Recursive Least-squares Identification Research Articles

Research on Direct Lift Carrier-Based Unmanned Aerial Vehicle Landing Control Based on Performance Index Intelligent Optimization/Dynamic Optimal Allocation

High-precision control problems for carrier-based UAVs are challenging due to the requirements for safety, high-performance operation and uncertain ocean environments. To address such problems, this paper proposes a direct lift landing control method that can ensure the safe operation of UAVs using intelligent optimization of control performance indicators and dynamic optimal allocation methods. The direct lift control (DLC) scheme is adopted to improve the operability of the control by introducing flap channels to achieve the fast correction of vertical disturbances. To improve the landing control performance, an intelligent optimization method for DLC gain is proposed, and a neural network relationship between parameter uncertainty and optimal DLC gain is established. In addition, a recursive least-squares identification method is used to estimate the uncertain parameters in real time, so that the established neural network can be used to generate the optimal DLC commands online, and the generated control commands can be assigned to multiple actuators of the carrier-based UAV through a dynamic optimal assignment algorithm. Finally, the superiority of the method is verified using simulation comparison.

A Novel Digital Predistortion Identification Algorithm Based on Variable Forgetting Factor Recursive Least Square Method

The transmitting signal of wireless communication system is impaired by the nonlinearity of RF power amplifier (PA) which leads to signal distortion and spectrum spillover, by which the signal transmission quality is affected. Digital predistortion (DPD) is an efficient and economical way to correct the nonlinear effects of power amplifiers. The recursive least square (RLS) recognition algorithm is commonly used to extract the correction coefficients of the DPD model, and the accuracy of the extraction directly affects the system performance. In this paper, a new variable forgetting factor identification algorithm (new variable forgetting factor recursive least square, NVFFRLS) is proposed for recursive least square (RLS) identification algorithm. The 64-QAM signal is combined with a memory polynomial (MP) predistortion model for predistortion system simulation. The experimental results show that, compared with the RLS identification algorithm and two kinds of variable forgetting factor RLS identification algorithms, the algorithm has smaller estimation error, faster convergence, and better tracking capability, stability, and adaptability; the predistortion system based on NVFFRLS identification algorithm can compensate the nonlinear memory effects of power amplifier more effectively.

A Method of Reducing Invalid Steering for AUVs Based on a Wave Peak Frequency Tracker

The motion control of autonomous underwater vehicles (AUVs) is affected by waves near the ocean surface or in shallow-water areas. Therefore, to counteract the influence of waves, we need to remove them by designing a filter. The wave peak frequency is important in wave filter design. This paper focuses on the identification of the wave peak frequency using the least-squares parameter estimation algorithm. The input–output expression of the wave disturbance model is derived by eliminating the intermediate variable. Based on the obtained identification model, an auxiliary model-based recursive extended least-squares identification algorithm is developed to estimate the model parameters. The effectiveness of the proposed method is verified with simulated tests of the heading control system of an AUV. The simulation results demonstrate that the proposed method is effective for the identification of the wave peak frequency, and an observer with a wave peak frequency tracker can significantly reduce invalid steering.

Adaptive backstepping controller design on Buck converter with a novel improved identification method

An adaptive backstepping method is presented by this paper for a DC–DC Buck converter utilising a strategy for system identification with pulse width modulation in the presence of parametric uncertainties, load variations, and high variance noises. In this control structure, the system is assumed as a black-box block that can decrease the computational burden providing faster dynamics. An adaptive mechanism is adopted for the BSM using the Lyapunov definition, providing robust dynamics for the controller against various disturbances. In addition, a novel improved exponential recursive least-squares identification algorithm is proposed, which shows higher robustness in parametric estimations and can decrease the negative impact of disrupting factors on the estimator. Moreover, a particle swarm optimisation algorithm-based PID controller is designed to be compared with the proposed controller. Finally, the merits of the presented controller are validated for various working conditions through simulations and experiments. It can be seen that the adaptive backstepping method with the improved identification technique provides much better results with faster dynamics.

Identification of continuous-time hybrid “Box–Jenkins” systems with multiple unknown time delays using two-stage parameter estimation algorithm

PurposeThis study/paper aims to present a separable identification algorithm for a multiple input single output (MISO) continuous time (CT) hybrid “Box–Jenkins”.Design/methodology/approachThis 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.FindingsThe effectiveness of the proposed scheme is shown with application to a simulation example.Originality/valueA 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.

