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The problem of how best to maximise the ratio of mean target intensity to mean background intensity for slowly moving targets in sets of multi-channel synthetic aperture radar images is discussed for highly non-Gaussian background clutter. The problem is formulated as a direct maximisation of target-to-clutter ratio thus giving a true maximisation of that ratio. Complex-valued weights derived using generalised eigensystem theory are used to maximise the ratio of quadratic forms representing the mean intensity of the target and background derived from their coherence matrices. For two to four channels it is shown that when the target is highly coherent an optimum steering vector is a discrete Fourier transform. For more than two channels it is shown that the optimal solution is only valid within a subspace of the whole parameter space defined by the correlation parameters of the background clutter. Images from a publically released ground moving target indicator dataset are filtered using the results for three channels. The method outperform a standard space-time adaptive processing algorithm in suppressing the stationary background urban clutter image intensity relative to the image intensity because of a known slowly moving ground vehicle. Moreover, the steering vector is much simpler to implement.