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This study focuses on the parameter estimation of the dual-rate Hammerstein-controlled autoregressive moving average (CARARMA) system. Because dual-rate systems have variables that cannot be directly measured, we use the auxiliary model to obtain a transformed model which can be directly identified. Aiming at the dual-rate Hammerstein CARARMA system, a multi-innovation improved differential evolution identification method is proposed, and its effectiveness is experimentally verified. By comparing with the improved differential evolution algorithm, it can be found that the proposed algorithm can give more accurate parameter estimates. [ABSTRACT FROM AUTHOR]

Summary: This paper deals with the problem of the parameter estimation for feedback nonlinear output‐error systems. The auxiliary model‐based recursive least squares algorithm and the auxiliary model‐based stochastic gradient algorithm are derived for parameter estimation. Based on the stochastic process theory, the convergence of the proposed algorithms are proved. The simulation results indicate that the proposed algorithms can estimate the parameters of feedback nonlinear output‐error systems effectively. [ABSTRACT FROM AUTHOR]

Abstract For the ship motion with large inertia coupled system identification modeling inaccuracy, the ship scale effect and the existence of partial unmeasured ship data problems. In this paper, an auxiliary model nonlinear innovation least squares identification algorithm is proposed. The new algorithm uses the output of the auxiliary model instead of the unmeasurable variables in the full-scale test data of the ship, and optimizes the error using the tangent function. Compared with the existing algorithm, the error of the improved algorithm decreases with the increase of time and continuously approaches to zero, which greatly improves the identification accuracy and convergence efficiency. The results show that the improved algorithm has significant identification accuracy and reliability. The identification method designed in this paper can be applied to the field of ship intelligent navigation engineering.

Summary: In practical applications, many processes have nonlinear characteristics that require nonlinear models for accurate description. However, constructing such models and determining their parameters are a challenging task. This article explores filtered identification methods for estimating the parameters of a particular type of nonlinear Hammerstein systems with ARMA noise. An auxiliary model‐based least squares algorithm is developed for such systems based on the auxiliary model identification idea. A hierarchical least squares algorithm that utilizes the hierarchical identification principle is proposed to enhance computational efficiency. Additionally, a key term separation technique is employed to express the system output as a linear combination of parameters, allowing the system to be decomposed into smaller subsystems for more efficient estimation of parameters. Simulation results demonstrate the effectiveness of these proposed algorithms. [ABSTRACT FROM AUTHOR]

Outliers usually occur during industrial data collection process and can lead to poor system identification performance. This paper considers the parameter estimation probelm for Hammerstein nonlinear systems whose output measurements are contaminated with additive outliers. By incorporating a lasso-type penalty on the outlier vector, a regularization based least squares identification algorithm that can interactively estimate the system parameters and outliers is proposed based on the auxiliary model identification idea. To further reduce the impact of outliers on the identification effect, each observation is assigned an individual weight, which decreases as the number of iterations increases once the corresponding data is determined to be an outlier. Finally, the outliers can be excluded from the contaminated data without any prior knowledge and the estimation bias is reduced. A numerical example and a benchmark system are given to confirm the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This article studies the parameter estimation problems of nonlinear systems with colored noise using the covariance matrix adaptation evolution strategy (CMA‐ES), which is one of the most competitive evolutionary algorithms available and has been applied in the area of reinforcement learning and process control. However, a major limitation that impedes the application of the CMA‐ES is the high computational complexity caused by matrix decomposition. To solve this problem, an efficient Cholesky CMA‐ES which uses the Cholesky factor instead of the covariance matrix to reduce the computational complexity, and updates the search direction and distribution mean based on the conjugate gradient method to improve the search accuracy is proposed. By using the auxiliary model identification idea, the Cholesky CMA‐ES can be applied to solve the parameter estimation problems of the Hammerstein nonlinear systems with colored noise. Two simulation examples are provided to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