Adaptive Unified Monitoring System Design for Tire-Road Information

Knowledge of the tire-road information is not only very crucial in many active safety applications but also significant for self-driving cars. The tire-road information mainly consists of tire-road friction coefficient and road-tire friction forces. However, precise measurement of tire-road friction coefficient and tire forces requires expensive equipment. Therefore, the monitoring of tire-road information utilizing either accurate models or improved estimation algorithms is essential. Considering easy availability and good economy, this paper proposes a novel adaptive unified monitoring system (AUMS) to simultaneously observe the tire-road friction coefficient and tire forces, i.e., vertical, longitudinal, and lateral tire forces. First, the vertical tire forces can be calculated considering vehicle body roll and load transfer. The longitudinal and lateral tire forces are estimated by an adaptive unified sliding mode observer (AUSMO). Then, the road-tire friction coefficient is observed through the designed mode-switch observer (MSO). The designed MSO contains two modes: when the vehicle is under driving or brake, a slip slope method (SSM) is used, and a recursive least-squares (RLS) identification method is utilized in the SSM; when the vehicle is under steering, a comprehensive friction estimation method is adopted. The performance of the proposed AUMS is verified by both the matlab/simulinkCarSim co-simulation and the real car experiment. The results demonstrate the effectiveness of the proposed AUMS to provide accurate monitoring of tire-road information.

Bias Compensated Recursive Least-squares Identification for the Systems under Poor Observation Condition

For the autoregressive signal under poor observation condition, a bias compensated recursive least-square identification algorithm is presented based on the incremental observation equation. Moreover, it is easy to know that the obtained estimates of model parameters and noise variance converge to the corresponding true values with probability one, i.e. they are strongly consistent. A simulation example shows its effectiveness.

Maximum Likelihood-Based Recursive Least-Squares Algorithm for Multivariable Systems with Colored Noises Using the Decomposition Technique

This paper considers the parameter estimation problems for a class of multivariable equation-error systems with colored noises. By using the decomposition technique, a multivariable system is transformed into several subsystems to reduce the computational burden, and a maximum likelihood-based recursive least-squares identification algorithm is developed for estimating the parameters of each subsystem. As a comparison, a multivariable recursive extended least-squares algorithm is presented. The analysis indicates that the proposed algorithm has lower computational complexity than the multivariable recursive extended least-squares algorithm, and the numerical simulation results demonstrate that the proposed method is effective.

Identification of Hammerstein systems with time delay under load disturbance

To cope with load disturbance often encountered when performing identification tests on non-linear systems with input delay in industrial applications, a bias-eliminated Hammerstein-type output error (OE) model identification method is proposed in this study. By taking into account the load disturbance response as a time-varying parameter for estimation, two recursive least-squares (RLS) identification algorithms is established to estimate the Hammerstein-type model parameters and the time-varying disturbance response. A one-dimensional searching approach is adopted to determine the integer-type delay parameter by minimising the fitting error of output response. Moreover, an auxiliary OE model is constructed to ensure consistent estimation under stochastic noise. In addition, two adaptive forgetting factors are introduced into the proposed RLS algorithms to enhance the estimation convergence on the model parameters and the disturbance response. Asymptotic properties of parameter estimation are analysed along with a proof, in particular for unbiased estimation against a constant disturbance. Two illustrative examples are given to demonstrate the effectiveness of the proposed identification method.

Multi-innovation based Identification of Output Error Model with Time Delay under Load Disturbance

In this paper, a robust output error model identification method is proposed for industrial processes with time delay subject to load disturbance. By viewing the load disturbance response as a time-variant parameter to be estimated, an extended recursive least-squares (RLS) identification method is established to simultaneously estimate the model parameters and the disturbance response, based on a multi-innovation fitting strategy. The integer type time delay parameter is determined by using a one-dimensional searching approach. An auxiliary model is used to estimate the noise-free output against stochastic noise. Besides, two adaptive forgetting factors are introduced to improve the convergence rates of estimating the time-invariant model parameters and the time-variant disturbance response, respectively. The effectiveness and merit of the proposed method is demonstrated by an illustrative example.

