Recursive Total Least Squares Research Articles

Online Identification of Lithium-ion Battery Model Parameters with Initial Value Uncertainty and Measurement Noise

Online parameter identification is essential for the accuracy of the battery equivalent circuit model (ECM). The traditional recursive least squares (RLS) method is easily biased with the noise disturbances from sensors, which degrades the modeling accuracy in practice. Meanwhile, the recursive total least squares (RTLS) method can deal with the noise interferences, but the parameter slowly converges to the reference with initial value uncertainty. To alleviate the above issues, this paper proposes a co-estimation framework utilizing the advantages of RLS and RTLS for a higher parameter identification performance of the battery ECM. RLS converges quickly by updating the parameters along the gradient of the cost function. RTLS is applied to attenuate the noise effect once the parameters have converged. Both simulation and experimental results prove that the proposed method has good accuracy, a fast convergence rate, and also robustness against noise corruption.

Model-Based Condition Monitoring of a Vanadium Redox Flow Battery

The safe, efficient and durable utilization of a vanadium redox flow battery (VRB) requires accurate monitoring of its state of charge (SOC) and capacity decay. This paper focuses on the unbiased model parameter identification and model-based monitoring of both the SOC and capacity decay of a VRB. Specifically, a first-order resistor-capacitance (RC) model was used to simulate the dynamics of the VRB. A recursive total least squares (RTLS) method was exploited to attenuate the impact of external disturbances and accurately track the change of model parameters in realtime. The RTLS-based identification method was further integrated with an H-infinity filter (HIF)-based state estimator to monitor the SOC and capacity decay of the VRB in real-time. Experiments were carried out to validate the proposed method. The results suggested that the proposed method can achieve unbiased model parameter identification when unexpected noises corrupt the current and voltage measurements. SOC and capacity decay can also be estimated accurately in real-time without requiring additional open-circuit cells.

Online Model Identification and State-of-Charge Estimate for Lithium-Ion Battery With a Recursive Total Least Squares-Based Observer

The state-of-charge (SOC) observer with online model adaption generally has high accuracy and robustness. However, the unexpected sensing of noises is shown to cause the biased identification of model parameters. To address this problem, a novel technique which integrates a recursive total least squares (RTLS) with an SOC observer is proposed to enhance the online model identification and SOC estimate. An efficient method is exploited to solve the Rayleigh quotient minimization which lays the basis of the RTLS. The number of multiplies, divides, and square roots is elaborated to show the low computational complexity of the developed RTLS. Simulation and experimental results show that the proposed RTLS-based observer attenuates the model identification bias caused by noise corruption effectively, and, thereby, provides a more reliable estimation of SOC. The proposed method is further compared with several available methods to highlight its superiority in terms of accuracy and the robustness to noise corruption.

Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

In this paper an ell _1-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed ell _1-RTLS algorithm is an RLS like iteration using the ell _1 regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed ell _1-regularized RTLS for the sparse system identification setting.

Mixed norm regularized recursive total least squares for group sparse system identification

SummaryA mixed lp,0‐regularized recursive total least squares (RTLS) algorithm is considered for group sparse system identification. Regularized recursive least squares (RLS) has been successfully applied to group sparse system identification; however, the estimation performance in regularized RLS‐based algorithms deteriorates when both input and output are contaminated by noise (the error‐in‐variables problem). We propose an lp,0‐RTLS algorithm to handle group sparse system identification with errors‐in‐variables. The proposed algorithm is an RLS‐like solution that utilizes lp,0‐regularization. The proposed algorithm provides excellent performance as well as reduces the required complexity by effective inversion matrix handling. Simulations demonstrate the superiority of the proposed lp,0‐regularized RTLS for a group sparse system identification setting. Copyright © 2015 John Wiley & Sons, Ltd.

A Rayleigh Quotient-Based Recursive Total-Least-Squares Online Maximum Capacity Estimation for Lithium-Ion Batteries

The maximum capacity, the amount of maximal electric charge that a battery can store, not only indicates the state of health, but also is required in numerous methods for state-of-charge estimation. This paper proposes an alternative approach to perform online estimation of the maximum capacity by solving the recursive total-least-squares (RTLS) problem. Different from prior art, the proposed approach poses and solves the RTLS as a Rayleigh quotient optimization problem. The Rayleigh quotient-based approach can be readily generalized to other parameter estimation problems including impedance estimation. Compared with other capacity estimation methods, the proposed algorithm enjoys the advantages of existing RTLS-based algorithms for instance, low computation, simple implementation, and high accuracy, and thus is suitable for use in real-time embedded battery management systems. The proposed method is compared with existing methods via simulations and experiments.

Sparsity regularized recursive total least-squares

This paper introduces a new family of recursive total least-squares (RTLS) algorithms for identification of sparse systems with noisy input vector. We regularize the RTLS cost function by adding a sparsifying term and utilize subgradient analysis. We present ℓ1 norm and approximate ℓ0 norm regularized RTLS algorithms, and we elaborate on the selection of algorithm parameters. Simulation results show that the presented algorithms outperform the existing RLS and RTLS algorithms significantly in terms of mean square deviation (MSD). Furthermore, we demonstrate the virtues of our automatic selection for regularization parameter when ℓ1 norm regularization is applied.

