Research on the application range and accuracy for series formula in the numerical calculation of SLF signal field strength

The SLF signal is stable, and the field strength of the transmitter is predictable. Therefore, the receiver can evaluate the performance of the SLF signal in advance, so as to improve the performance of the SLF receiver. The first derivative and two derivative of the first class Legendre’s function to the core angle (distance) are involved in the field intensity numerical calculation of the SLF signal. Accurate calculation can use infinite series to express these two derivatives, and some cases can also use approximate expressions. At present, there is no further discussion on the numerical calculation method of infinite series in the calculation of SLF field strength, and the application range and accuracy of some approximate formulas are not clearly introduced. This will greatly affect the accuracy and calculation speed of the numerical calculation of the SLF field strength prediction, and influence the pre-receiver effect of the receiver. In this paper, the numerical calculation model of SLF signal field strength is set up, and the simulation analysis is carried out. The application range and precision of the series formula are discussed in order to determine the applicable conditions and precision differences of various formulas, so as to improve the precision and operation speed of the SLF field strength numerical calculation.