New developments in the CAPTAIN Toolbox for Matlab with case study examples ⋆ C. J. Taylor * P. C. Young ** W. Tych *** E. D. Wilson * * Engineering Department, Lancaster University, UK (e-mail: c.taylor@lancaster.ac.uk, e.d.wilson1@lancaster.ac.uk) ** Lancaster Environment Centre, Lancaster University, UK; Fenner School of Environment and Society, Australian National University, Canberra; Australia (e-mail: p.young@lancaster.ac.uk) *** Lancaster Environment Centre, Lancaster University, UK (e-mail: w.tych@lancaster.ac.uk) Abstract: The CAPTAIN Toolbox is a collection of Matlab algorithmic routines for time series analysis, forecasting and control. It is intended for system identification, signal extraction, interpolation, forecasting and control of a wide range of linear and non–linear stochastic systems across science, engineering and the social sciences. This article briefly reviews the main features of the Toolbox, outlines some recent developments and presents a number of examples that demonstrate the performance of these new routines. The examples range from consideration of global climate data, through to electro–mechanical systems and broiler chicken growth rates. The new version of the Toolbox consists of the following three modules that can be installed independently or together: off–line, time–varying parameter estimation routines for Unobserved Component (UC) modelling and forecasting; Refined Instrumental Variable (RIV) algorithms for the identification and estimation of both discrete and ‘hybrid’ continuous–time transfer function models; and various routines for Non–Minimal State Space (NMSS) feedback control system design. This new segmented approach is designed to provide new users with a gentler introduction to Toolbox functionality; one that focuses on their preferred application area. It will also facilitate more straightforward incorporation of novel algorithms in the future. Keywords: Identification; estimation; forecasting; signal processing; control system design; robotic systems; climate data; chicken growth 1. INTRODUCTION The Computer–Aided Program for Time Series Analysis and Identification of Noisy Systems (CAPTAIN) Toolbox provides access to novel algorithms for various important aspects of system identification, estimation, nonstationary time series analysis, signal processing, adaptive forecasting and automatic control system design. These algorithms have been developed by the first three authors of this article, and their colleagues (see Acknowledgements), over many years. In fact, CAPTAIN was originated by the second author over 40 years ago, whilst the first Matlab implementation was released in 2000 (Pedregal et al., 2007; Taylor et al., 2007). The books on Recursive Estimation and Time Series Analysis (Young, 2011) and True Digi- tal Control: Statistical Modelling and Non–Minimal State Space Design (Taylor et al., 2013) contain information on the history, derivation and use of all of the algorithms in the Toolbox. ⋆ This work is supported by the Engineering and Physical Sciences Research Council (EPSRC), EP/M015637/1 and EP/R02572X/1; and project Programa Estatal de Investigacion 2013–2016, Spain (ECO2015–70331–C2–1–R). In essence, the Toolbox represents the output of various on–going investigations into Matlab implementations of the underlying algorithms, as well as default and optional values of the input parameters to the routines. This should help both expert and less experienced modellers to use these routines when they are considering the analysis of data sets across a wide range of scientific disciplines, as illustrated by the citations to e.g. Taylor et al. (2007) that have appeared in diverse areas of the open literature. As explained later in the article, the latest version of the Toolbox includes improved routines and new modelling tools. Furthermore, the Toolbox has recently been reorgan- ised significantly and now consists of the following three distinct modules: (1) TVPMOD: Time Variable Parameter (TVP) MODels. For the identification of Unobserved Com- ponent (UC) models, with a particular focus on time–variable and state–dependent parameter mod- els, including the popular Dynamic Harmonic Re- gression (DHR), all of which can be used for signal extraction, interpolation and forecasting.