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This paper presents a novel recursive parameter estimation method to identify the gradient radial basis function based varying-coefficient autoregressive (GRBF-AR) model with colored noises. Considering the global nonlinearity and local linearity of the model, the identification process is divided into several stages to identify the linear parameters and the nonlinear parameters separately. Then, several improved stochastic gradient sub-algorithms are derived for estimating the separated parameters correspondingly, incorporating the multi-innovation theory to improve the estimation accuracy. To mitigate the negative influence of colored noises, this paper designs a linear prefilter to whiten the colored noise for obtaining the unbiased parameters. The convergence analysis and the simulation results demonstrate the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

ABSTRACT The state of charge (SOC) is an extremely important indicator of the lithium cell. Currently, traditional identification algorithms and integer‐order models are poorly adaptive and unable to respond to the dynamic characteristics of batteries in real time, whereas unscented Kalman filtering is often accompanied by the problem that the covariance matrix is not positively determined, leading to algorithmic collapse. This study combines the multi‐innovation theory with online identification and provides an improved fractional‐order multi‐innovation double unscented Kalman filter (DFOMIUKF) joint estimation algorithm. The algorithm contains a multi‐timescale framework that allows full parametric identification of fractional‐order models, which guarantees the algorithm's ability to cope with complex working conditions, and the problem of failure of the Kalman filtering algorithm is solved by modifying the covariance matrix in real time by singular value decomposition (SVD). On the basis of the fractional RC model, the FOMIUKF1 algorithm allows real‐time updating of model parameters on a macro scale, and the obtained parameters at the microscale are passed to the FOMIUKF2 algorithm for real‐time updating of the charge level of the lithium battery. Then, the DFOMIUKF algorithm is validated under different working environments, respectively. The findings indicate that the proposed algorithm predicts the SOC with the maximum values of root mean square error (RMSE) and mean absolute error (MAE) not exceeding 0.77% and 0.66%, respectively, and maintains high accuracy even at low temperatures. It is illustrated that the proposed algorithm solves the problems of the above offline algorithms with high precision and robustness. [ABSTRACT FROM AUTHOR]

This paper mainly studies the issue of fractional parameter identification of generalized bilinear-in-parameter system(GBIP) with colored noise. Hierarchical fractional least mean square algorithm based on the key term separation principle(K-HFLMS) and multi-innovation hierarchical fractional least mean square algorithm based on the key term separation principle (K-MHFLMS) are presented for the effective parameter estimation of GBIP system. The K-MHFLMS expands the scalar innovation into the vector innovation by making full use of the system input and output data information at each recursive step. The detailed performance analyses of the K-MHFLMS strategy are compared with the K-HFLMS algorithm for GBIP identification model based on the Fitness metrics, the mean square error metrics and the average predicted output error. The effectiveness and reliability of K-HFLMS and K-MHFLMS algorithms are further verified through the simulation experimentation under different noise variances, fractional orders and innovation lengths, and the K-MHFLMS yields faster convergence speed than the K-HFLMS by increasing the innovation length. [ABSTRACT FROM AUTHOR]

This paper proposes a joint multi-innovation fractional gradient descent identification algorithm for fractional order systems. First, the flexibility of fractional calculus is leveraged to design a joint fractional gradient descent algorithm capable of estimating system parameters and unknown orders. The estimated system parameters are used as the initial conditions to identify the unknown order, and the identified order is used as the update conditions for the system parameters. Through the joint iteration of two fractional order gradients, both the identified order and parameters are updated. In addition, multi-innovation theory is applied to extend the joint fractional gradient descent algorithm to a joint multi-innovation fractional gradient descent algorithm, which improves the system identification accuracy. Then, the convergence of the algorithm is theoretically analyzed. Finally, the effectiveness of the algorithm is verified through numerical simulation and an experiment on the identification of an actual flexible linkage system. [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]

