A Continuous-Time Linear System Identification Method for Slowly Sampled Data

• Published in: IEEE transactions on signal processing Vol. 58; no. 5; pp. 2521 - 2533
• Main Authors: Marelli, Damian, Minyue Fu
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aliasing; Ambiguity; Applied sciences; Asymptotic properties; Biological system modeling; Continuous time systems; Detection, estimation, filtering, equalization, prediction; Estimates; Exact sciences and technology; Frequency; identification; Information, signal and communications theory; Linear systems; Mathematical models; Miscellaneous; Parameter estimation; Physics; Sampled data; Sampled data systems; Sampling; Sampling methods; Sampling, quantization; Signal and communications theory; Signal processing; Signal, noise; Systems biology; Telecommunications and information theory; Time domain analysis; Sampled system; Parameter estimation; Input signal; Continuous time; Continuous time systems; Output signal; Linear model; Sampling frequency; Direct method; Accuracy; Linear system; identification; sampled data systems; Indirect method; Aliasing; Sampling rate; Discrete time; Signal processing; System identification; Sampling; Continuous system
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2040017

Both direct and indirect methods exist for identifying continuous-time linear systems. A direct method estimates continuous-time input and output signals from their samples and then use them to obtain a continuous-time model, whereas an indirect method estimates a discrete-time model first. Both methods rely on fast sampling to ensure good accuracy. In this paper, we propose a more direct method where a continuous-time linear model is directly fitted to the available samples. This method produces an exact model asymptotically, modulo some possible aliasing ambiguity, even when the sampling rate is relatively slow. We also state conditions under which the aliasing ambiguity can be resolved, and we provide experiments showing that the proposed method is a valid option when a slow sampling frequency must be used but a large number of samples is available.