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An array of SQUID biomagentometers may be used to measure the spatio-temporal neuromagnetic field produced by the brain in response to a given sensory stimulus. A popular model for the neural activity that produces these fields is a set of current dipoles. We present here a common linear algebraic framework for three common spatio-temporal dipole models: i) moving and rotating dipoles, ii) rotating dipoles with fixed location, and iii) dipoles with fixed orientation and location. Our intent here is not to argue the merits of one model over another, but rather show how each model may be solved efficiently, and within the same framework as the others. In all cases, we assume that the location, orientation, and magnitude of the dipoles are unknown. We present the parameter estimation problem for these three models in a common framework, and show how, in each case, the problem may be decomposed into the estimation of the dipole locations using nonlinear minimization followed by linear estimation of the associated moment time series. Numerically efficient means of calculating the cost function are presented, and problems of model order selection and missing moments are also investigated. The methods described are demonstrated in a simulated application to a three dipole problem.
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