Nonlinear Adaptive Estimation Research Articles

Wavelet estimations of the derivatives of variance function in heteroscedastic model

<abstract><p>This paper studies nonparametric estimations of the derivatives $ r^{(m)}(x) $ of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed. The convergence rates under $ L^{\tilde{p}} (1\leq \tilde{p} < \infty) $ risk of those two wavelet estimators are considered with some mild assumptions. A simulation study is presented to validate the performances of the wavelet estimators.</p></abstract>

Wavelet estimations of the derivatives of variance function in heteroscedastic model

<abstract><p>This paper studies nonparametric estimations of the derivatives $ r^{(m)}(x) $ of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed. The convergence rates under $ L^{\tilde{p}} (1\leq \tilde{p} < \infty) $ risk of those two wavelet estimators are considered with some mild assumptions. A simulation study is presented to validate the performances of the wavelet estimators.</p></abstract>

Wavelet Estimation of Function Derivatives from a Multichannel Deconvolution Model

This paper considers a multichannel deconvolution model with Gaussian white noises. The goal is to estimate the d -th derivatives of an unknown function in the model. For super-smooth case, we construct an adaptive linear wavelet estimator by wavelet projection method. For regular-smooth case, we provide an adaptive nonlinear wavelet estimator by hard-thresholded method. In order to measure the global performances of our estimators, we show upper bounds on convergence rates using the L p -risk ( 1 ≤ p < ∞ ).

Performance evaluation of a novel adaptive variable structure state estimator

An improved nonlinear adaptive state estimator called Adaptive Smooth Variable Structure Filter ASVSF has been proposed and its algorithm described. ASVSF extends the functionality and performance of a previously reported robust smooth variable structure filter (SVSF) with optimal boundary layer (SVSF-OBL). Improvement in performance includes the provision for accommodating unknown and time varying process noise covariance, which generally characterizes modelling uncertainty. The novelty of this proposed ASVSF estimator, which inherits the features of the SVSF, is that it adaptively provides an estimate of the unknown time varying process noise covariance (and hence called adaptive SVSF or ASVSF) which is required for determining the optimal boundary layer width of SVSF-OBL thus obviating the need of the prior knowledge of the process noise covariance. This makes the proposed estimator performance to be insensitive to (and therefore robust with respect to) unknown time varying process noise covariance while retaining the optimality of SVSF-OBL. The performance of the proposed ASVSF estimator is evaluated using Monte Carlo simulation and is compared with previously reported state estimators using a case of maneuvering civilian aircraft where a simplified and grossly approximate process model is used in the estimator/filter for tracking and thereby generating a time varying and unknown process noise covariance situation. Three different measures of Root Mean Square (RMS) error over the trajectory have been used for comparison which demonstrates the strengths of the proposed ASVSF estimator.

Quadrotor Accelerometer and Gyroscope Sensor Fault Diagnosis Using Nonlinear Adaptive Estimation Methods

This paper presents the design, analysis, and real-time experimental evaluation results of a nonlinear sensor fault diagnosis scheme for quadrotor unmanned air vehicles (UAV). The objective is to detect, isolate, and estimate sensor bias faults in accelerometer and gyroscope measurements. Based on the quadrotor dynamics and sensor models under consideration, the effects of sensor faults are represented as virtual actuator faults in the quadrotor state equation. Two nonlinear diagnostic estimators are designed to provide structured residualsfor fault detection and isolation. Additionally, after the fault is detected and isolated, a nonlinear adaptive estimation scheme is employed for estimating the unknown fault magnitude.The proposed fault diagnosis scheme is capable of handling simultaneous faults in the accelerometer and gyroscope measurements. The effectiveness of the fault diagnosis method is demonstrated using an indoor real-time quadrotor UAV test environment.

Convergence Rates of Wavelet Density Estimators for Strongly Mixing Samples

This paper considers wavelet estimations for a multivariate density function based on strongly mixing data. We first construct a linear wavelet estimator and provide a convergence rate over $$L^{p} (1\le p<\infty )$$ risk in Besov space $$B^{s}_{r,q}(\mathbb {R}^{d})$$ . However, this estimator depends on the smoothness of density function, which means that the estimator is not adaptive. A nonlinear adaptive wavelet estimator is proposed by thresholding method. Moreover, the convergence rate of nonlinear estimator is better than the linear one in the case of $$r\le p$$ .

Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids

We address the problem of non-parametric density estimation under the additional constraint that only privatised data are allowed to be published and available for inference. For this purpose, we adopt a recent generalisation of classical minimax theory to the framework of local $\alpha$-differential privacy and provide a lower bound on the rate of convergence over Besov spaces $\mathcal{B}^{s}_{pq}$ under mean integrated $\mathbb{L}^{r}$-risk. This lower bound is deteriorated compared to the standard setup without privacy, and reveals a twofold elbow effect. In order to fulfill the privacy requirement, we suggest adding suitably scaled Laplace noise to empirical wavelet coefficients. Upper bounds within (at most) a logarithmic factor are derived under the assumption that $\alpha$ stays bounded as $n$ increases: A linear but non-adaptive wavelet estimator is shown to attain the lower bound whenever $p\geq r$ but provides a slower rate of convergence otherwise. An adaptive non-linear wavelet estimator with appropriately chosen smoothing parameters and thresholding is shown to attain the lower bound within a logarithmic factor for all cases.

Wavelet pointwise estimations under multiplicative censoring

In this paper, we investigate the wavelet-based estimators of a kind of censored mixture density and discuss their pointwise asymptotic convergence rates over Hölder spaces. We first consider the linear wavelet estimator and give its upper bound. However, the linear one is nonadaptive and not applicable since it is related to the unknown space parameter. Finally, we use the hard threshold method to explore adaptive nonlinear wavelet estimator and obtain the same convergence order as the linear one up to a logarithmic penalty.

Global Adaptive Finite-Time Stabilization of Uncertain Time-Varying $p$-Normal Nonlinear Systems Without Homogeneous Growth Nonlinearity Restriction

The problem of global finite-time stabilization for $p$ -normal nonlinear systems subject to uncertain time-varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated in this paper. By virtue of the technique of homogeneous domination, a new dual-layer adaptive approach is presented to address the uncertainties and nonlinearities of the system. For one layer of the adaptive mechanism, a nonlinear adaptive parameter estimator is proposed to reconstruct the upper bounds of the unknown uncertainties. For the other, an explicit construction approach of a new adaptive dynamic gain mechanism is presented for the first time to cope with the uncertain time-varying control coefficients of the $p$ -normal nonlinear systems. It is shown that the global boundedness of the systems under consideration is guaranteed by the presented approach, and in addition the time taken to converge to the equilibrium is rendered to be finite time.

Adaptive state estimation for tracking of civilian aircraft

Tracking of manoeuvring subsonic aerospace vehicles has traditionally been handled by state estimators. Ordinary state estimators perform poorly as the concerned process model can only be defined imprecisely. This contribution evaluates and compares the performance of adaptive single mode non-linear estimators against several versions of other estimators. The primary comparison is with the recently introduced smooth variable structure filter (SVSF) which is claimed to inherit the robustness of variable structure approach. Both the above types of estimators are then benchmarked with a well-known version of interacting multiple model (IMM) estimator which treats the manoeuvring aircraft as a hybrid system consisting of multiple modes. Monte Carlo simulation has been used and several descriptors have been used for comparison. The comparison demonstrates that a version of non-linear adaptive estimators incorporating sigma points and a single constant turn model performs substantially better than the SVSF and its tracking performance approaches that obtainable by the IMM estimator. Novelty of this contribution lies in providing a detailed comparison of the above three families of estimators, which provides adequate insight for selecting tracking estimators by trading off estimation accuracy, algorithm complexity, tuning requirement, and computational load.

Active fault tolerant control scheme for satellite attitude system subject to actuator time‐varying faults

This study investigates the active fault tolerant control (FTC) problem for the attitude system of a rigid satellite, which is affected by parameter uncertainty, unknown exogenous disturbance and actuator time-varying faults. The upper bounds of the actuator time-varying fault and the generalised perturbation are unknown. A novel adaptive non-linear fault estimation observer is designed in order to obtain the estimated value of unknown time-varying faults. Then, an active fault tolerant attitude control approach is proposed under the framework of both backstepping control and adaptive control theory. Consequently, the Lyapunov theory is used to prove the robust asymptotic stability for the closed-loop attitude system of a faulty satellite under the proposed FTC scheme. Finally, simulation results on an in-orbit rigid satellite are provided to show the good fault tolerant performance, which validate the effectiveness and feasibility of the proposed scheme.