For generalized time-varying systems with colored noise, the difficulty of identification lies in time-varying parameters and colored noise. The recursive estimation problem of a controlled autoregressive generalized time-varying system with autoregressive moving average noise is studied. By means of the hierarchical principle, the identification model is decomposed into two subsystems with fewer variables and different characteristics, which simplifies the original model and processes the colored noise based on the idea of the auxiliary model. Then a two-stage auxiliary model-based recursive least squares (TS-AM-RLS) algorithm is proposed, which realizes the parameter estimation of the subsystem based on the least squares method. In order to improve the identification accuracy and convergence speed, the scalar innovation is extended to the innovation vector, and a multi-innovation least squares algorithm is proposed by using the multi-innovation identification theory. A numerical experiment is given to illustrate the performances of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article investigates the parameter identification problems of the stochastic systems described by the input‐nonlinear output‐error (IN‐OE) model. This IN‐OE model consists of two submodels, one is an input nonlinear model and the other is a linear output‐error model. The difficulty in the parameter identification of the IN‐OE model is that the information vector contains the unknown variables, which are the noise‐free (true) outputs of the system, the approach taken here is to replace the unknown terms with the outputs of the auxiliary model. Based on the over‐parameterization model and the hierarchical identification principle, an over‐parameterization auxiliary model hierarchical gradient‐based iterative algorithm and an over‐parameterization auxiliary model hierarchical least‐squares‐based iterative algorithm are proposed to estimate the unknown parameters of the IN‐OE systems. Finally, two numerical simulation examples are given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper discusses the parameter estimation problems for the output-error moving average (OEMA) systems under stochastic environments. The estimation problems with unknown inner variables and unmeasurable noise terms existed in the information vector are solved by the auxiliary model framework. Meanwhile, the algorithms utilize the continues mixed p-norm (CMPN) method to control the proportions of the error norms, which take into account each p-norm of errors for 1 ⩽ p ⩽ 2. To improve the identification accuracy further, a multiinnovation CMPN optimization algorithm is developed by expanding the scalar innovation to the innovation vector. The proposed optimal algorithms offer faster tracking speed and can obtain higher parameter estimation accuracy for both stochastic white noise and α-stable noise. Two examples of identification of OEMA systems are given to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations.

Split learning, a distributed learning framework, has garnered significant attention from academic and industrial communities. In contrast to federated learning, split learning offers a more flexible architecture for participants with limited computing resources. However, the security of split learning has been questioned due to the separation of data and model control rights from usage rights. Currently, most research work focuses on inference attacks in split learning. In this paper, we first reveal the vulnerability of split learning to backdoor attacks and present two backdoor attack frameworks from both the server and client perspectives. Regarding the client-side attacker, we insert backdoor samples into the training data by utilizing the client's direct control over local data, and propose two methods for labeling backdoor samples that can be adapted to various application scenarios. Due to the server's lack of control over the client in split learning, it is infeasible for server-side attackers to inject backdoor samples into training data. Our strategy involves leveraging the server's control over the training process to shape the optimization direction of the client model, thereby enabling it to encode backdoor samples. Moreover, we introduce an auxiliary model into the attack framework to enhance the effectiveness of the backdoor attack. The auxiliary model can increase the distinction between backdoor samples and clean samples in the feature space to improve the sensitivity of the client model to backdoor samples. Extensive evaluations demonstrate the high attack accuracy of both proposed attack frameworks without causing any compromise to the performance of the main task. Our research uncovers the potential security risks and rings the alarm for the application of split learning. [ABSTRACT FROM AUTHOR]

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Drainage & Irrigation Machinery Engineering / Paiguan Jixie Gongcheng Xuebao is the property of Editorial Department of Drainage & Irrigation Machinery Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary: Missing data often occur in industrial processes. In order to solve this problem, an auxiliary model and a particle filter are adopted to estimate the missing outputs, and two unbiased parameter estimation methods are developed for a class of nonlinear systems (e.g., bilinear systems) with irregularly missing data. Firstly, an auxiliary model is constructed to estimate the unknown output, and an auxiliary model‐based multi‐innovation recursive least squares algorithm is presented by expanding the scalar innovation to an innovation vector. Secondly, according to the bias compensation principle, an auxiliary model‐based bias compensation multi‐innovation recursive least squares algorithm is proposed to compensate the bias caused by the colored noise. Thirdly, for further improving the parameter estimation accuracy, the unknown true output is estimated by a particle filter, and a particle filtering‐based bias compensation multi‐innovation recursive least squares algorithm is developed. Finally, a numerical example is selected to validate the effectiveness of the proposed algorithms. The simulation results indicate that the proposed algorithms have good performance in identifying bilinear systems with irregularly missing data. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the identification problem of an output‐error nonlinear system with saturation and dead‐zone nonlinearity. Introducing a switching function and by means of the auxiliary model identification idea, an auxiliary model hierarchical least squares‐based iterative algorithm is proposed for estimating the parameters of the nonlinear system. Based on the hierarchical identification model, an auxiliary model hierarchical gradient‐based iterative algorithm is presented for the nonlinear system by utilizing the gradient search. In order to take full advantage of the system data, an auxiliary model hierarchical multi‐innovation gradient‐based iterative algorithm is derived for the nonlinear system according to the multi‐innovation identification theory. Finally, the numerical simulation results illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

