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The Cramer-Rao Lower Bound establishes a fundamental performance baseline for gauging parameter estimation accuracy in tracking and data fusion. However, it is known to be a weak lower bound for some problems. This paper presents a set of tighter alternatives: the Bhattacharyya, Bobrovsky-Zakai and Weiss-Weinstein lower bounds. General mathematical expressions are obtained for these bounds and their calculation is described. Then the bounds are applied to a nonlinear/non-Gaussian estimation problem. It is found that the alternative bounds are tighter than the Cramer-Rao bound, but they are still somewhat conservative.