Many sensor network applications monitor continuous phenomena by sampling, and fit time-varying models that capture the phenomena's behaviors. We introduce Pulse, a framework for processing continuous queries over these continuous-time data models. Pulse allows users to declaratively specify both their queries and models, and transforms these queries into simultaneous equation systems, which in many cases are significantly cheaper to process than a stream of discrete tuples. Pulse is able to guarantee user-defined error bounds between query results from continuous-time data models and sampled data, including cases of null results. We present a high-level overview of the design and architecture of Pulse and propose several query optimization techniques that are novel to our context, such as the simplification of our equation systems. We also discuss our plans for extending Pulse to support several novel model types, including differential equations and time series, and an abstract...