A Multifunctional GPV System Using Adaptive Observer Based Harmonic Cancellation Technique

This paper presents a multipurpose three-phase double-stage grid interfaced photovoltaic (GPV) system using an adaptive nonlinear control strategy. Along with a peak power extraction from a photovoltaic array, the proposed system is capable of harmonics currents elimination, reactive power compensation, grid currents balancing, and adaptive dc-link voltage control. The fundamental and harmonics information from the polluted load current are precisely estimated using an adaptive observer. A strictly positive real Lyapunov function is used to derive update laws for an adaptive observer. The DC-link voltage is adaptively adjusted in proportion to the point of common coupling voltage to minimize switching losses in voltage source converter and to avoid its tripping in sensitive distribution grids. A feed-forward loop for PV contribution is included to improve system response under dynamic conditions. Simulated and test results depict the performance of the GPV system with aforementioned functionalities. Improved steady-state and dynamic performances are observed with the proposed nonlinear adaptive estimation based control approach. The total harmonic distortions in grid currents are found well within the limits prescribed by an IEEE-519 standard.

Quadrotor Actuator Fault Diagnosis and Accommodation Using Nonlinear Adaptive Estimators

This brief presents the systematic design and real-time experimental results of a fault detection, isolation, and accommodation algorithm for quadrotor actuator faults using nonlinear adaptive estimation techniques. The fault diagnosis architecture consists of a nonlinear fault detection estimator and a bank of nonlinear adaptive fault isolation estimators designed based on the functional structures of the faults under consideration. Adaptive thresholds for fault detection and isolation are systematically designed to enhance the robustness and fault sensitivity of the diagnostic algorithm. After fault isolation, the fault parameter estimate generated by the matched isolation estimator is used for accommodating the fault effect. Using an indoor quadrotor test environment, real-time experimental results are shown to illustrate the effectiveness of the algorithms.

Improved estimation and fault detection scheme for a class of non‐linear hybrid systems using time delayed adaptive CD state estimator

An improved fault detection scheme for a non-linear hybrid system with delayed measurement by using a modified non-linear adaptive state estimator is proposed. The proposed estimator performs acceptably even when the (i) covariance of the measurement noise is unknown and also (ii) when the measurements are delayed. The algorithm for the proposed estimator called time-delayed R-adaptive central difference Kalman filter (TD-RACDKF) uses a modified R-adaptive 2nd order Central Difference estimator, also called Central Difference Kalman Filter (CDKF) in some literature. Algorithm for the proposed TD-RACDKF has been presented and its performance evaluated as well as characterised with Monte Carlo simulation on two standard non-linear systems with delayed measurements. The characterisation includes comparison with existing estimators. Having demonstrated the improved performance of the proposed state estimator, its use for fault detection of non-linear hybrid systems was investigated. The performance of the fault detection scheme has been illustrated with the help of a benchmark non-linear hybrid system, namely ‘three tank system’ and by comparison with a previously available extended KF-based estimator.

Backlash estimation for industrial drive-train systems

Backlash in gearing and other transmission components is a common positioning-degrading phenomenon that develops over time in industrial machines. High-performance machine tool controls use backlash compensation algorithms to maintain accurate positioning of the tool to cope with such deadzone phenomena. As such, estimation of the magnitude of deadzones is essential. This paper addresses the generic problem of accurately estimating the width of the deadzone in a single-axis mechanical drive train. The paper suggests a scheme to estimate backlash between motor and load, employing a sliding mode observer and a nonlinear adaptive estimator. The efficacy of the approach is illustrated via simulations.

