Multiple light-emitting diode (LED) arrays are often used as light sources because of the high lamp-emitting port intensity and large light outlet size of navigation lights in airports. Online fault detection of such navigational lights is challenging, and no convenient and effective detection method has been developed. In this study, an illumination approximation algorithm based on Fourier series fitting is proposed. The illumination distribution of a single LED light source is obtained within a suitable detection distance, and the intensity distribution approximating to real value of the single LED light source is obtained via iterative calculations. Aiming at the problem of high peak-region error of traditional Fourier series fitting, a single-point variance threshold index is introduced to suppress the peak-region error of fitting and improve the matched degree of the single LED light source by 1%. The simulation results of the five typical array faults show that the proposed method exhibits high versatility, and the matched degree of common faults exceeds 94%.