Accurate determination of magnetic field gradients from four-point vector measurements. II. Use of natural constraints on vector data obtained from four spinning spacecraft

For part I see ibid., vol.32, p.377 (1996). The errors that result from an inadequate knowledge of the orientations, zero levels, and scale factors of the magnetometer sensor assemblies become particularly troublesome when the objective is to measure spatial gradients using several spacecraft. In an accompanying paper, we introduced an efficient approach to the intracalibration of a sensor assembly onboard a spinning spacecraft which provides accurate values for 8 of the 12 calibration parameters. The approach relies on the concept that errors in these parameters generate coherent monochromatic 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 intercalibrate magnetometers on a group of four spacecraft to reduce the effects of the errors in the remaining calibration parameters to negligible levels. The intercalibration technique relies on the concept that ∇·B is zero everywhere and ∇×B is vanishingly small in certain regions of the magnetosphere. If the data have not been properly intercalibrated, they yield nonzero averages for ∇·B and ∇×B in those regions. Correct calibration parameters are determined by requiring that the final data set must yield values of ∇·B and ∇×B close to zero. The technique is extremely efficient provided appropriate input data are available, and should prove useful for the Cluster mission