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The purpose of this paper is to probe the recursive identification of piecewise affine Hammerstein models directly by using input-output data. To explain the identification process of a parametric piecewise affine nonlinear function, the authors prove that the inverse function corresponding to the given piecewise affine nonlinear function is also an equivalent piecewise affine form. Based on this equivalent property, during the detailed identification process with respect to piecewise affine function and linear dynamical system, three recursive least squares methods are proposed to identify those unknown parameters under the probabilistic description or bounded property of noise.

First, the basic recursive least squares method is used to identify those unknown parameters under the probabilistic description of noise. Second, multi-innovation recursive least squares method is proposed to improve the efficiency lacked in basic recursive least squares method. Third, to relax the strict probabilistic description on noise, the authors provide a projection algorithm with a dead zone in the presence of bounded noise and analyze its two properties.

Based on complex mathematical derivation, the inverse function of a given piecewise affine nonlinear function is also an equivalent piecewise affine form. As the least squares method is suited under one condition that the considered noise may be a zero mean random signal, a projection algorithm with a dead zone in the presence of bounded noise can enhance the robustness in the parameter update equation.

To the best knowledge of the authors, this is the first attempt at identifying piecewise affine Hammerstein models, which combine a piecewise affine function and a linear dynamical system. In the presence of bounded noise, the modified recursive least squares methods are efficient in identifying two kinds of unknown parameters, so that the common set membership method can be replaced by the proposed methods.

The purpose of this paper is to present a new methodology for identification of the parameters of the local linear Takagi‐Sugeno fuzzy models using weighted recursive least squares. The weighted recursive least squares (WRLS) is sensitive to initialization which leads to no converge. In order to overcome this problem, Euclidean particle swarm optimization (EPSO) is employed to optimize the initial states of WRLS. Finally, validation results are given to demonstrate the effectiveness and accuracy of the proposed algorithm. A comparative study is presented. Validation results involving simulations of numerical examples and the liquid level process have demonstrated the practicality of the algorithm.

A new method for nonlinear system modelling. The proposed algorithm is employed to optimize the initial states of WRLS algorithm in two phases of learning algorithm.

The results obtained using this novel approach were comparable with other modeling approaches reported in the literature. The proposed algorithm is able to handle various types of modeling problems with high accuracy.

In this paper, a new method is employed to optimize the initial states of WRLS algorithm in two phases of the learning algorithm.

Discusses recursive estimation techniques which can be used to update or revise estimates of the parameters of an economic model to account for new data. Such methods admit the possibility of proceeding with the gathering of observed data until a specified accuracy of the parameters is achieved or if the economic processes are time‐varying the parameters can be tracked. Recursive methods can also be used for adaptive learning, forecasting and control. Examines both single equation ‐ static as well as dynamic ‐ economic models.

Previous evidence suggests that the relationship between different stock markets is unstable over time. In particular, the Finnish and Japanese financial economies are interrelated and exhibit non‐linear behaviour. Presents an approximation of the influence of the Japanese stock market on the Finnish derivatives market by an adaptive recursive least squares (RLS) algorithm. The parameters are allowed to change over time through a discounting factor, thus providing a convenient means for recognizing past information to a specified degree. Following the reasoning of Bera et al. (1992), shows that the RLS algorithm is, theoretically, able to cope with conditional heteroscedasticity. Compares the results with different values on the discount factor and when choosing a suitable value the ARCH‐like effects in the residuals seem to vanish. On the other hand, some new peculiarities in the RLS residuals emerge when ARCH effects are eliminated. The results indicate that the standard RLS algorithm combined with a proper specification of the discount factor could be useful in studying relationships of this kind.

This study/paper aims to present a separable identification algorithm for a multiple input single output (MISO) continuous time (CT) hybrid “Box–Jenkins”.

This paper proposes an optimal method for the identification of MISO CT hybrid “Box–Jenkins” systems with unknown time delays by using the two-stage recursive least-square (TS-RLS) identification algorithm.

The effectiveness of the proposed scheme is shown with application to a simulation example.

A two-stage recursive least-square identification method is developed for multiple input single output continuous time hybrid “Box–Jenkins” system with multiple unknown time delays from sampled data. The proposed technique allows the division of the global CT hybrid “Box–Jenkins” system into two fictitious subsystems: the first one contains the parameters of the system model, including the multiple unknown time delays, and the second contains the parameters of the noise model. Then the TS-RLS identification algorithm can be applied easily to estimate all the parameters of the studied system.

In spite of the vehicle, magnetic field interference can be reduced by some measures and techniques in ammunition design and manufacturing stage, the corruption of the vehicle magnetic field can still reach hundreds to thousands of nanoteslas. Besides, the magnetic field that the ferromagnetic materials generate in response to the strong magnetic field in the vicinity of the body. So, a real-time and accurate vehicle magnetic field calibration method is needed to improve the real-time measurement accuracy of the geomagnetic field for spinning projectiles.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time. In the method, the elliptical model of magnetometer measurement is established to convert the coefficients of hard and soft iron errors into the parameters of the elliptic equation. Then, the parameters are estimated by recursive least square estimator in real-time. Finally, the initial conditions for the estimator are established using prior knowledge method or static calibration method.

