Realizing the Calculation of a Fully Normalized Associated Legendre Function Based on an FPGA.

Area of Science:

• Geodesy and Geophysics
• Computer Engineering
• High-Performance Computing

Background:

• Calculating Earth's gravity field requires extensive associated Legendre function (fnALF) computations.
• Current CPU-based methods face speed and power efficiency limitations due to shared memory architectures.
• Rising demand for gravity field data exacerbates computation time and energy consumption.

Purpose of the Study:

• To develop a novel, efficient computational implementation for fnALF calculations.
• To overcome the limitations of traditional CPU-based approaches in surveying and mapping.
• To accelerate the computation of Earth's gravity field elements.

Main Methods:

• Designed a task-parallel "pipeline" architecture on the ZYNQ platform.
• Converted serial fnALF logic into a more efficient hardware implementation.
• Utilized a redundant calculation layer for repetitive coefficient computations.

Main Results:

• Achieved accurate and rapid fnALF calculations.
• Demonstrated significant efficiency gains (over three times) compared to MATLAB R2020b for multiple latitudes.
• Measured computation times for high-order coefficients (360-1080) in milliseconds.
• Determined geoid height with an error of less than ±0.1m, confirming reliability.

Conclusions:

• The ZYNQ-based fnALF implementation offers substantial improvements in speed and power efficiency.
• The developed pipeline architecture effectively addresses the computational bottlenecks of gravity field modeling.
• This approach provides a reliable and efficient solution for high-order gravity field computations in geodesy and surveying.