Space debris is becoming an ever increasing problem in space operations. Mitigation techniques exist, but require knowledge about debris objects in order to track them and predict where they will be in the future. One technique that is commonly used to estimate this information is called light curve inversion. The apparent brightness of an object passing overhead is measured from the ground, and information like orbit and attitude states can be estimated and object shapes can be characterized. This thesis focused on improving existing techniques for state estimation and shape characterisation for LEO objects. The state-of-the-art method, Multiple-Model Adaptive Estimation (MMAE), was implemented, tested and improved upon. Additionally, Variable-Structure Multiple-Model methods were implemented and tested. Testing involved simulating measurements for LEO satellites and running estimations. The improved MMAE algorithm was able to correctly identify the shapes of test objects for almost all test cases, with low attitude estimation errors.