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In this thesis, I present a decentralized sparse Gaussian process regression (DSGPR) model with event-triggered, adaptive inducing points. This DSGPR model brings the advantages of sparse Gaussian process regression to a decentralized implementation. Being decentralized and sparse provides advantages that are ideal for multi-agent systems (MASs) performing environmental modeling. In this case, MASs need to model large amounts of information while having potential intermittent communication connections. Additionally, the model needs to correctly perform uncertainty propagation between autonomous agents and ensure high accuracy on the prediction. For the model to meet these requirements, a bounded and efficient real-time sparse Gaussian process regression (SGPR) model is needed. I improve real-time SGPR models in these regards by introducing an adaptation of the mean shift and fixed-width clustering algorithms called radial clustering. Radial clustering enables real-time SGPR models to have an adaptive number of inducing points through an efficient inducing point selection process. I show how this clustering approach scales better than other seminal Gaussian process regression (GPR) and SGPR models for real-time purposes while attaining similar prediction accuracy and uncertainty reduction performance. Furthermore, this thesis addresses common issues inherent in decentralized frameworks such as high computation costs, inter-agent message bandwidth restrictions, and data fusion integrity. These challenges are addressed in part through performing maximum consensus between local agent models which enables the MAS to gain the advantages of decentralization while keeping data fusion integrity. The inter-agent communication restrictions are addressed through the contribution of two message passing heuristics called the covariance reduction heuristic and the Bhattacharyya distance heuristic. These heuristics enable user to reduce message passing frequency and message size through the Bhattacharyya distance and properties of spatial kernels. The entire DSGPR framework is evaluated on multiple simulated random vector fields. The results show that this framework effectively estimates vector fields using multiple autonomous agents. This vector field is assumed to be a wind field; however, this framework may be applied to the estimation of other scalar or vector fields (e.g., fluids, magnetic fields, electricity, etc.). Keywords: Sparse Gaussian process regression, clustering, event-triggered, decentralized, sensor fusion, uncertainty propagation, inducing points