Recursive Total Least-Squares Algorithm Based on Inverse Power Method and Dichotomous Coordinate-Descent Iterations

We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS, outperforms the previously proposed RTLS algorithms, which are based on the line-search method, with reduced computational complexity. We perform a comprehensive analysis of the DCD-RTLS algorithm and show that it is asymptotically unbiased as well as being stable in the mean. We also find a lower bound for the forgetting factor that ensures mean-square stability of the algorithm and calculate the theoretical steady-state mean-square deviation (MSD). We verify the effectiveness of the proposed algorithm and the accuracy of the predicted steady-state MSD via simulations.

Linearly-Constrained Recursive Total Least-Squares Algorithm

We develop a new linearly-constrained recursive total least squares adaptive filtering algorithm by incorporating the linear constraints into the underlying total least squares problem using an approach similar to the method of weighting and searching for the solution (filter weights) along the input vector. The proposed algorithm outperforms the previously proposed constrained recursive least square (CRLS) algorithm when both input and output data are observed with noise. It also has a significantly smaller computational complexity than CRLS. Simulations demonstrate the efficacy of the proposed algorithm.

Fast Approximate Inverse Power Iteration Algorithm for Adaptive Total Least-Squares FIR Filtering

The presence of contaminating noises at both the input and the output of an finite-impulse-response (FIR) system constitutes a major impediment to unbiased parameter estimation. The total least-squares (TLS) method is known to be effective in achieving unbiased estimation. In this correspondence, we develop a fast recursive algorithm with a view to finding the TLS solution for adaptive FIR filtering. Given the fact that the TLS solution is obtainable via inverse power iteration, we introduce a novel but approximate inverse power iteration in combination with Galerkin method so that the TLS solution can be updated adaptively at a lower computational cost. We also take advantage of the regular form of the TLS solution to constrain the last element of the filter parameter vector to the negative one. We further reduce the computational complexity of the developed algorithm by making efficient computation of the fast gain vector defined in and using rank-one update of the augmented autocorrelation matrix. The developed algorithm saves seven M MAD's (number of multiplies, divides, and square roots) when compared with the recursive TLS algorithm in . Moreover, unlike the algorithms given in and , the developed algorithm does not deal with the solution to a one-variable quadratic equation and it avoids square root operation. Therefore, it has the simpler structure and may be more easily implemented. We then make a careful investigation into global convergence of the developed algorithm. Simulation results are provided that clearly illustrate appealing performance of the developed algorithm, including its good long-term numerical stability

A New TLS-Based MRAS Speed Estimation With Adaptive Integration for High-Performance Induction Machine Drives

This paper presents a new model reference adaptive system (MRAS) speed observer for high-performance field-oriented control induction motor drives which employs the flux error for estimating the rotor speed, but overcomes the pure integration problems by using a novel adaptive integration method based on neural adaptive filtering. A linear neuron (the ADALINE) is employed for the estimation of both the rotor speed and the rotor flux-linkage with a recursive total least-squares (TLS) algorithm (the TLS EXIN neuron) for online training. This neural model is also used as a predictor, that is with no feedback loops between the output of the neural network and its input. The proposed scheme has been implemented in a test setup and compared with an MRAS ordinary least-squares speed estimation with low-pass filter integration, with the well-known Schauder's scheme and with the latest Holtz's scheme. The experimental results show that in the high and medium-speed ranges with and without load, the four algorithms give practically the same results, while in low-speed ranges (that is, below 10 rad/s ) the TLS-based algorithm outperforms the other three algorithms. Successful experiments have also been made to verify the robustness of the algorithm to load perturbations and to test its performance at zero-speed operation.

A modified Gram–Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems

The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be updated and downdated much faster than the SVD, hence its utility in the solution of recursive total least squares (TLS) problems. However, the robust implementation of ULVD after the addition and deletion of rows (called updating and downdating, respectively) is not altogether straightforward. When updating or downdating the ULVD, the accurate computation of the subspaces necessary to solve the TLS problem is of great importance. In this paper, algorithms are given to compute simple parameters that can often show when good subspaces have been computed.

Rotor-speed estimator for induction motors using voltage and current measurements

This paper presents a rotor-speed estimator for induction motor drives which uses only stator voltage and current measurements. First of all, the identifiability of the rotor speed is analysed in relation to the operating point, giving a good insight into when and why rotor speed can be estimated. Secondly, a computation method is proposed for the rotor speed. Its sensitivity to errors in both model parameters and measurements is discussed in detail. In order to produce effective noise attenuation, a state-variable filter and a recursive total least-squares (TLS) algorithm are used. The estimator is validated by simulation and by field tests.

An efficient recursive total least squares algorithm for FIR adaptive filtering

An algorithm for recursively computing the total least squares (TLS) solution to the adaptive filtering problem is described. This algorithm requires O(N) multiplications per iteration to effectively track the N-dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix. It is shown that the recursive least squares (RLS) algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise. The TLS solution on the other hand, is seen to produce unbiased solutions. Examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited. Computer simulations comparing the relative performance of RLS and recursive TLS are described. >