Studies show the proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real-time. A turntable experiments indicate that the post-calibration residuals approximate the measurement noise of the magnetometer and the roll accuracy is better than 1°. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers' calibration in real-time.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time and the calculation is small. Besides, it does not take up storage space. The proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real time. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers’ calibration in real-time.

The purpose of this study is to build a high accuracy thrust model under various small turbojet engine shaft speeds by using robust, ordinary, linear and nonlinear least squares estimation methods for target drone applications.

The dynamic shaft speeds from the test experiment of a target drone engine is conducted. Then, thrust values are calculated. Based on these, the engine thrust is modeled by robust linear and nonlinear equations. The models are benefited from quadratic, power and various series expansion functions with several coefficients to optimize the model parameters.

The error terms and accuracy of the model are given using sum of squared errors, root mean square error (RMSE) and R-squared (R²) error definitions. Based on the multiple analyses, it is seen that the RMSE values are no more than 17.7539 and the best obtained result for robust least squares estimation is 15.0086 for linear at all cases. Furthermore, the R² value is found to be 0.9996 as the highest with the nonlinear Fourier series expansion model.

The motivation behind this paper is to propose robust nonlinear thrust models based on power, Fourier and various series expansion functions for dynamic shaft speeds from the test experiments.

The purpose of this paper is to study the identification methods for multivariable nonlinear Box‐Jenkins systems with autoregressive moving average (ARMA) noises, based on the auxiliary model and the multi‐innovation identification theory.

A multi‐innovation generalized extended least squares (MI‐GELS) and a multi‐innovation generalized ex‐tended stochastic gradient (MI‐GESG) algorithms are developed for multivariable nonlinear Box‐Jenkins systems based on the auxiliary model. The basic idea is to construct an auxiliary model from the measured data and to replace the unknown terms in the information vector with their estimates (i.e. the outputs of the auxiliary model).

It is found that the proposed algorithms can give high accurate parameter estimation compared with existing stochastic gradient algorithm and recursive extended least squares algorithm.

In this paper, the AM‐MI‐GESG and AM‐MI‐GELS algorithms for MIMO Box‐Jenkins systems with nonlinear input are presented using the multi‐innovation identification theory and the proposed algorithms can improve the parameter estimation accuracy. The paper provides a simulation example.

Listed real estate securities have historically been used to achieve an exposure to the real estate asset class and to obtain a broad spectrum of other specific features such as return enhancement, but whether they must be associated to the direct property or to the broad stock market is deceptive on a merely theoretical basis. Moreover, the global financial crisis (GFC) has questioned their risk/return characteristics. The purpose of this paper is to asses if listed real estate securities are still enough dissimilar from the broad stock market to provide remarkable diversification benefits for a long term investor.

The analysis has been developed on the FTSE EPRA/NAREIT Developed Index and at country level (USA, UK, France, Japan, Singapore, Hong Kong and Australia) from November 2001 to October 2013. The authors analysed the real estate index over a broad market index and adjusted for a possible bias related to heteroskedasticity and autocorrelation, using a least squared regression with Newey-West HAC Correction. A Recursive Least Squares (RLS) was also used to test the stability of the parameters with the CUSUM squared test and the Chow test. Finally the authors tested for cointegration with the Augmented Dickey Fuller and the Engle Granger tests.

The authors found that after the GFC the Beta-risk related to the stock market has witnessed a sharp increase, but with differences among country. While the USA, the UK and France have experienced a trend similar to the one described for the FTSE EPRA/NAREIT Developed Index, Asian Markets depict a quite stable Beta over the full sample (gradual increase for the Australian market). Evidence of a structural break in conjunction with 2008 crisis has been found only in USA, UK and France.

Listed real estate securities, even if characterised by time varying Beta-risk and partially reduced diversification benefits, are still worth to be included in long term horizon portfolios. However, more wary considerations should be drafted before investing in the Asian markets where evidence of cointegration was found only for the Japanese market.

Analysis of post GFC effect on direct property investment vs indirect listed investment worldwide.

Simple algoritims are developed to track the harmonic structure of the voltages or currents in a power system. The algorithms are based on fitting the measured signal adaptively to an appropriate model in a least mean squares (LMS) sense. The update is accomplished employing the well known adaptive LMS and signed LMS algorithms. The input sequence at each iteration consists of samples of harmonic sinusoids with a fundamental equal to the power frequency. It is shown that such input satisfies the persistence of excitation condition. It is also shown that the algorithms are computationally simple, practically tractable, and exhibit guaranteed stability. The performance of the algorithms and their efficiency in digital relaying in power system protection problems are demonstrated.