# Phase tracking based on GPGPU and applications in Planetary radio Science

## TL;DR

This paper presents a GPU-accelerated phase tracking method for planetary radio science that improves computational efficiency and accuracy over traditional techniques, enabling real-time analysis of spacecraft tracking data.

## Contribution

The paper introduces a novel phase tracking algorithm using Taylor polynomial fitting and Differential Evolution optimized for GPU implementation, enhancing real-time processing capabilities.

## Key findings

- Achieved real-time processing within 6.5 seconds for large data blocks.
- Demonstrated high precision in Doppler measurements (2-4 mrad/s).
- Validated method on Mars Express and Chang'E 4 satellite data.

## Abstract

This paper introduces a phase tracking method for planetary radio science research with computational algorithm implemented fo r NVIDIA GPUs. In contrast to the phase-locked loop (PPL) phase counting method used in traditional Doppler data processing, this method fits the tracking data signal into the shape expressed by the Taylor polynomial with optimal phase and amplitude coefficients. The Differential Evolution (DE) algorithm is employed for polynomial fitting. In order to cope with high computational intensity of the proposed phase tracking method, the graphics processing units (GPUs) are employed. As a result, the method estimates the instantaneous phase, frequency, derivative of frequency (line-of-sight acceleration) and the total count phase of different integration scales. This data can be further used in planetary radio science research to analyze the planetary occultation and gravitational fields. The method has been tested on MEX (Mars Express, ESA) and Chang'E 4 relay satellite (China) tracking data. In a real experiment with 400K data block size and $\sim$80,000 DE solver objective function evaluations we were able to acheive the target convergence threshold in 6.5 seconds and do real-time processing on NVIDIA GTX580 and 2$\times$ NVIDIA K80 GPUs, respectively. The precision of integral Doppler (60s) is 2 mrad/s and 4 mrad/s for MEX(3-way) and Chang'E 4 relay satellite(3-way) respectively.