The authors have applied estimation theory to the problem of determining primary current distributions from measured neuromagnetic fields. In this procedure, essentially nothing is assumed about the source currents, except that they are spatially restricted to a certain region. Simulation experiments show that the results can describe the structure of the current flow fairly well. By increasing the number of measurements, the estimate can be made more localised. The current distributions may be also used as an interpolation and an extrapolation for the measured field patterns.