Exponentially decreasing error model in approximating measured magnetic field of a body

A method of introducing an exponentially decreasing error model is described in approximating the measured magnetic field of a magnetic body where the errors due to the uncertainty of the location of the magnetometer probes used, and the orientation of their axes, are large. In this method the field is expanded in a series of spherical or spheroidal harmonic functions, and the errors are modeled to be normally distributed with zero mean and standard deviation sigma that decreases with some power of the coordinate corresponding to the distance from the body. The unknown exponent is evaluated simultaneously with the approximating functions during the approximating process in which the sum of the weighted squares of the residuals referred to a definite coordinate is minimized. An experiment showed that the estimated mean and standard deviation of the errors agreed with the actual ones within an extent of 0.3 sigma .