Data fusion in interdependent signal systems via orthogonal projection

We describe a system monitored in terms of dynamic/algebraic equations of respective state variables. Often, important system variables cannot be directly measured and have to be calculated from the model equations. The practical difficulty is that due to various reasons (distortions of measurement signals, model simplifications, etc.) there is an inconsistency between measured variables and the mathematical model. This makes it difficult to infer changes in system state. We propose a method that estimates (both measured and unmeasured) state variables by fusing information from measurement data and a mathematical model. First we introduce the mathematical formulation of the method. The idea is to represent the problem in a Hilbert space spanned by an appropriate function basis. By an appropriate choice of the basis functions, the resulting variables can also satisfy regularity conditions such as smoothness or continuity that we may impose on them. The system variables that we obtain by the method are simultaneously close to the measurement and the model we impose. Finally we present an algorithmic scheme that can be used in practice to localise low frequency distortions with respect to the model.