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We present techniques for bridging the gap between idealized inversecovariance weighted quadratic estimation of 21 cm power spectra and thereal-world challenges presented universally by interferometric observation. Bycarefully evaluating various estimators and adapting our techniques for largebut incomplete data sets, we develop a robust power spectrum estimationframework that preserves the so-called "EoR window" and keeps track ofestimator errors and covariances. We apply our method to observations from the32-tile prototype of the Murchinson Widefield Array to demonstrate theimportance of a judicious analysis technique. Lastly, we apply our method toinvestigate the dependence of the clean EoR window on frequency--especially thefrequency dependence of the so-called "wedge" feature--and establish upperlimits on the power spectrum from z = 6.2 to z = 11.7. Our lowest limit isDelta(k) < 0.3 Kelvin at 95% confidence at a comoving scale k = 0.046 Mpc^-1and z = 9.5.

Overcoming real-world obstacles in 21 cm power spectrum estimation: A method demonstration and results from early Murchison Widefield Array data