Ústav teorie informace a automatizace

## Partial Forgetting in Bayesian Estimation

Kamil Dedecius
Typ obhajoby:
Ph.D.
Datum konání:
19.11.2010
Místo:
FD ČVUT, Na Florenci 25, 110 00 Praha 1
Mail:
Stav:
obhájeno
The parametric models represent a very popular approach to description of various phenomena. However, in real situations, the assumption of constant parameter would usually be violated. In order to make the modelling process stable and to avoid growing discrepancy between the model and the reality, we need to reflect the parameter time variations. The conceptually correct solutions model explicitly parameter variations, using Kalman filter and its extensions, H-inf filter etc. Still, there is a lot of cases when the precise description of model parameter evolution is not known. Therefore, the parameter filtering was weaken to tracking, employing techniques formally known as `forgetting'. The exponential forgetting method, from the Bayesian viewpoint flattening of the posterior parameter distribution, dominates this class of solutions. In the thesis, a new method called `partial forgetting' is developed. Its purpose is to solve the main drawbacks of most forgetting techniques. In comparison to most of them, it is defined in the Bayesian framework as a general method, theoretically independent of the underlaying parametric model and practically directly usable for a wide class of models. It is specified for one popular member of that class - the Gaussian (auto)regressive model with external disturbances. Though the mathematics related to it is nontrivial, the derivation was done almost analytically and only a minor need of numerical approximation of the digamma function appeared. By formulation of hypotheses about the multivariate parameter entries, the method allows to track them independently and to forget them with different rates. It possesses stabilizing property, which, in the Gaussian autoregressive model, helps to prevent the parameter covariance blow-up phenomenon, when the gain of the estimation algorithm grows without bounds for nonexciting signals. The method is suitable for modelling of various traffic variables, e.g., traction force or traffic intensities in towns. Its use is demonstrated for the latter one.
03.05.2018 - 08:01