Algorithm for the estimation of upper and lower bounds of the emissivity and temperature of a target from thermal multispectral airborne remotely sensed data

This paper describes a method to estimate the bounds of temperatures and emissivities from thermal data. This method is then tested with remotely sensed data obtained from NASA's Thermal Infrared Multispectral Scanner (TIMS) -- a 6 channel thermal sensor. Since this is an under-determined set of equations i.e., there are seven unknowns (six emissivities and one temperature) and six equations (corresponding to the 6 channel fluxes), there exist theoretically an infinite combination of values of emissivities and temperature that can satisfy these equations. However, using some realistic initial bounds on the emissivities, bounds on the temperature are calculated. These bounds on the temperature are refined to estimate a tighter bound on the emissivity of the source. An error analysis is also carried out to quantitatively determine the extent of uncertainty introduced in the estimate of these parameters. This method is useful only when a realistic set of bounds can be obtained for the emissivities of the data. In the case of water the lower and upper bounds were set at 0.97 and 1.00, respectively. A set of images obtained with the TIMS are then used as real imagery data. The data was acquired over Utah Lake, Utah, a large freshwater lake near Salt Lake City, Utah, in early April 1991. It will be used to identify water temperatures for detection of underwater thermal, saline, and fresh water springs. An image consisting mostly of water is analyzed. The temperatures of the pixels are calculated to an accuracy of less than 1 deg K and the emissivities are calculated to an accuracy of less than .01.