Differential sensitivity analysis for the orthorectification of small satellite images

By using differential sensitivity analysis, horizontal and vertical accuracy of orthorectification of monoscopic images taken by small satellites without using Ground Control Points (GCP) is predicted. The analysis is performed by differentiating the colinearity equation of orthorectification procedure with respect to the satellite´s interior and exterior parameters, and elevation obtained from digital elevation model (DEM). Square of the differential equations with respect to parameters are multiplied with the variance covariance matrix of the parameters and horizontal uncertainty of the orthorectification is obtained by summing the results of this multiplication. Vertical uncertainty is caused by the uncertainty of DEM and the uncertainty of the horizontal position. Vertical uncertainty caused by the horizontal uncertainty is predicted by estimating a trend by generating a surface polynomial from DEM on the basis of covariance function of Hirvonen. Contribution of each error source is illustrated and the most sensitive parameter is obtained. With this knowledge, special weight can be given to the most sensitive parameter and the uncertainty of the orthorectification can be decreased in the most efficient way.