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Summary: This paper mainly investigates the issue of parameter identification for the fractional‐order input nonlinear output error autoregressive (IN‐OEAR) model. In order to avoid the problem of large computation of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the key term separation. Through employing the hierarchial identification principle, the fractional‐order IN‐OEAR model is decomposed into two sub‐models with a smaller number of parameters. On the basis of the recursive identification methods, a recursive least squares sub‐algorithm and a gradient stochastic sub‐algorithm are proposed to estimate the parameters and the fractional‐order, respectively. With the aim of achieving more accurate parameter estimates, a two‐stage multi‐innovation least recursive algorithm is proposed by means of the multi‐innovation identification theory. The numerical simulation results test the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Fractional differential equations are used to construct mathematical models and can describe the characteristics of real systems. In this paper, the parameter estimation problem of a fractional Wiener system is studied by designing linear filters which can obtain smaller tunable parameters and maintain the stability of the parameters in any case. To improve the identification performance of the stochastic gradient algorithm, this paper derives two modified stochastic gradient algorithms for the fractional nonlinear Wiener systems with colored noise. By introducing the forgetting factor, a forgetting factor stochastic gradient algorithm is deduced to improve the convergence rate. To achieve more efficient and accurate algorithms, we propose a multi-innovation forgetting factor stochastic gradient algorithm by means of the multi-innovation theory, which expands the scalar innovation into the innovation vector. To test the developed algorithms, a fractional-order dynamic photovoltaic model is employed in the simulation, and the dynamic elements of this photovoltaic model are estimated using the modified algorithms. Concurrently, a numerical example is given, and the simulation results verify the feasibility and effectiveness of the proposed procedures. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problem of nonlinear models, which are related to the impulse or step response functions of linear time-invariant (LTI) dynamical systems, based on the response data. In terms of the nonlinear characteristic of the models, the nonlinear dynamical optimization scheme is adopted for obtaining the system parameter estimates. By constructing a gradient criterion function, a gradient recursion algorithm is derived. In order to overcome the difficulty of determining the step-size in the gradient recursion algorithm, a trying method and a numerical approach are proposed to achieve the step-size. On this basis, a stochastic gradient estimation method is presented by using a recursive step-size. Furthermore, a multi-innovation stochastic gradient method is deduced for enhancing the estimation accuracy by using the dynamical window data. Finally, a dynamical length stochastic gradient estimation technique is offered to obtain more accurate parameter estimates by using dynamical length measured data from the step response. The examples are provided to examine the algorithm performance and the simulation results indicate that the presented approaches are effective. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the parameter estimation issues of multivariate equation‐error autoregressive moving average systems. By applying the gradient search and the multi‐innovation theory, we derive a multi‐innovation gradient based iterative (MI‐GI) algorithm. In order to improve the computational efficiency and the parameter estimation accuracy, a filtering and decomposition based gradient iterative (F‐D‐GI) algorithm is presented by using the data filtering technique and the decomposition technique. The key is to choose an appropriate filter to filter the input‐output data and to transform an original system into several subsystems. Compared with the MI‐GI algorithm, the F‐D‐GI algorithm can generate more accurate parameter estimates. Finally, an illustrative example is provided to indicate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article proposes a novel multi-innovation fractional order least mean square algorithm for estimating harmonic parameters in power systems with unknown amplitudes and phases. The algorithm incorporates fractional order calculus with variable initial values, which, in contrast to the fixed initial value approach, overcomes the non-locality issue, and converges to its true extreme value. In addition, by extending scalar innovation term to a vector form, the algorithm fully utilizes innovation within a fixed window to improve computational accuracy. The convex combination between integer order and novel fractional order ensures that the performance of the algorithm will not change significantly with the fractional order. Finally, the effectiveness is verified by numerical simulations and comparisons. [ABSTRACT FROM AUTHOR]

The parameter estimation methods for the nonlinear exponential autoregressive model are investigated in this paper. We develop a forgetting factor gradient parameter estimation algorithm for improving the estimation accuracy. For the purpose of improving the identification accuracy further, a forgetting factor multi-innovation stochastic gradient algorithm is derived by using the multi-innovation theory. The effectiveness of the proposed algorithms is proved by a simulation example. [ABSTRACT FROM AUTHOR]

This paper researches the identification problem for the unknown parameters of the multivariate equation-error autoregressive systems. Firstly, the original identification model is decomposed into several sub-identification models according to the number of system outputs. Then, based on the characteristic that the information vector and the parameter vector are common among the sub-identification models, the coupling identification concept is used to propose a partially coupled generalized stochastic gradient algorithm. Furthermore, by expanding the scalar innovation of each subsystem model to the innovation vector, a partially coupled multi-innovation generalized stochastic gradient algorithm is proposed. Finally, the numerical simulations indicate that the proposed algorithms are effective and have good parameter estimation performances. [ABSTRACT FROM AUTHOR]

Piecewise‐linear nonlinearity is an effective representation for hard nonlinearities such as saturation, dead zone, and backlash, which can be also used as a general tool for approximating nonlinear characteristics. For the input piecewise‐linear output‐error autoregressive systems, we develop a parametric expression of the piecewise‐linear nonlinearity through a switching function and position functions, and derive the identification model of the system by using the key item separation. Based on the optimization criterion, an auxiliary model‐based multi‐innovation recursive generalized least‐squares algorithm is deduced for estimating the unknown parameters according to the obtained model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The filtering identification model of the system is derived and a filtering‐based multi‐innovation recursive generalized least‐squares algorithm is proposed. The simulation example demonstrates the effectiveness of the proposed algorithms and shows that the filtering‐based multi‐innovation recursive generalized least‐squares algorithm has better identification performance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve the accurate analysis of the sports training project, research its video data profoundly, and discover deficiencies and summarize experience from the existing videos, thereby promoting China's sports industry. According to previous works, the existing sports training target detection system has the problem of nonlinear video and low target detection accuracy, which can easily cause target loss or tracking failure. Therefore, the Kalman Filter (KF) is studied in-depth and applied to detect the targets in sports videos. Combined with the Multi-Innovation (MI) theory, an MI-Extended KF (EKF) algorithm model based on nonlinear dynamic technology is proposed. This model can effectively solve the filtering accuracy problem under the strong nonlinear system. Finally, the performance analysis through different datasets has verified the effectiveness of the model proposed further. Results demonstrate that the model proposed can effectively improve the filtering accuracy of nonlinear systems. As the angle module changes, the accuracy of sports recognition also changes. The final accuracy of the model proposed can reach above 96%. The simulation results and convergence are better than other algorithms, which also proves the effectiveness of the model proposed. The results can provide a theoretical basis for the research related to the detection of training sports targets in sports videos. [ABSTRACT FROM AUTHOR]

