Error Analysis of an Algorithm for Magnetic Compensation of Aircraft

The Tolles and Lawson equations were programmed on the IBM 370-65 computer. These equations predict the magnetic signals which are generated by the permanent moments, the induced moments and the eddy-current terms of an aircraft as it maneuvers in the Earth´s magnetic field. The least mean squared (LMS) solution of these equations, which was developed for the microprocessor compensation program, was also simulated on the IBM 370 computer. By measuring the simulated figure of merit (FOM) before and after applying compensation, several types of error were studied. It was found that the error introduced by truncation effects on a 16-bit microprocessor limits the FOM to 50 milligammas. Since this figure is an order of magnitude smaller than the design goal, it is concluded that the algorithm is not limited by the microprocessor capacity. Other studies show that although the baseline model is insensitive to bearing separation, the bearing separation should be 900° ± 7.50° if 3 iterations are used in the post processor and 900° ± 15° if 5 iterations are used. Although the algorithm is robust and relatively insensitive to various types of noise, experimental evidence suggests that hysteresis can cause temporal variations in the Tolles and Lawson model. It is suggested that whitening and/or adaptive techniques could be used to minimize such variations.