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Abstract We study Bayesian data assimilation (filtering) for time-evolution Partial differential equations (PDEs), for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier–Stokes equations of fluid dynamics, are characterized by a high sensitivity of solutions to perturbations of the initial data, a lack of rigorous global well-posedness results as well as possible non-convergence of numerical approximations. Under very mild and readily verifiable general hypotheses on the forward solution operator of such PDEs, we prove that the posterior measure expressing the solution of the Bayesian filtering problem is stable with respect to perturbations of the noisy measurements, and we provide quantitative estimates on the convergence of approximate Bayesian filtering distributions computed from numerical approximations. For the Navier–Stokes equations, our results imply uniform stability of the filtering problem even at arbitrarily small viscosity, when the underlying forward problem may become ill-posed, as well as the compactness of numerical approximants in a suitable metric on time-parametrized probability measures. 

In an IoP environment, edge computing has been proposed to address the problems of resource limitations of edge devices such as smartphones as well as the high-latency, user privacy exposure and network bottleneck that the cloud computing platform solutions incur. This paper presents a context management framework comprised of sensors, mobile devices such as smartphones and an edge server to enable high performance, context-aware computing at the edge. Key features of this architecture include energy-efficient discovery of available sensors and edge services for the client, an automated mechanism for task planning and execution on the edge server, and a dynamic environment where new sensors and services may be added to the framework. A prototype of this architecture has been implemented, and an experimental evaluation using two computer vision tasks as example services is presented. Performance measurement shows that the execution of the example tasks performs quite well and the proposed framework is well suited for an edge-computing environment.