Integral equation approach to joint state and parameter estimation in continuous-time MIMO systems

Abstract

This paper shows how the problem of simultaneous estimation of the continuous-time (CT) model parameters and the state of a multi-input multi-output (MIMO) system can be decoupled into a set of multi-input single-output (MISO) subproblems. It then shows how the MISO problem can be solved following an integral equation approach with a common denominator (CD) model. The key observation is that the initial condition terms arising out of integration in the data vector, heretofore considered to be an unnecessary burden on the estimator, form the initial state of a canonical realisation. State estimation is then computationally simple. The method is suitable for real-time implementation. It is also general and permits realisation of the measures of signals and their integrals by spectral methods employing orthogonal functions (OF), numerical methods from signal samples etc. An implementation of the algorithm based on block pulse functions (BPF) has been made. A discussion on related aspects of real-time implementation, accuracy and convergence of estimates, possible variants of the scheme etc. is also presented, along with a comparison with other existing methods and scope for further improvement.