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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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