Nonlinear Error Model Research Articles

A nonlinear quaternion-based fault-tolerant SINS/GNSS integrated navigation method for autonomous UAVs

The fault-tolerant integrated navigation methods using strapdown inertial navigation system (SINS) and global navigation satellite system (GNSS) for unmanned aerial vehicles (UAVs) are studied herein to address two types of possible faults, system fault and measurement fault. Two typical approximation-based nonlinear filters, extended Kalman filter (EKF) and divided difference Kalman filters (DDKFs), are modified to be fault-tolerant for accurate navigation even in the presence of these faults. Criteria are presented to detect the faults, and related covariance matrices of the predicted errors are enlarged using fault accommodation factors to make the faulty state or measurement components be normally treated. Navigation simulations using the nonlinear quaternion-based navigation error model are given to demonstrate the effectiveness of the proposed methods.

Weighted total least squares for solving non-linear problem: GNSS point positioning

In this contribution, two algorithms are developed for parameter estimation in a non-linear measurement error model with errors in both the coefficient matrix and the vector of measurement. They are based on the complete description of the variance–covariance matrices of the observation errors and of the coefficient matrix errors without any restriction. The paper reinvestigates the nonlinear measurement model associated with GNSS point positioning. Various simulation experiments indicate that GNSS point positioning is much better formulated as a non-linear WTLS problem with errors in both the coefficient matrix and measurement variables. The efficacy of the proposed algorithms is verified through the numerical results.

Adaptive Extended Kalman Filter for Nonlinear System with Noise Compensating Technology

This paper is concerned with the development of new adaptive nonlinear Kalman estimators which incorporate nonlinear model errors and noise statistical characteristic errors. With the adoption of fictitious noise compensation technique and actual non-divergent computation method, the new filters are aimed at compensating the nonlinear dynamics as well as the system modeling errors by adaptively estimating the noise statistics and unknown parameters. The performance of the proposed adaptive estimators is demonstrated using six-state with varying model parameters as a simulation example.

Analysis and Compensation Strategy of Non-Linear Error in Five-Axis CNC Machining

This paper presents a new strategy of analysis and compensation of non-linear error. Non-linear error is an important source of machining error in multi-axis numerical controlled machining and it is unavoidable. In view of tool positions optimization in five-axis CNC machining of complex surface, this paper presents a strategy for non-linear error compensation in five-axis machining: Firstly, non-linear error caused by the change of tool axis vector is analyzed and the non-linear error model is established, in order to get the maximum non-linear error of interpolation segment; Then, the tool position that meets the machining accuracy is obtained; Finally, Simulation and analysis of the model show that the proposed method is effective and greatly improves the geometric accuracy.

Modeling and Optimizing of Random Gyro Drift Based on AR and GP

Gyroscope is the key component in an Inertial Navigation System (INS). It depends on the precision of the INS. The nonlinear random drift error model based on autoregressive (AR) and genetic programming (GP) was established. The linear model is established based on AR technique. After that, the nonlinear model is built based on GP technique. The result indicates that the square error of the random gyro drift is reduced by 74.5%. The hybrid modeling method can effectively compensate the random gyro drift and improve the stability of the system.

Carrier Aircraft Urgent Takeoff In-Flight Alignment Extended Set-Membership Estimation

This paper considers the nolinear system robust estimation problem with measurement time delay. The purpose is to provide algorithm for inertial navigation system nonlinear error model in transmittion delay case. Considering that innovation regroup method can treat the measurement delay problem better with no addition of system state dimension, and decrease the system computation, therefore, that algorithm is combined with extended set-membership estimation and deduce the distrete nonlinear system extended set-membership estimation algorithm with measurement delay, realize nonlinear system varying state estimation and the treatment of measurement delay. At last, apply the algorithm to carrier aircraft in-flight alignment and validate the effecitiveness.

