Understanding of Group Activities (GA) has significant applications in civilian and military domains. The process of understanding GA is typically involved with spatiotemporal analysis of multi-modality sensor data. Video imagery is one popular sensing modality that offers rich data, however, data associated with imagery source may become fragmented and discontinued due to a number of reasons (e.g., data transmission, or observation obstructions and occlusions). However, making sense out of video imagery is a real challenge. It requires a proper inference working model capable of analyzing video imagery frame by frame, extract and inference spatiotemporal information pertaining to observations while developing an incremental perception of the GA as they emerge overtime. In this paper, we propose an ontology based GA recognition where three inference Hidden Markov Models (HMM's) are used for predicting group activities taking place in outdoor environments and different task operational taxonomy. The three competing models include: a concatenated HMM, a cascaded HMM, and a context-based HMM. The proposed ontology based GA-HMM was subjected to set of semantically annotated visual observations from outdoor group activity experiments. Experimental results from GA-HMM are presented with technical discussions on design of each model and their potential implication to Persistent Surveillance Systems (PSS).