  Atmospheric wavefront prediction based on previous wavefront sensor
measurements can greatly enhance the performance of adaptive optics systems. We
propose an optimal linear approach based on the Empirical Orthogonal Functions
(EOF) framework commonly employed for atmospheric predictions. The approach
offers increased robustness and significant performance advantages over
previously proposed wavefront prediction algorithms. It can be implemented as a
linear pattern matching algorithm, which decomposes in real time the input
(most recent wavefront sensor measurements) into a linear sum of previously
encountered patterns, and uses the coefficients of this linear expansion to
predict the future state. The process is robust against evolving conditions,
unknown spatio-temporal correlations and non-periodic transient events, and
enables multiple sensors (for example accelerometers) to contribute to the
wavefront estimation. We illustrate the EOFs advantages through numerical
simulations, and demonstrate filter convergence within 1 minute on a 1 kHz rate
system. We show that the EOFs approach provides significant gains in high
contrast imaging by simultaneously reducing residual speckle halo and producing
a residual speckle halo that is spatially and temporally uncorrelated.