This paper concerns the parameter identification methods of multivariable equation-error systems. By means of the decomposition technique, the multivariable identification model is transformed into two sub-identification models and a decomposition-based stochastic gradient (D-SG) algorithm is presented for estimating the parameters of these two submodels. In order to further improve the convergence rate and the parameter estimation accuracy, we expand the innovation vectors to the innovation matrices and develop a decomposition-based multi-innovation stochastic gradient (D-MISG) algorithm. The simulation results confirm that the D-MISG algorithm can provide more accurate parameter estimates than the D-SG algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification problem for multivariable equation-error systems with autoregressive moving average noise using the hierarchical identification principle and the multi-innovation identification theory. We propose a hierarchical gradient-based iterative (HGI) identification algorithm and give a gradient-based iterative (GI) identification algorithm for comparison. Meanwhile, the multi-innovation theory is used to derive the hierarchical multi-innovation gradient-based iterative (HMIGI) identification algorithm. The analysis shows that the HGI algorithm has smaller computational burden and can give more accurate parameter estimates than the GI algorithm and the HMIGI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Considering changes in the structural size and mass caused by the on-orbit assembly process in a planar space solar power satellite, this study proposes an improved robust recursive algorithm to identify the time-varying inertia tensor parameters of the system. In this algorithm, to decrease the effect of impulsive disturbance on inertial parameter identification during the on-orbit assembly and improve computational accuracy, robust weighted factor and multi-innovation theory are involved. Then, the time-varying inertia tensor parameters of this large flexible structure are identified based on the distributed measurement results of multiple attitude sensors. The simulation results indicate that the proposed algorithm improves the identification accuracy and has better robustness than the original method under the impulsive disturbance. The relative values of the average relative error caused by the impulsive disturbance under the proposed algorithm are approximately 27.8–73.0% less than those under the original method. Additionally, the results also demonstrate that the proposed algorithm has higher noise immunity than the classical recursive least-squares method in a time-varying system. When the impulsive disturbance and zero-mean Gaussian white noise are applied to the system, compared with the conventional recursive least-squares method, the proposed algorithm yields lower absolute and relative values of the average relative error by approximately 4.2% and 44.9%, respectively. [ABSTRACT FROM AUTHOR]

This paper considers the state and parameter estimation problem of a state-delay system. On the basis of the stochastic gradient algorithm (i.e., the gradient based search estimation algorithm), this work extends the scalar innovation into an innovation vector and presents a multi-innovation gradient parameter estimation algorithm for a state-space system with d-step state-delay by means of the multi-innovation identification theory. For thesystems whose states are unknown, we use the states of the state observer for the parameter estimation and use the estimated parameters for the state estimation. This forms a joint multi-innovation state and parameter estimation algorithm for the state-delay systems with immeasurable states. The simulation results indicate that the proposed algorithms can work well. [ABSTRACT FROM AUTHOR]

Due to the lack of powerful model description methods, the identification of Hammerstein systems based on the non-uniform input-output dataset remains a challenging problem. This paper introduces a time-varying backward shift operator to describe periodically non-uniformly sampled-data Hammerstein systems, which can simplify the structure of the lifted models using the traditional lifting technique. Furthermore, an auxiliary model-based multi-innovation stochastic gradient algorithm is presented to estimate the parameters involved in the linear and nonlinear blocks. The simulation results confirm that the proposed algorithm is effective and can achieve a high estimation performance. [ABSTRACT FROM AUTHOR]

This paper investigates the recursive parameter and state estimation algorithms for a special class of nonlinear systems (i.e., bilinear state space systems). A state observer-based stochastic gradient (O-SG) algorithm is presented for the bilinear state space systems by using the gradient search. In order to improve the parameter estimation accuracy and the convergence rate of the O-SG algorithm, a state observer-based multi-innovation stochastic gradient algorithm and a state observer-based recursive least squares identification algorithm are derived by means of the multi-innovation theory. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

• Study the parameter and time-delay estimation algorithm for linear systems. • Present a two-stage stochastic gradient and gradient-based iterative algorithm. • Present a multi-innovation stochastic gradient algorithm to improve the accuracy. In this paper, we study the parameter estimation problem of a class of linear time-delay systems. Based on the frequency responses and harmonic balance methods and by means of the gradient search, a two-stage stochastic gradient and gradient-based iterative algorithm is developed by using the collected data under the sinusoidal excitation. To improve the estimation accuracy, a two-stage multi-innovation stochastic gradient and gradient-based iterative algorithm is presented. Two simulation examples are provided to test the proposed algorithms. [ABSTRACT FROM AUTHOR]