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Signal estimation is very important for communication and many digital processing applications. Most conventional estimation techniques are based on solving an optimization problem. Key drawback of these conventional approaches are that they rely, too much, on questionable criteria. Therefore, they may produce a so-called optimal solution but violate known information about the problem. Alternatively, set theoretic estimation does not provide an optimal solution but a set of solutions which is consistent with all the priori knowledge and observed data. The goal of set theoretic estimation is to generate a feasible solution instead of best solution. In this thesis, we describe some fundamental contributions about using the unknown noise distribution in a general set theoretic estimation. Although noise is usually bounded and nonuniformly distributed, we propose using the triangular distribution to approximate the unknown noise distribution. We then construct the feasible solution sets accordingly to the solution space. Adding these sets to the collection of sets describing the solution space will then yeild a smaller global feasibility set and more reliable estimates. In addition, the mismatch effects on the triangular and unknown noise distribution (which may be asymmetric) is also studied. Finally, simulation results are used to verify our theoretical developments.
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