A General Algorithm for the Linear and Quadratic Gradients of Physical Quantities Based on 10 or More Point Measurements

A novel algorithm for estimating both the linear and quadratic gradients of physical quantities based on multiple spacecraft observations using the least squares method is put forward. Using 10 or more spacecraft constellation measurements as input, this new algorithm can yield both the linear and quadratic gradients at the barycenter of the constellation. Iterations were used in the algorithm. Tests on cylindrical flux ropes, dipole magnetic field, and modeled geomagnetospheric field were carried out. The results of these tests indicate that the linear gradient obtained is of second-order accuracy, while the quadratic gradient is of first-order accuracy. The test on the modeled geomagnetospheric field showed that, the greater the number of spacecraft in the constellation, the greater the accuracy of the quadratic gradient calculated. However, the accuracy of the linear gradient obtained was independent of the number of spacecraft. The feasibility, reliability, and accuracy of this algorithm have been successfully verified. This algorithm could find wide applications in the design of future multiple spacecraft missions as well as in the analysis of multiple-point measurement data.

Automated summary

A novel algorithm is proposed to estimate linear and quadratic gradients of physical quantities based on multiple spacecraft observations using the least squares method. The algorithm shows high accuracy in both linear and quadratic gradient calculations, making it suitable for future multiple spacecraft missions and analysis of multi-point measurement data.