Continuous-time system identification using compactly-supported filter kernels generated from Laguerre basis functions

This paper studies a continuous-time system identification method based on system transformation using generalized orthonormal basis functions, especially the Laguerre basis. It is known that the expansion of observation signals with Laguerre basis functions is useful for analyzing linear dynamical systems. This processing however, involves the calculation with infinite integral, hence, the problem with truncation occurs at the stage of implementation. The proposed method of signal transformation using finitely-supported filter kernels avoids this problem, still preserves the exact system transformation. It turns out that the instrumental variable subspace identification method successfully works with the transformed signals and achieve consistent estimates for systems disturbed with possibly colored noise. The proposed method is applicable to recursive identification. Some numerical examples are presented to demonstrate the results.