HR: 1330h
AN: AE22A-1113    [PDF]
TI: Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration
AU: * Koshak, W J
EM: william.koshak@nasa.gov
AF: NASA Marshall Space Flight Center, 320 Sparkman Drive, Bldg. NSSTC, Huntsville, AL 35805 United States
AB: It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the "relationship" between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product MixEx is the contribution of the Ex field to the ith mill output. Similarly, net aircraft charge (described by a "charge field component" Eq) contributes an amount MiqEq to the output of the ith sensor. The central difficulty in obtaining M stems from the fact that the impressed field (Ex, Ey, Ez, Eq) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Though numerical tests show that some of the iterative methods do improve the initial estimates, none of the iterative methods guarantee absolute convergence to the true values, or even to values reasonably close to the true values when measurement errors are present. In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector b that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). To avoid retrieving the trivial solution b = 0, appropriate external constraints are applied. Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.
DE: 3260 Inverse theory
DE: 3304 Atmospheric electricity
DE: 3324 Lightning
SC: Atmospheric and Space Electricity [AE]
MN: 2003 Fall Meeting