Tracking and characterizing the space debris population in Earth orbit is necessary to ensure that space can continue to be used safely. However, because space objects are affected by non-conservative forces like drag and solar radiation pressure, predicting the long-term evolution of their orbits is impossible without knowledge of their attitude profiles. Such knowledge may be unavailable for inactive satellites or objects of which the observer is not the owner or operator. In many cases, attitude cannot be measured directly because resolved images of space objects are unavailable due to the distance between the object and the observer, and the effects of atmospheric seeing. However, the total brightness of objects can still be measured. A set of brightness measurements over time is referred to as a "light curve.'' An object's observed brightness is influenced by its attitude and other factors such as its orbit, shape, and reflective properties. If some of these other factors are known, attitude information may be extracted from a light curve. Existing methods of solving this attitude inversion problem either require a good initial guess for an object's rotational states or do not provide a full state estimate. The work in this thesis avoids both problems and provides a full state estimate without requiring an initial state guess.The attitude estimation process assumes that the observation geometry and the observed object's shape, reflection properties, and inertia tensor are known. In this thesis, an initial method of searching for attitudes that could correspond to each measurement using the viewing sphere is described. These possible attitudes or "pseudo-measurements'' are then used to initialize a probability hypothesis density filter that is theoretically capable of representing the multi-modal nature of the attitude estimate using a Gaussian mixture model. However, the probability hypothesis density filter is found to often diverge from the truth because it is necessary to merge and prune components of the Gaussian mixture model to avoid computational intractability. In its place, a particle swarm optimizer method for performing an attitude inversion has been developed. This method uses analytic attitude solutions to quickly propagate a large number of attitude time histories simultaneously. The particle swarm optimizer method is validated using simulated light curves for several objects. A preliminary attempt is made to estimate the attitude of an object using real light curve measurements.