External vibration, shock, unbalanced torque and other uncertain disturbances are mainly transmitted to the motor rotor through the bearing friction. To restrain the uncertain friction disturbances and improve the speed stability of a permanent magnet synchronous motor (PMSM), an optimized active disturbance rejection control (ADRC) algorithm is proposed in this study. Firstly, an auxiliary model of friction and a reduced-order processing method are introduced into extended state observation (ESO) to reduce the burden of single ESO and promote the compensation accuracy of disturbances. In addition, a supervisory radial basis function (SRBF) is employed to supervise and promote the error elimination efficiency of the nonlinear state error feedback rate (NLSEF). The hybrid control algorithm makes up for the deficiency of typical ADRC through the fusion of multiple control quantities. Simulation and experimental results show that the proposed algorithm has strong anti-disturbance performance and effectively solves the problem of low-speed crawling. [ABSTRACT FROM AUTHOR]

Summary: This study investigates the parameter identification issues of bilinear‐in‐parameter systems through fractional adaptive algorithms. An auxiliary model based ε‐normalized$$ \varepsilon \hbox{-} \mathrm{normalized} $$ modified fractional least mean square algorithm is proposed for accelerating the parameter estimation accuracy based on the auxiliary model identification idea and the introduced convergence index, a normalized modified hierarchical fractional least mean square algorithm is presented for improving the computational efficiency based on the hierarchical identification principle. The proposed normalized fractional adaptive strategies are effective and could provide more accurate parameter estimates comparing with conventional counterparts for bilinear‐in‐parameter identification model based on the mean square error metrics and the average predicted output error. The effectiveness and accuracy of the proposed algorithms are further verified and validated through numerical simulations for different noise variances, fractional orders and gain parameters. [ABSTRACT FROM AUTHOR]

This article considers the parameter estimation problems of two‐input single‐output Hammerstein output‐error moving average systems. The system is decomposed into two subsystems based on the hierarchical principle. The first model is used to identify the linear parameters and the parameters of the unknown measurable information vector. The second model is for identifying non‐linear parameters. By using the auxiliary model, we introduce a forgetting factor to improve the parameter estimation accuracy. The auxiliary model‐based forgetting factor recursive least squares algorithm and the auxiliary model‐based forgetting factor multi‐innovation recursive least squares algorithm are presented. The simulation results indicate that the proposed algorithms are effective. [ABSTRACT FROM AUTHOR]

Growth traits, such as fresh weight, diameter, and leaf area, are pivotal indicators of growth status and the basis for the quality evaluation of lettuce. The time-consuming, laborious and inefficient method of manually measuring the traits of lettuce is still the mainstream. In this study, a threestage multi-branch self-correcting trait estimation network (TMSCNet) for RGB and depth images of lettuce was proposed. The TMSCNet consisted of five models, of which two master models were used to preliminarily estimate the fresh weight (FW), dry weight (DW), height (H), diameter (D), and leaf area (LA) of lettuce, and three auxiliary models realized the automatic correction of the preliminary estimation results. To compare the performance, typical convolutional neural networks (CNNs) widely adopted in botany research were used. The results showed that the estimated values of the TMSCNet fitted the measurements well, with coefficient of determination (R2) values of 0.9514, 0.9696, 0.9129, 0.8481, and 0.9495, normalized root mean square error (NRMSE) values of 15.63, 11.80, 11.40, 10.18, and 14.65% and normalized mean squared error (NMSE) value of 0.0826, which was superior to compared methods. Compared with previous studies on the estimation of lettuce traits, the performance of the TMSCNet was still better. The proposed method not only fully considered the correlation between different traits and designed a novel self-correcting structure based on this but also studied more lettuce traits than previous studies. The results indicated that the TMSCNet is an effective method to estimate the lettuce traits and will be extended to the high-throughput situation. Code is available at https://github.com/lxsfight/TMSCNet.git. [ABSTRACT FROM AUTHOR]

