Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE credits
With the rapid development of new technologies during the last decades,
the demand of complex algorithms to work in real-time applications has increased
considerably. To achieve the real time expectations and to assure
the stability and accuracy of the systems, the application of numerical methods
and matrix decompositions have been studied as a trade-off between
complexity, stability and accuracy. In the first part of this thesis, a survey
of state-of-the-art QR Decomposition methods applied to matrix inversion
is done. Stability and accuracy of these methods are analyzed analytically
and the complexity is studied in terms of operations and level of parallelism.
Besides, a new method called Modified Gaussian Elimination (MGE) is proposed.
This method is shown to have better accuracy and less complexity
than the previous methods while keeping good stability in real time applications.
In the second part of this thesis, different techniques of extended
Kalman Filter implementations are discussed. The EKF is known to be numerically
unstable and various methods have been proposed in the literature
to improve the performance of the filter. These methods include square-root
and unscented versions of the filter that make use of numerical methods such
as QR, LDL and Cholesky Decomposition. At the end of the analysis, the
audience/reader will get some idea about best implementation of the filter
given some specifications.
2014. , 73 p.