Correlation analysis-based error compensation recursive least-square identification method for the Hammerstein model

ABSTRACTIn this paper, the correlation analysis based error compensation recursive least-square (RLS) identification method is proposed for the Hammerstein model. Firstly, the covariance matrix between input and output data points of the Hammerstein model is derived by using separable signal to realize that the unmeasurable internal variable is replaced by the covariance matrix of input. Thus, the correlation analysis method can be accordingly used to estimate parameters of the linear part, which results in the identification problem of the nonlinear part separated from the linear part. In addition, a correction term is added to least-square estimation to compensate error caused by output noise, further the error compensation-based RLS method is obtained for the observed data from the Hammerstein model. As a result, the least-square identification method, which generates error in the presence of noise distribution, can be compensated. Finally, simulation experiments are conducted to illustrate the performance of the proposed identification method.

Combined RLS-ΕKF Method for SOC and Parameter Estimation of Lithium-Ion Batteries

Due to their high energy density, lithium-ion rechargeable batteries have been increasingly used in various electronic devices as useful and efficient electric energy storages. On the other hand, it is well known that some critical states such as over-charge or over-discharge of a lithium-ion battery may lead to dangerous situations and may accelerate the aging of its capacity. it is thus necessary to accurately estimate the State-of-Charge (SOC) of the the batteries for safe and long lasting operations[1]. Recently, some SOC estimation methods employing the extended Kalman filtering (EKF) technique have been reported based on the state-space representation of an equivalent circuit model (Figure 1) [2]-[5]. One of the main difficulties in these model-based methods is that the physical parameters of the equivalent circuit change in time depending on the SOC and temperature of the battery. A typical approach to cope with this is to model a priorithe SOC- and temperature-dependences of these parameters from the measurements obtained from AC impedance experiments [4],[5]. This approach requires a lot of time to acquire the experimental data. In this work, we take a different approach from the above previous works. We present a method for simultaneous estimation of the SOC and the equivalent circuit parameters by combining the EKF and the recursive least-squares (RLS) identification algorithm. The schematic diagram of the proposed method is illustrated in Figure 2. The advantages of the proposed method are as follows. The equivalent circuit parameters can be accurately estimated on-line by the RLS in various operating conditions without prior information nor preliminary experiments. The parameter estimation part of the proposed method is indenpendent from the nonlinear characteristics of the SOC dependence of the open circuit voltage (OCV). The effectiveness of the proposed method is verified through a discharge experiment of a LiFeO4 battery with the nominal capacity 48.5Ah and the maximum voltage 3.5V. The SOC estimation of a LiFeO4 battery is difficult because its SOC-OCV characteristic curve is almost flat in the middle range of the SOC. The terminal voltage and current are measured at the sampling period 1sec. The input current is a quasi-random sequence whose power is concentrated in the frequency bands around 0.07Hz and 0.03Hz (Figure 3). The RMS values of the SOC estimation errors are shown in Table1. It is seen from the table that the proposed method improves the estimation accuracy than the previous method due to Oya et al.[5]. Table1 RMS errors of SOC estimates Proposed method 1.069[%]Previous method[3] 1.998[%] The accuracy of the parameter estimates is assessed in terms of the Cole-Cole plots in Figure 4, where the x- and o-indications respectively denote the points at the Nyquist frequency 0.5Hz and the lowest frequency 0.08Hz measurable by our impedance analyzer. For both SOC=20% and 50%, in the operating frequency band lower around 0.08Hz, the estimates by the RLS (blue) are much closer to the measured values (red) than the previous method due to Oya et al.[5] (green). This is not the case for SOC=80%, which is because of the transient behavior of the RLS algorithm during the initial period of the discharge experiment. From the above experimental results, we conclude the following as the main finding of this work. The RLS algorithm can provide a good estimation of the equivalent circuit model in the sense that the obtained parameter estimates well describe the battery behavior in the operating frequencies rather than all frequencies, and this fact accounts for the SOC estimation accuracy of the proposed combined RLS-EKF method. It may also be noted that the frequency domain analysis presented in this paper will be helpful in assessment or validations of various model-based SOC estimation algorithms.

