Centre for Research on Environmental Systems and Statistics Captain Toolbox

CAPTAIN Toolbox website

Overview & availability

User interface & examples

Time variable parameter subset

Multivariable transfer function subset

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Lancaster University
Systems and Control
Environmental Science

Transfer Function (TF) modelling subset

The input-output modelling functions allow for robust unbiased estimation of multiple-input transfer function models. Either discrete-time models, represented in terms of the backward shift operator, or continuous-time models based on the Laplace Transform operator, are possible.

There are numerous algorithms for estimating transfer functions. However, the primary technique employed in the Captain Toolbox is the Instumental Variable approach. In particular, the toolbox provides the recursive and en-block Refined Instrumental Variable (RIV) and Simplified Refined Instrumental Variable (SRIV) algorithms, as well as more conventional least squares approaches. These algorithms are accessed through the functions riv (discrete) and rivc (continuous).


The toolbox functions riv/rivc allow for the estimation of transfer functions based on a user specified model structure. However, for a given physical system, an appropriate model structure first needs to be identified, i.e., the most appropriate values for the time delay and the orders of the numerator and denominator polynomials. The toolbox functions rivid/rivcid are employed for this purpose. The two main statistical measures utilised here are the coefficient of determination RT2, based on the response error, which is a simple measure of model fit (where unity indicates perfect fit) and the more sophisticated Young Identification Criterion (YIC), which provides a combined measure of fit and parametric efficiency with large negative values indicating a model which explains the output data well, without over-parameterisation.

Selected references

A link to the abstract is provided for some papers.

  • Jarvis, A.J., Young, P.C., Taylor, C.J. and Davies, W.J., (1999), An analysis of the dynamic response of stomatal conductance to a reduction in humidity over leaves of cedrella odorata, Plant, Cell and Environment, 22, 13-924.
  • Lees, M., Young, P.C., Ferguson, S., Beven, K.J. and Burns, J., (1994), An adaptive flood warning scheme for the River Nith at Dumfries, in White, W.R. and Watts, J. (Eds.), River Flood Hydraulics, John Wiley and Sons, Chichester, 65-75.
  • Young P.C., (1984), Recursive Estimation and Time Series Analysis, Springer-Verlag, Berlin.
  • Young, P.C., (1996), Identification, estimation and control of continuous-time and delta operator systems, in M.I. Friswell J.E. Mottershead (Eds.), Identification in Engineering Systems, University of Wales, Swansea, 1-17.
  • Young, P., (1998), Data-based mechanistic modelling of Engineering Systems, Journal of Vibration and Control, 4, 5-28.
  • Young, P., (1998), Data-based mechanistic modelling of environmental, ecological, economic and engineering systems, Environmental Modelling and Software, 13, 105-122.
  • Young, P.C. and Beven, K.J., (1994), Data-Based Mechanistic Modelling and the Rainfall Flow Nonlinearity, Environmetrics, 5, 335-363.
  • Young, P.C., Lees, M., Chotai, A., Tych, W. and Chalabi, Z.S., (1994), Modelling and PIP Control of a Glasshouse Micro-Climate, Control Engineering Practice, 2, 4, Pergamon Press, Oxford, 591-604.
  • Young, P.C., Parkinson, S. and Lees, M.J., (1996), Simplicity out of complexity: Occam's razor revisited, Journal of Applied Statistics, 23, 165-210.

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c.taylor@lancaster.ac.uk 23-FEB-2011