Captain Toolbox for System Identification, Time Series Analysis, Forecasting and True Digital Control

The CAPTAIN Toolbox is a collection of MATLAB functions for non-stationary time series analysis, forecasting and control. It is useful for system identification, signal extraction, interpolation, data-based mechanistic modelling and control of a wide range of linear and non-linear stochastic systems. The toolbox consists of three modules as follows:

UPDATE (July 2017) The latest version merges the previously available CAPTAIN and TDC toolboxes into one package, which now consists of three folders as above. The toolbox is presently developed and tested for MATLAB R2017b onwards, although some backwards compatibility is maintained through to MATLAB 2014a.

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Toolbox Overview

CAPTAIN is a MATLAB compatible toolbox for non-stationary time series analysis and forecasting. Based around a powerful state space framework, it extends MATLAB to allow, in the most general case, for the identification of Unobserved Components models. Here, the time series is assumed to be composed of an additive or multiplicative combination of different components that have defined statistical characteristics but which cannot be observed directly. With Maximum Likelihood estimation of most models and the inclusion of several popular model forms, such as the Basic Structural Model and the Dynamic Linear Model, together with a standard set of data pre-processing, system identification and model validation tools, CAPTAIN is a wide-ranging package for signal processing and general time series analysis.

Uniquely, however, CAPTAIN focuses on Time Variable Parameter (TVP) models, where the stochastic evolution of each parameter is assumed to be described by a generalised random walk process. In this regard, the state space formulation utilised is particularly well suited to estimation based on optimal recursive estimation, in which the time variable parameters are estimated sequentially whilst working through the data in temporal order. In the off-line situation, where all the time series data are available for analysis, this Kalman filtering operation is accompanied by optimal recursive smoothing. Here the estimates obtained from the forward pass filtering algorithm are updated sequentially whilst working through the data in reverse temporal order using a backwards-recursive Fixed Interval Smoothing algorithm.

In this manner, CAPTAIN provides novel tools for TVP analysis, allowing for the optimal estimation of dynamic regression models, including linear regression, auto-regression and harmonic regression. Furthermore, a closely related algorithm for state dependent parameter estimation provides for the non-parametric identification and forecasting of a very wide class of nonlinear systems, including chaotic systems. The identification stage in this process again exploits the recursive smoothing algorithms, combined with special data re-ordering and back-fitting procedures, to obtain estimates of any state dependent parameter variations.

Of course, in many cases, specifying time invariant parameters for the model yields the equivalent, conventional, stationary model. In this regard, one model that has received special treatment in the toolbox is the multiple-input, single-output Transfer Function model. CAPTAIN includes functions for robust unbiased identification and estimation of both discrete-time and continuous-time Transfer Function models. One advantage of the Transfer Function model is its simplicity and ability to characterise the dominant modal behaviour of a dynamic system. This makes such a model an ideal basis for control system design. Hence, the toolbox also includes a set of functions for True Digital Control, based on the Proportional-Integral-Plus (PIP) control system design methodology (see below).

Some of the estimation algorithms in CAPTAIN have been in constant use for over 30 years (e.g. RIV in the microCAPTAIN package for MS-DOS). However, the MATLAB implementation is much more flexible and includes the latest innovations and improvements. The authors hope that the toolbox will allow interested researchers to add to the ever expanding list of successful applications, which already includes the analysis of numerous biological, environmental, engineering and socio-economic processes, as illustrated by some of the articles in the scientific literature that cite the following article (see e.g. Google Scholar):

Taylor, C.J., Pedregal, D.J., Young, P.C. and Tych, W. (2007) Environmental time series analysis and forecasting with the Captain toolbox, Environmental Modelling and Software, 22, pp. 797–814.

True Digital Control

Statistical Modelling and Non–Minimal State Space Design

Book by C J Taylor, A Chotai and P C Young (2013)

Published by John Wiley & Sons Ltd

Practical modern control and stochastic system identification for students and professionals.

This book develops a true digital control design philosophy that encompasses data–based model identification, through to control algorithm design, robustness evaluation and implementation. With a heritage from both classical and modern control system synthesis, this book is supported by detailed practical examples based on the authors’ research into environmental, mechatronic and robotic systems. Treatment of both statistical modelling and control design under one cover is unusual and highlights the important connections between these disciplines.

Starting from the ubiquitous proportional–integral controller, and with essential concepts such as pole assignment introduced using straightforward algebra and block diagrams, this book addresses the needs of those students, researchers and engineers, who would like to advance their knowledge of control theory and practice into the state space domain; and academics who are interested to learn more about non–minimal state variable feedback control systems. Such non–minimal state feedback is utilised as a unifying framework for generalised digital control system design. This approach provides a gentle learning curve, from which potentially difficult topics, such as optimal, stochastic and multivariable control, can be introduced and assimilated in an interesting and straightforward manner.

Cover page and chapter descriptions.

Key features:

The book offers a comprehensive and practical guide for students and professionals who wish to further their knowledge in the areas of modern control and stochastic system identification.

Dr C. James Taylor
Engineering Department
Faculty of Science & Technology
Lancaster University, LA1 4YW, UK

Office Phone +44 (0) 1524 594076
Department +44 (0) 1524 593093
E-mail c.taylor AT

Updated 29th June 2017. CJT