ACCURATE DETERMINATION OF MAGNETIC-FIELD GRADIENTS FROM 4-POINT VECTOR MEASUREMENTS .2. USE OF NATURAL CONSTRAINTS ON VECTOR DATA OBTAINED FROM 4 SPINNING SPACECRAFT

The errors that result from an inadequate knowledge of the orientation s, zero levels, and scale factors of the magnetometer sensor assemblie s become particularly troublesome when the objective is to measure spa tial gradients using several spacecraft. In an accompanying paper [1], we introduced an efficient approach to the intracalibration of a sens or assembly onboard a spinning spacecraft which provides accurate valu es for 8 of the 12 calibration parameters, The approach relies on the concept that errors in these parameters generate coherent monochromati c signals at the first and second harmonics of the spin frequency, In this work, we show how a least squares technique may be used to interc alibrate magnetometers on a group of four spacecraft to reduce the eff ects of the errors in the remaining calibration parameters to negligib le levels. The intercalibration technique relies on the concept that d el . B is zero everywhere and del x B is vanishingly smalt in certain regions of the magnetosphere. If the data have not been properly inter calibrated, they yield nonzero averages for del . B and del x B in tho se regions, Correct calibration parameters are determined by requiring that the final data set must yield values of del . B and del x B clos e to zero, The technique is extremely efficient provided appropriate i nput data are available, and should prove useful for the Cluster missi on.