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Online monitoring and diagnostics are important functions in the operation and maintenance of electric power systems. In this preliminary paper we present two new methods for electric power grid state and parameter estimation when a limited amount of grid information is available. The methods are based on developing a constrained optimization problem whose solution provides a set of desired grid information. The first method attempts to estimate an approximate state of the grid from a set of measurements at a relatively small number of sites. Constrained to the power balance manifold, this method minimizes an objective function based on generic grid behavior as well as any available information about the particular state of the grid to estimate a selected set of grid states and parameters. The second approach uses time data from a small number of sites to try to detect and localize an event such as a faulted line in the grid. This method minimizes an objective function defined on the time-varying power balance manifold that is designed to be sensitive to abrupt local state and parameter changes. This detection and localization tool is intended as an early warning system or a supplemental check within a larger multi-modal detection system. The capabilities of the approaches are demonstrated through simulation on a IEEE power flow test grid.