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Parameter estimation for spatiotemporal dynamics for coupled map lattices andcontinuous time domain systems is shown using a combination of multipleshooting, Karhunen-Loeve decomposition and Galerkin's projection methodologies.The resulting advantages in estimating parameters have been studied anddiscussed for chaotic and turbulent dynamics using small amounts of data fromsubsystems, availability of only scalar and noisy time series data, effects ofspace-time parameter variations, and in the presence of multiple time-scales.Comment: 11 pages, 5 figures, 4 Tables Corresponding Author - V. Ravi Kumar,  e-mail address: ravi@che.ncl.res.i

Parameter estimation in spatially extended systems: The Karhunen-Lóeve and Galerkin multiple shooting approach