The iterative parameter estimation methods for a class of nonlinear systems with interval-varying measurements are studied in this paper. According to the auxiliary model identification idea, an auxiliary model is constructed to estimate the unknown noise-free process outputs, and an interval-varying auxiliary model gradient-based iterative identification algorithm is developed. Furthermore, a particle filter, which uses some discrete random sampling points to approximate the posterior probability density function, is adopted to compute the output estimates. Then an interval-varying particle filtering gradient-based iterative algorithm is derived, and an interval-varying auxiliary model based stochastic gradient (V-AM-SG) algorithm is presented for comparison. The simulation results indicate that the proposed algorithms are effective for identifying the nonlinear systems with interval-varying measurements, and can generate more accurate parameter estimates than the V-AM-SG algorithm. [ABSTRACT FROM AUTHOR]

Aiming at a kind of dual-rate Hammerstein system, based on the auxiliary model identification idea, using the maximum likelihood principle and recursive identification technology, this paper proposes a maximum likelihood recursive least squares algorithm. The main method is to construct an auxiliary model for the unknown output in the model, and use the output of the auxiliary model to predict the unknown output. This method can directly identify parameters based on the dual-rate input and output data. The simulation experiments show that the proposed algorithm can effectively identify the dual-rate Hammerstein system, and the final error tends to be about 1%.

This paper addresses a modified auxiliary model stochastic gradient recursive parameter identification algorithm (M-AM-SGRPIA) for a class of single input single output (SISO) linear output error models with multi-threshold quantized observations. It proves the convergence of the designed algorithm. A pattern-moving-based system dynamics description method with hybrid metrics is proposed for a kind of practical single input multiple out- put (SIMO) or SISO nonlinear systems, and a SISO linear output error model with multi-threshold quantized observations is adopted to approximate the unknown system. The system input design is accomplished using the measurement technology of random repeatability test, and the probabilistic characteristic of the explicit metric value is employed to estimate the implicit metric value of the pattern class variable. A modified auxiliary model stochastic gradient recursive algorithm (M-AM-SGRA) is designed to identify the model parameters, and the contraction mapping principle proves its convergence. Two numerical examples are given to demonstrate the feasibility and effectiveness of the achieved identification algorithm. [ABSTRACT FROM AUTHOR]

For the fractional-order Hammerstein nonlinear ARMAX system with colored noise, there are many identification parameters and coupling variables, difficulty in estimating the fractional order, slow convergence of the identification algorithm and low accuracy, and this paper proposes a new multi-innovation principle based on the principle of multi-innovation information identification method. First, construct a fractional-order Hammerstein nonlinear ARMAX discrete system model with colored noise; secondly, a multi-innovative Levenberg–Marquardt algorithm with an innovation vector composed of fractional-order variables as the model input is designed, and the auxiliary model method is combined to solve the unknown noise variables to estimate the system parameters and fractional order. Finally, a fractional-order Hammerstein nonlinear ARMAX system with colored noise and a flexible manipulator system are taken as examples to prove the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

External vibration, shock, unbalanced torque and other uncertain disturbances are mainly transmitted to the motor rotor through the bearing friction. To restrain the uncertain friction disturbances and improve the speed stability of a permanent magnet synchronous motor (PMSM), an optimized active disturbance rejection control (ADRC) algorithm is proposed in this study. Firstly, an auxiliary model of friction and a reduced-order processing method are introduced into extended state observation (ESO) to reduce the burden of single ESO and promote the compensation accuracy of disturbances. In addition, a supervisory radial basis function (SRBF) is employed to supervise and promote the error elimination efficiency of the nonlinear state error feedback rate (NLSEF). The hybrid control algorithm makes up for the deficiency of typical ADRC through the fusion of multiple control quantities. Simulation and experimental results show that the proposed algorithm has strong anti-disturbance performance and effectively solves the problem of low-speed crawling.

