdly, an additional problem with implementing a KF-based RTK is that the ratio tests of the estimated integer ambiguities from LAMBDA often fail when new GNSS measurements are included with an initial estimate of the state values and their covariance. As a result, it can take several tens of epochs for the resolved integer ambiguities with the newly incorporated satellites to pass the ratio test threshold. Therefore, in this paper, we briefly explained why the ratio test can fail in the presence of newly added KF states and introduced a dual KF structure to solve this problem. The limited exploration of the aforementioned three problems in previous studies is attributed to the understanding that no single algorithm can address them all. Instead, they are best solved by distinct logical approaches within the RTK process. The primary contribution of this work lies in identifying the key factors impeding the attainment of centimeter-level RTK position solutions when dealing with two UAVs flying in close proximity. Additionally, it proposes a comprehensive RTK process aimed at addressing these challenges, incorporating measurement time synchronizations, cycle slip detection methods tailored for small UAVs, and dual KF structures. These proposed methods were validated through extensive flight test data. Note that the overall methods proposed in this study primarily focused on a short baseline RTK method for situations where two UAVs equipped with GNSS receivers and antennas are moving, as shown in Figure 1.  
This paper is structured as follows: Section 2 outlines the GNSS measurement model and the time synchronization process between measurements from two different GNSS receivers. Section 3 describes techniques for detecting single- and dual-frequency GNSS carrier phase cycle slips for a UAV. In Section 4, the implementation of a dual KF structure is discussed with its rationales, in order to derive an accurate and robust navigation solution when the number of GNSS measurements varies and to cope with ratio test failures. Section 5 evaluates the performance improvements of the proposed methods using the flight test data collected from UAVs, followed bv conclusions in Section 6.