The deployment of ubiquitous sensor systems and algorithms has led to many challenges, such as matching sensor systems to compatible algorithms which are capable of satisfying a task. Compounding the challenges is the lack of the requisite knowledge models needed to discover sensors and algorithms and to subsequently integrate their capabilities to satisfy a specific task. A novel ontological problem-solving framework has been designed to match sensors to compatible algorithms to form synthesized systems, which are capable of satisfying a task and then assigning the synthesized systems to high-level missions. The approach designed for the ontological problem-solving framework has been instantiated in the context of a persistence surveillance prototype environment, which includes profiling sensor systems and algorithms to demonstrate proof-of-concept principles. Even though the problem-solving approach was instantiated with profiling sensor systems and algorithms, the ontological framework may be useful with other heterogeneous sensing-system environments.