We describe spectral estimation principles that are useful for color balancing, color conversion, and sensor design. The principles extend conventional estimation methods, which rely on linear models of the input data, by characterizing the distribution or structure of the linear model coefficients. When the linear model coefficients of the input data are highly structured, it is possible to improve the quality of a simple linear model by estimating coefficients that are invisible to the sensors. We illustrate these principles using the synthetic example of estimating blackbody radiator spectral power distributions. Then, we apply the principles to typical daylight illuminants that we measured over the course of twenty days in Stanford, California. We show that the distribution of the daylight linear model coefficients that approximate the daylight spectral power distributions are highly structured. We further show that from knowledge of the coefficient structure, nonlinear algorithms using N sensors estimate the data as well as linear algorithms using N+1 sensors.