Identification of dual‐rate sampled systems with time delay subject to load disturbance

A discrete-time model identification method is proposed for dual-rate sampled systems with time delay subject to load disturbance with unknown dynamics. By viewing the output response arising from such load disturbance as a dynamic parameter for estimation, two recursive least-squares identification algorithms are developed to estimate the linear model parameters and the load disturbance response, respectively, while the integer delay parameter is derived by using a one-dimensional searching approach to minimise the output fitting error. An auxiliary model is constructed to estimate the unknown noise-free output such that consistent estimation of the model parameters can be obtained under stochastic noise in the output measurement. Moreover, two adaptive forgetting factors are introduced to expedite the convergence rates of estimating the model parameters and the load disturbance response, respectively. Theoretical analysis is given to clarify the convergence of parameter estimation. Two illustrative examples are presented to demonstrate the effectiveness and merit of the proposed identification method.

Recursive subspace identification subject to relatively slow time-varying load disturbance

ABSTRACTIn this paper, a recursive subspace identification method is proposed to identify linear time-invariant systems subject to load disturbance with relatively slow dynamics. Using the linear superposition principle, the load disturbance response is decomposed from the deterministic-stochastic system response in the form of a time-varying parameter. To ensure unbiased estimation of the deterministic system matrices, a recursive least-squares (RLS) identification algorithm is established with a fixed forgetting factor, while another RLS algorithm with an adaptive forgetting factor is constructed based on the output prediction error to quickly track the time-varying parameter of load disturbance response. By introducing a deadbeat observer to represent the deterministic system response, two extended observer Markov parameter matrices are constructed for recursive estimation. Consequently, the deterministic matrices are retrieved from the identified system Markov parameter matrices. The convergence of the proposed method is analysed with a proof. Two illustrative examples are shown to demonstrate the effectiveness and merit of the proposed identification method.

Identification of non-uniformly sampled Wiener systems with dead-zone non-linearities

ABSTRACTIn multi-rate systems, identifying non-uniformly sampled data (NUSD) models is a challenge. This study proposes an iteratively recursive least-squares identification algorithm for non-uniformly sampled Wiener systems with dead-zone non-linearities. First, an extended information vector is designed, in which both unknown parameters and inner variables exist. Then, based on the auxiliary model and iterative method, an auxiliary model-based iteratively recursive least-squares algorithm is developed to estimate the system parameters directly. Furthermore, to improve the convergence rate and disturbance rejection, a new modified forgetting factor function is presented. Compared with no or fixed forgetting factor algorithms, the proposed algorithm has a higher convergence speed and is more robust to white noise with different variances. The numerical simulation shows the effectiveness of the proposed algorithm, and it can be extended to other NUSD non-linear systems.

An In Situ Full Charge Capacity Estimation Algorithm for Li-Ion Batteries Using Recursive Least-Squares Identification with Adaptive Forgetting Factor Tuning

This paper discuss a full charge capacity (FCC) estimation system for lithium ion batteries based on the recursive least-squares identification. The accuracy of the estimation is depended on accuracy of the state of charge (SOC) estimation. The authors have newly formulated the adaptive forgetting factor for recursive least- squares identification. As the result, the error rate of the SOC estimation has been improved. The evaluation shows the new FCC estimation system can be used for various temperature conditions.

Identification of discrete-time output error model for industrial processes with time delay subject to load disturbance

In this paper, a bias-eliminated output error model identification method is proposed for industrial processes with time delay subject to unknown load disturbance with deterministic dynamics. By viewing the output response arising from such load disturbance as a dynamic parameter for estimation, a recursive least-squares identification algorithm is developed in the discrete-time domain to estimate the linear model parameters together with the load disturbance response, while the integer delay parameter is derived by using a one-dimensional searching approach to minimize the output fitting error. An auxiliary model is constructed to realize consistent estimation of the model parameters against stochastic noise. Moreover, dual adaptive forgetting factors are introduced with tuning guidelines to improve the convergence rates of estimating the model parameters and the load disturbance response, respectively. The convergence of model parameter estimation is analyzed with a rigorous proof. Illustrative examples for open- and closed-loop identification are shown to demonstrate the effectiveness and merit of the proposed identification method.