Summary: Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein‐Wiener nonlinear systems based on non‐uniform sampling. By means of the auxiliary model identification idea, an auxiliary model‐based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model‐based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: This article considers the parameter estimation for a fractional‐order nonlinear finite impulse response system with colored noise. For the fractional‐order systems, the challenge and difficulty are to identify the order and parameters of the systems simultaneously under colored noise disturbances. In order to reduce the problem of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the separation of the key term separation. A key term separation auxiliary model gradient‐based iterative algorithm is derived by using the negative gradient search. Meanwhile, to achieve the higher estimation accuracy, we propose a key term separation auxiliary model multiinnovation gradient‐based iterative algorithm by utilizing the multiinnovation theory. Finally, the simulation results test the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

For 2-D causal systems, the variables depend both on time, and on spatial coordinates. This article develops two identification algorithms for two-dimensional causal systems. First, a maximum likelihood estimation algorithm is developed for two-dimensional causal systems when there is no missing data. Second, an expectation–maximization based auxiliary model algorithm, and an expectation–maximization based modified Kalman filtering and smoothing algorithm are derived for 2-D causal systems with missing outputs. It is demonstrated that the modified Kalman filtering, and smoothing algorithm is more effective for systems with missing outputs. The effectiveness of these two algorithms is verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper presents a hierarchical identification model for multiple-input multiple-output (MIMO) systems. An auxiliary model-based hierarchical stochastic gradient (AM-HSG) algorithm is derived by means of the auxiliary model identification idea and the hierarchical identification principle. Furthermore, an auxiliary model-based hierarchical multi-innovation stochastic gradient (AM-HMISG) algorithm is derived by utilizing the multi-innovation identification theory. In order to compare the computational efficiency of the AM-HSG and AM-HMISG algorithms for identifying MIMO systems, this paper gives the existing traditional gradient algorithms and discusses the complexity of these algorithms in detail. Finally, the simulation example tests the effectiveness of all four algorithms. [ABSTRACT FROM AUTHOR]

Compared with the systems with white noise disturbances, the parameter identification of the systems with colored noises (i.e., correlated noises) is more difficult. In this letter, we use the model transformation to study the identification problem for the systems with colored noises by using the filtering identification idea. The basic idea is to transform a system with colored noise into two identification models with white noises and then to propose a novel parameter estimation algorithms, which can generate more accurate parameter estimates than some related existing identification algorithm. The proposed method can be applied to other linear or nonlinear stochastic systems with different structures and colored disturbance noises. The provided simulation example tests the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: Model‐based state of charge (SOC) estimation method depends on the accuracy of the online identified battery model. However, when battery model parameters are identified by conventional recursive least squares (RLS), voltage and current noise will lead to the deviation of parameters and further affect the accuracy of SOC estimation. To analyze the difference influence of voltage and current noise, a simulation is carried out under the same noise variance of both voltage and current. Results indicate that voltage noise is the main cause of parameter deviation. Based on these results, a novel method, the auxiliary model recursive least square (AM‐RLS) which enjoys low computational complexity is proposed to compensate the parameter deviation caused by voltage noise. The AM‐RLS method is further combined with an extended Kalman filter (EKF) to estimate SOC in real time. Both simulation and experimental results show that AM‐RLS can effectively attenuate the parameter deviation and SOC estimation error under noise interference. Compared with RLS, the maximum SOC errors of the proposed method are reduced by 2.6% and 5.86% respectively under two current profiles. [ABSTRACT FROM AUTHOR]

This study aims to determine how to deal with the identification from input and output data of switched linear systems (SLSs) with Box and Jenkins models. The identification difficulties of this system are that there exist unknown switched signal, unknown middle variables, and colored noise terms in the identification process. To address these issues, the proposed identification method proceeds in two stages, including the estimation of the switched signal of SLSs and the identification of the parameters of all subsystems. First, the Gaussian mixture model is established to represent the distribution of the input and output data of SLSs. Then, the posterior probability is calculated by the expectation-maximization (EM) algorithm and the naive Bayes classifier, and the switched signal is estimated according to the maximum probability criterion. Next, the auxiliary model based multi-innovation generalized extended least square (AM-MI-GELS) algorithm is used to estimate the parameters of all subsystems. Finally, the effectiveness of the proposed method is verified through the simulation example. [ABSTRACT FROM AUTHOR]

