Prediction of Context Information Using Kalman Filter Theory

R.E. Kalman presented in 1960 a novel approach [3] for an efficient solution of the discrete-data linear filtering problem from a computational point of view. The set of recursive equations usually called the Kalman filter has been exploited in a large number of application fields from automatic control systems to weather forecasting. We apply the Kalman filter theory to the analysis of the time series of values that represent context information. Firstly, we need to have a representation of the problem according a typical state space model, since we have a set of observations and we derive a prediction model based on an inner state that is represented by a set of vectors. In the following section, we give a general introduction to state space models and, in the remainder of this appendix, we present the ways in which we have applied these concepts to the analysis and the prediction of context information, discussing three cases according to the different behaviour of the time series. More specifically, we consider the cases of time series characterised by local trends and seasonal trends [1]. Clearly, the complete model introduces more computational overhead; however, it provides more accurate results.