The state and observation equations of space objects are nonlinear and therefore it is hard to estimate the conditional probability density of the space object trajectory states given EO/IR, radar or other nonlinear observations. Moreover, space object trajectories can suddenly change due to abrupt changes in the parameters affecting a perturbing force or due to unaccounted forces. Such trajectory changes can lead to the loss of existing tracks and may cause collisions with vital operating space objects such as weather or communication satellites. In this talk, Scientific Systems Company, Inc. (SSCI) and Lockheed Martin Corporation (LMCO) joint work on algorithms and methods for Space Situational Awareness (SSA) is presented including problem formulation, derivation of mathematical methods for modeling and estimation of space-based object states, derivation of observation models, estimation algorithm derivation, numerical implementations, simulation testbed, and simulation results. The presented estimation methods will aid in preventing the occurrence of collisions in space and also provide warnings for collision avoidance.