Summary: This article studies the identification problem of the nonlinear sandwich systems. For the sandwich system, because there are inner variables which cannot be measured in the information vector of the identification models, it is difficult to identify the nonlinear sandwich systems. In order to overcome the difficulty, an auxiliary model is built to predict the estimates of inner variables by means of the output of the auxiliary model. For the purpose of employing the real‐time observed data, a cost function with dynamical data is constructed to capture on‐line information of the nonlinear sandwich system. On this basis, an auxiliary model stochastic gradient identification approach is proposed based on the gradient optimization. Moreover, an auxiliary model multiinnovation stochastic gradient estimation method is developed, which tends to enhance estimation accuracy by introducing more observed data dynamically. The numerical simulation is provided and the simulation results show that the proposed auxiliary model identification method is effective for the nonlinear sandwich systems. [ABSTRACT FROM AUTHOR]

This paper focuses on the parameter estimation of a class of bilinear systems, for which the input-output representation is derived by eliminating the state variables in the systems. Based on the obtained identification model and the hierarchical identification principle, a hierarchical auxiliary model based least squares iterative algorithm is derived, to improve the computation efficiency and the parameter estimation accuracy by using the auxiliary model identification idea and the interval-varying input-output data. For comparison, an auxiliary model based least squares iterative algorithm is presented. The simulation results show that the proposed algorithm has better performance in estimating the parameters of bilinear systems.

A stochastic gradient (SG)-based particle filter (SG-PF) algorithm is developed for an ARX model with nonlinear communication output in this paper. This ARX model consists of two submodels, one is a linear ARX model and the other is a nonlinear output model. The process outputs (outputs of the linear submodel) transmitted over a communication channel are unmeasurable, while the communication outputs (outputs of the nonlinear submodel) are available, and both of the two-type outputs are contaminated by white noises. Based on the rich input data and the available communication output data, a SG-PF algorithm is proposed to estimate the unknown process outputs and parameters of the ARX model. Furthermore, a direct weight optimization method and the Epanechnikov kernel method are extended to modify the particle filter when the measurement noise is a Gaussian noise with unknown variance and the measurement noise distribution is unknown. The simulation results demonstrate that the SG-PF algorithm is effective. [ABSTRACT FROM AUTHOR]

This paper considers the parameter identification for a class of nonlinear stochastic systems with colored noise. An input-output representation is derived by eliminating the state variables in the bilinear system. Based on the obtained identification model, a recursive generalized extend least squares algorithm is proposed by using the auxiliary model identification idea. Moreover, a two-stage recursive generalized extended least squares algorithm is presented to reduce the computational burden by using the hierarchical identification principle and the auxiliary model identification idea, respectively. A stochastic gradient identification algorithm is proposed for comparison. The simulation results show that the proposed algorithms have a good performance in estimating the parameters of the bilinear systems with colored noises. [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear system identification problem, which is a basic premise of control and fault diagnosis. For Hammerstein output-error nonlinear systems, we propose an auxiliary model-based multi-innovation fractional stochastic gradient method. The scalar innovation is extended to the innovation vector for increasing the data use based on the multi-innovation identification theory. By establishing appropriate auxiliary models, the unknown variables are estimated and the improvement in the performance of parameter estimation is achieved owing to the fractional-order calculus theory. Compared with the conventional multi-innovation stochastic gradient algorithm, the proposed method is validated to obtain better estimation accuracy by the simulation results.

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive moving average (M-OEARMA) systems. By applying the auxiliary model identification idea and the decomposition technique, we derive a two-stage recursive least squares algorithm for estimating the M-OEARMA system. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm possesses higher identification accuracy. The simulation results confirm the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the data filtering technique and the auxiliary model identification idea, we derive a filtering-based auxiliary model recursive generalized least squares algorithm. The key is to filter the input-output data and to derive two identification models, one of which includes the system parameters and the other contains the noise parameters. Compared with the auxiliary model-based recursive generalized least squares algorithm, the proposed algorithm requires less computational burden and can generate more accurate parameter estimates. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a new filter‐based stochastic gradient algorithm for dual‐rate ARX models. Algorithm analysis is based upon the Kalman filter and smoother method. The new filter applies the measurable outputs to adjust the estimated outputs during each interval of the slow sampled rate. A comparative study reveals that the present consideration makes the estimated outputs more accurate than the classical auxiliary model. A stochastic gradient algorithm is developed for the estimation of parameters using all data. The simulation made further guarantees the usefulness of the proposed algorithm. [ABSTRACT FROM AUTHOR]