Rank reduction algorithms for filtering and parameter estimation in inverse problems with applications

The method of rank reduction has been proposed for electrodynamically weighing systems for non-parametric modeling. The algorithms are based on the rank reduction paradigm with emphasis on signal subspace techniques. The general principle of rank reduction for signal synthesis modeling and signal whitening has been treated. In this very application where the method of rank reduction was applied to the electrodynamically weighing system, the order of the system was known to be two. We also knew the source(s) of the different heterogeneous inputs. Thus, the prior knowledge which is subject to the optimal rank of the objective function was known beforehand and so it was incorporated into the model. From this application specific perspective, we showed that if we are able to incorporate a good knowledge about the optimal rank into the overall system model, the signal estimate obtained can outperform the general principle of rank reduction which is based on the trade off between the model bias and model variance. On the other hand, if the rank was unknown, we might have had the difficulty of choosing the best signal estimate since the signal estimate obtained from the signal synthesis modeling is very different from signal estimate obtained from the model based on signal whitening. The addition of prior knowledge into the model of rank reduction algorithms can improve upon the performance in terms of both accuracy and speed since the computational resource(s) that is spent in the determination of the rank may also be reduced.