The accurate, comprehensive estimation of computational error has long been a key problem in the design of automated target recognition (ATR) algorithms due to the extensive manual computation customarily required, as well as lack of theory and software support for automated error analysis. For example, ATR algorithms often perform poorly in the presence of sensor noise at the algorithm input, which is propagated through detection, segmentation, or recognition processes. Since computational error increases with each nontrivial computation, tracking of such error in ATR and image processing algorithms would be advantageous for a variety of applications. In this series of two paper, we present an automated, compilation-based technique for profiling computational error. Our method is similar in concept to the well-known software engineering technique of execution profiling. Such performance estimation procedures accept algorithm source code and produce statistical data that describe the frequency with which various user-defined or built-in functions are invoked. Given such data, algorithm performance can be analyzed in terms of cost measures such as space and time complexity, which supports performance optimization. We herein extend the concept of execution profiling to include the profiling of computational error. Our method employs error probability distributions computed from error functions that are derived from the parse tree which represents a given expression or algorithm. Distributions are characterized in terms of customary descriptors derived from a bivariate probability density map. In this paper, we present basic theory and algorithms for automated error analysis, together with a description of our prototype software system called ERSIA. ERSIA, written in ANSI-standard FORTRAN-77, is portable to numerous workstations and parallel processors.