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Tracking of a ballistic re-entry object from radar observations is a highly complex problem in nonlinear filtering. The paper adopts a one-dimensional vertical motion model with unknown ballistic coefficient, derives and analyses the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compares the error performance of three nonlinear filters against the theoretical CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Taking into account the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.