and corrections can been made to x and y magnetometers after corrections the diagram is a circle centered at the origin when there are errors in scale factors in x and y magnetometers the diagram is in general an ellipse in fig2 the diagram corresponds to a case where y magnetometer scale factor is smaller than the correct value prior art short collar algorithms can be used to correct the bias errors so that the corrected diagram is centered at the origin however it remains elliptical in shape in this invention the x and y magnetometer scale factors are also corrected in addition to bias corrections they are determined by requiring the diagram in fig2 to be deformed into a circle centered at the origin constant magnitude constraint the circular requirement only determines the relative scale factor error between x and y magnetometers if both magnetometers have identical scale factor errors the diagram is still a circle the cross axial scale factor errors are corrected in two steps in the first step step 3 in the summary of the invention errors in biases in x and y magnetometers and a relative scale factor error between the two magnetometers are determined by the centered circle requirement the cross axial scale factor error common to both cross axial magnetometers and the correct axial magnetic field component b z are determined in the second step step 4 in the summary of the invention after two steps errors of bias and scale factor in the x and.