We present a new technique for mapping high-latitude electric fields and currents and their associated magnetic variations from sets of localized observational data. The technique generalizes earlier ones that were designed to deduce these electrodynamic features from ground-based magnetometer data alone. In the new technique, many different types of measurements can potentially be used: electric fields from radars and satellites; electric currents from radars; and magnetic perturbations at the ground and at satellite heights. The technique also makes use of available statistical information about averages and variances of the electrodynamic fields. One of its advantages over earlier techniques is that it quantifies the errors inherent in the mapped fields, taking into account the distribution of available data, their errors, and the statistical variances of the fields. A related application of the procedure is used for estimating the distributions of high-latitude ionospheric conductances, using available direct and indirect measurements. The new technique is illustrated by application to an example of a substorm that was previously analyzed by Kamide et al. (1982a) with an earlier technique. The new technique tends to yield much simpler patterns of high-latitude ionsopheric convection in regions of low ionospheric conductance. When magnetometer data alone are used, as in this example, the statistical uncertainty in the derived electric fields is largest in regions of low conductance, because the electric fields in these regions have little influence on the magnetic perturbations. A companion paper (Richmond et al., this issue) presents a detailed application of the technique using multiple data sets. ¿ American Geophysical Union 1988