Adaptive nonlinear predictive control and estimation of microaerobic processes

Compared to other sectors, industrial biotechnology only employs a limited number of automatic control strategies. The applied control strategies are mainly recipe-based and often do not take directly the high variability and flexibility of biological systems into account. While this provides sharply defined conditions and quality by design guarantees, process are operated significantly below the optimum, with inefficient product yields and limited reproducibility. The information that is available online, the data from previous batches and the additional biological knowledge are not considered, usually because the integration of this information requires the use of control strategies with an adaptive character, which increases the the design complexity and the implementation cost.We present an approach which allows to optimize biotechnological production process and the corresponding growth model at the same time with reasonable computational cost. Employing a basal model with unknown parameters, the combination of moving horizon estimation and adaptive nonlinear model predictive control enables the identification of parameters for the whole growth range of the respective organism online. The adapted model is then used for prediction and control of the process, leading to an optimized process performance within one experiment. Such an adaptive strategy accelerates the design, characterization and optimization of new production processes. It furthermore reduces time and cost intensive traditional process development.

Quadrotor Actuator Fault Diagnosis with Real-Time Experimental Results

Quadrotor Unmanned Aerial Vehicles (UAVs) have attracted significant attention in recent years due to their potentials in various military and commercial applications. Four propellers mounted on the shafts of four brushless DC motors generate the required thrust and torques needed for altitude and attitude control of quadrotors. However, structural damage to the propellers and rotor degradation can lead to actuator faults in the form of a partial loss of effectiveness in a rotor, which may result in degraded tracking performance or even loss of stability of the control system. This paper presents the systematic design, analysis, and real-time experimental results of a fault detection and isolation algorithm for quadrotor actuator faults using nonlinear adaptive estimation techniques. The fault diagnosis architecture consists of a nonlinear fault detection estimator and a bank of nonlinear adaptive fault isolation estimators designed based on the functional structures of the faults under consideration. Adaptivethresholds for fault detection and isolation are systematically designed to enhance the robustness and fault sensitivity of the diagnostic algorithm. Using an indoor quadrotor test environment, real-time experimental flight test results are shown to illustrate the effectiveness of the algorithms.

Nonlinear Recursive Estimation With Estimability Analysis for Physical and Semiphysical Engine Model Parameters

A methodology for nonlinear recursive parameter estimation with parameter estimability analysis for physical and semiphysical engine models is presented. Orthogonal estimability analysis based on parameter sensitivity is employed with the purpose of evaluating a rank of estimable parameters given multiple sets of observation data that were acquired from a transient engine testing facility. The qualitative information gained from the estimability analysis is then used for estimating the estimable parameters by using two well-known nonlinear adaptive estimation algorithms known as extended Kalman filter (EKF) and unscented Kalman filter (UKF). The findings of this work contribute on understanding the real-world challenges which are involved in the effective implementation of system identification techniques suitable for online nonlinear estimation of parameters with physical interpretation.

Adaptive Gauss–Hermite filter for non‐linear systems with unknown measurement noise covariance

A non-linear adaptive state estimator based on the Gauss–Hermite (GH) quadrature rule has been proposed to suit non-linear signal models where the measurement noise covariance remains unknown. The proposed algorithm which may be used for both parameter and state estimation incorporates online adaptation of the measurement noise covariance ( R ) following maximum-likelihood estimation-based method. The GH quadrature approach has been considered so that the proposed filter may inherit the enhanced estimation accuracy as exhibited by its non-adaptive counterpart. The proposed adaptation algorithm, in contrast to some other reported methods, automatically ensures positive definiteness of the adapted measurement noise covariance. The efficacy of the adaptive algorithm over the non-adaptive GH filter has been demonstrated using Monte Carlo simulation and two case studies. Performance comparison has also been carried out with respect to adaptive unscented Kalman filter with the help of same case studies.

Quadrotor Accelerometer and Gyroscope Sensor Fault Diagnosis with Experimental Results

&#x0D; &#x0D; &#x0D; This paper presents the design and real-time experimental results of a fault diagnosis scheme for inertial measurement unit (IMU) measurements of quadrotor unmanned air vehicles (UAVs). The objective is to detect, isolate, and estimate sensor bias fault in accelerometer and gyroscope measurements. Based on the quadrotor dynamics and sensor models under consideration, the effects of sensor faults are represented as virtual actuator faults in the quadrotor state equations. Two nonlinear diagnostic estimators are designed to provide structured residuals enabling the simultaneous detection and isolation of the sensor faults. Additionally, based on the detection and isolation scheme, two nonlinear adaptive estimators are employed for the estimation of the fault magnitude. The performance of the diagnosis method is evaluated and demonstrated through real-time flight experiments.&#x0D; &#x0D; &#x0D;