The optimal estimation problems for linear dynamic systems, and in particular for systems with aftereffect, reduce to different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of a variational problem determines an optimal estimator. In addition, frequently the optimal algorithm for one noise model must operate under another, more complex assumption about noise. Hence, simplified algorithms must be used. It is important to evaluate the level of nonoptimality for the simplified algorithms. Since the original variational problems can be very difficult, the estimate of nonoptimality must be obtained without solving the original variational problem. In this book, guaranteed levels of nonoptimality for simplified estimation and control algorithms are constructed. To obtain these levels the duality theory for convex extremal problems is used. Audience: This book will be of interest to applied mathematicians, researchers and engineers who deal with estimation and control systems. The material, which requires a good knowledge of calculus, is also suitable for a two-semester graduate or postgraduate course.