The linear inverse problem in magnetic interpretation arises when the distribution of magnetization or susceptibility is sought in a source region which is divided into blocks. The solution is usually achieved by deconvolution or matrix methods. Here we develop a simple, state-variable model of the magnetic field generating process in which the subsurface is divided into a number of vertical prisms with infinite depth extent. The magnetization in each prism is assumed to be a linear combination of adjacent prisms plus a random component. The discrete Kalman filter is used to obtain estimates of the magnetization distribution. Tests on synthetic data show the method compares favorably with conventional deconvolution techniques. The approach has been applied to part of the Abitibi greenstone belt and has proven effective in delineating the major lithologies there.