## 1 Introduction  
The global positioning system (GPS) stands out as one of the most extensively utilized technologies, mainly known for its applications in navigation. With the advancement in science, GPS has been shown to achieve an accuracy of up to several meters in an open sky condition; however, the accuracy deteriorates for an urban canyon setting [1]. Various factors influence the accuracy of a GPS system, with the performance of the receiver clock being a key determinant. Receivers employ diverse clocks, ranging from high-end chip-scale atomic clocks to lower-grade options, such as crystal oscillators.  
In Figure 1, we observe the performance of a specific low-cost GPS receiver (Ublox), which uses a lower-grade clock. The data are collected over a day at a fixed location. They show that the maximum 2D error can go up to 40 m. Vertical positioning for these receivers is even more challenging. The vertical accuracy of a GPS receiver is directly linked to the stability of the receiver clock. The higher the receiver clock bias error, the higher the error in vertical positioning [2, 3]. An error as big as that shown by Figure 1 is totally unacceptable, especially for autonomous vehicles. Real-time kinematic (RTK) signals or differential GPS (DGPS) are widely used techniques to improve the positioning accuracy of a GPS receiver [4, 5]. However, these methods only improve the positioning accuracy but do not improve the clock stability by correcting the receiver clock errors. Ourproposed method here focuses on improving the stability of low-cost receiver clocks. Once the stability is improved, the positioning accuracy will be enhanced. RTK signals and DGPS could be applied further to enhance the precision of results.  
The proposed methodology is to steer the GPS receiver periodically, hence improving its stability and accuracy. To achieve this, there are two main tasks: (a) generation of a precision timing source and (b) transfer of the steering information.  
(a) Precision Timing Source: Atomic clocks have long been used as a source of precision time [6]. The accuracy of such timing is verified by comparing to the Universal Coordinated Time (UTC) generated and maintained by the Bureau of Weights and Measurement (BIPM) [7]. According to BIPM [8], cesium clocks are the current standards for time and frequency. Precision timing is generated from clocks that are traceable to the cesium standards. In our Time Lab at the National Metrology Centre (NMC) in Singapore, we maintain cesium clocks and hydrogen masers. The Singapore time scale is established by deriving frequency outputs from these clocks, which are meticulously preserved under optimal temperature and humidity conditions. The process of generation of precision timing based on a number of atomic clocks is almost similar for different laboratories [9; 10; 11]. However, they differ in the way they choose to combine the readings from these atomic clocks. It is important to analyze the precision time generation process. A detailed discussion on the time-scale generation process is presented in Section 2.  
(b) Time Transfer: Once the precision signals are generated from the lab, they can be used to correct the low-cost oscillators. The GPS time transfer technique can be applied for this purpose [12; 13; 14]. The GPS time transfer technique has previously been applied either in common view mode or all-in-view mode for the purpose of time comparison between any two laboratories [15; 16]. This method has not been implemented yet for steering a low-cost GPS receiver. The paper will propose a machine-learning-based algorithm to explore the possibility of using this method to improve the stability of a low-cost GPS receiver. The details will be discussed in Section 3.2.