A Precise FCC Estimation Algorithm Based on Recursive Least-Squares Identification of Li-Ion Batteries with Adaptive Forgetting Factor Tuning

Li-ion batteries are remarkable devices due to their high capability to store energy densely. The FCC (full charge capacity) estimation is essential for capturing the state of secondary battery. In this paper, precise FCC estimation is devised by estimation of internal parameter and SOC (state of charge). Comparted with the conventional identification techniques [1], the adaptive forgetting factor is more suitable for Li-ion battery. The open circuit voltage, OCV, is affected by SOC value. Therefore, the rate of change of OCV is not linear to time. In order to solve this problem, a heuristic adaptive forgetting factor is introduced based on terminal voltage and terminal current. To apply the system identification approach, the battery equivalent circuit model shown in Fig.1 is used. The subject of the system identification is OCV. OCV is physical quantity depending on SOC, and the relationship between OCV and SOC is given as Fig. 2. OCV-SOC curve has a significant role to achieve SOC estimation. The difference equation of u L is obtained by the equivalent circuit. Then, Equation (1) is obtained as observation function using the variables defined in Equation (2), and adding w (k) which is observation noise. T s is the sampling period. In equation (1), parameterθ regards as a unknown parameter, being estimated by using recursive least-squares identification. The value of R a, R b, C b, u OCV can be calculated by parameterθ with equation (3). SOC is obtained by referring the OCV-SOC curve. A heuristic forgetting factor λ(k) is defined by Equation (4). In this equation, G is gain, m uL is average variance of voltage u L preserving in buffer, and i avg is average value of current i. Estimation of OCV is performed using discharge patterns indicated in Fig.3. Table1 shows the average values of SOC estimation error. The average error is the smallest in the case of using the adaptive forgetting factor. Table2 shows the error dependent on temperature in the case of using the adaptive forgetting factor. SOC estimation is successful since the maximum value of average SOC estimation error is less than 0.05. Then, FCC is estimated with the estimated SOC. FCC is calculated by quotient of the value of current accumulation from time t0 to t1 and the change of estimated SOC value from t0 to t1. Ten percent discharges are executed from the 10 points of SOCs. The starting points of the discharge are from 0.97 to 0.92 by 0.05 intervals. The result of FCC estimation is shown Fig.4. In the case of 0.5A, the maximum value of average SOC estimation error is 0.049. Compared with the conventional techniques [2], the amount of calculation with proposed method is much less. The conventional technique [3] needs huge amount of data before estimation. In contrast, proposed method needs few data. This FCC estimation system pulls the maximum capability of secondary batteries with precise SOC estimation, and controls the batteries’ state by grasp of FCC. In addition, the amount of calculation and data needed preparing before estimation are less than conventional technique. Therefore, this proposed method can be implemented easily with inexpensive microcomputer. The experimentation has been executed in several conditions, and similar accurate results were obtained. [1] C. Fleischera, W. Waaga, H. Heyna, and D. U. Sauera, “On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models: Part 1. Requirements, critical review of methods and modeling,” J. Power Sources, vol. 260, no. 15, pp. 276-291, 2014. [2] T. Kim, Y. Wang, Z. Sahinoglu, T. Wada, S. Hara, W. Qiao, “A rayleigh quotient-based recursive total-least-squares online maximum capacity estimation for litium-ion batteries, ”IEEE trans. on energy conversion, vol. 30, no.3, pp. 842-850, 2015. [3] C. Hu, G. Jain, C. Schmidt, C. Strief, M. Sullivan, “Online estimation of lithium-ion battery capacity using sparse Bayesian learning, ” J. Power Sources, 289, pp. 105-113, 2015 Figure 1

초저전력 마이크로 서보시스템의 모델식별을 위한 계측 파라미터 선정 기법

In micro-scale electromechanical systems, the power to perform accurate position sensing often greatly exceeds the power needed to generate motion. This paper explores the implications of sampling rate and amplifier noise density selection on the performance of a system identification algorithm using a capacitive sensing circuit. Specific performance objectives are to minimize or limit convergence rate and power consumption to identify the dynamics of a rotary micro-stage. A rearrangement of the conventional recursive least-squares identification algorithm is performed to make operating cost an explicit function of sensor design parameters. It is observed that there is a strong dependence of convergence rate and error on the sampling rate, while energy dependence is driven by error that may be tolerated in the final identified parameters.

Filtering-based recursive least-squares identification algorithm for controlled autoregressive moving average systems using the maximum likelihood principle

This paper considers the parameter estimation problem of controlled autoregressive moving average systems. The basic idea is to use the noise polynomial to filter the input-output data, then a controlled moving average identification model and a noise model are obtained. A maximum likelihood recursive least squares algorithm and a recursive least squares algorithm are used to interactively estimate the parameters of the two identification models by using the hierarchical identification principle. A numerical example is provided to show the effectiveness of the proposed algorithms.