This paper further develops the concept of an applied geographic information system (AGIS) for modeling search correlation-extreme navigation systems (CENSs), which was presented in [4]. As shown below, the AGIS can be configured to perform computational experiments with computer models of the existing CENSs and those undergoing various development stages without programming in universal languages. Strict reliability requirements for CENSs increase the role of testing their computer models under stress exposures. During stress testing, the negative effects of different exposures on autonomous navigation conditions are assessed in application areas. Such exposures are not considered at the CENS design stage (reference point masking, distortion of terrain objects borders, etc.). The exposures that prevent CENSs from performing their tasks effectively (critical exposures) are described. Stability to critical exposures is a strong motivation for improving all CENS elements: sensors of geophysical fields, onboard algorithms, and CENS preparation procedures for performing particular tasks in application areas. The mathematical model of approximation by generalized step functions [4] is used to analyze critical exposures on CENS operation. Computer simulation models of different shooting systems are considered as the most important sources of initial data on the approximated function. The mathematical model of stress exposures on CENSs that match images by the mutual correlation criterion is developed further.