Fault detection in multi-sensor networks based on multivariate time-series models and orthogonal transformations

We introduce the usage of multivariate orthogonal space transformations and vectorized time-series models in combination with data-driven system identification models to achieve an enhanced performance of residual-based fault detection in condition monitoring systems equipped with multi-sensor networks. Neither time-consuming annotated samples nor fault patterns/models need to be available, as our approach is solely based on on-line recorded data streams. The system identification step acts as a fusion operation by searching for relations and dependencies between sensor channels measuring the state of system variables. We therefore apply three different vectorized time-series variants: (i) non-linear finite impulse response models (NFIR) relying only on the lagged input variables, (ii) non-linear output error models (NOE), also including the lags of the own predictions and (iii) non-linear Box–Jenkins models (NBJ) which include the lags of the predictions errors as well. The use of multivariate orthogonal space transformations allows to produce more compact and accurate models due to an integrated dimensionality (noise) reduction step. Fault detection is conducted based on finding anomalies (untypical occurrences) in the temporal residual signal in incremental manner. Our experimental results achieved on four real-world condition monitoring scenarios employing multi-sensor network systems demonstrate that the Receiver Operating Characteristic (ROC) curves are improved over those ones achieved with native static models (w/o lags, w/o transformations) by about 20–30%.

Nonlinear measurement error models subject to additive distortion

We study nonlinear regression models when the response and predictors are unobservable and distorted in a multiplicative fashion by additive models of some observed confounding variables. After approximating the additive nonparametric components via polynomial splines and calibrating the error-prone response and predictors, we develop a semi-parametric profile nonlinear least squares procedure to estimate the parameters of interest. We show that the resulting estimators are asymptotically normal. We further suggest an empirical likelihood-based statistic for statistical inference to improve the accuracy of the associated normal approximation with the aim to avoid estimating the asymptotic covariance matrix that involves infinite-dimensional nuisance of additive distorting functions. We also show that the empirical likelihood statistic is asymptotically chi-squared. Moreover, a test procedure is proposed to check whether the parametric model is adequate or not under this distorted measurement error setting. A wild bootstrap procedure is suggested to compute p-values. Simulation studies are conducted to examine the performance of the proposed procedures. The methods are applied to analyze real data from a low birth infants weight for an illustration.

Application of Nonlinear H∞ Filtering Algorithm for Initial Alignment of the Missile-borne SINS

The H∞ filtering and Unscented Transformation(UT) algorithm are introduced to deal with the initial alignment error of missile-borne Strapdown Inertial Navigation System(SINS), which is caused by the nonlinear error model and the uncertainty of the disturbance noise. Firstly, on the basis of additional quaternion error, the error model of SINS is built up. Secondly, the nonlinear H∞ filter based on UT and H∞ filtering is constructed, which is with nonlinear approximation ability and strong robustness. Finally, simulations are made compared with UKF and the nonlinear H∞ filter under the conditions of disturbance model of strong wind. The result shows that nonlinear H∞ filter is more stable and faster than UKF under the disturbance conditions of strong wind and can effectively improve the accuracy of initial alignment and robustness of the algorithm.

A Nonlinear Multiparameters Temperature Error Modeling and Compensation of POS Applied in Airborne Remote Sensing System

The position and orientation system (POS) is a key equipment for airborne remote sensing systems, which provides high-precision position, velocity, and attitude information for various imaging payloads. Temperature error is the main source that affects the precision of POS. Traditional temperature error model is single temperature parameter linear function, which is not sufficient for the higher accuracy requirement of POS. The traditional compensation method based on neural network faces great problem in the repeatability error under different temperature conditions. In order to improve the precision and generalization ability of the temperature error compensation for POS, a nonlinear multiparameters temperature error modeling and compensation method based on Bayesian regularization neural network was proposed. The temperature error of POS was analyzed and a nonlinear multiparameters model was established. Bayesian regularization method was used as the evaluation criterion, which further optimized the coefficients of the temperature error. The experimental results show that the proposed method can improve temperature environmental adaptability and precision. The developed POS had been successfully applied in airborne TSMFTIS remote sensing system for the first time, which improved the accuracy of the reconstructed spectrum by 47.99%.

PMI based nonlinear H∞ estimation of unknown sensor error for INS/GPS integrated system

This paper deals with the problem of robust estimation for time-varying sensor errors of inertial navigation system (INS) and global positioning system integration. A nonlinear strapdown INS error model is established to describe the behavior of the the integrated system. Under assumptions of time-varying bias and noise being L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm bounded, a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> nonlinear estimator by Krein space theory is proposed and, based on this, a proportional and multi-integral H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> estimator is developed for simultaneous estimation of the navigation states and sensor errors. Finally, a flight experiment is implemented to show the effectiveness of the proposed method.

Model Reference Switching Quasi-LPV Control of a Four Wheeled Omnidirectional Robot

In this paper, the problem of trajectory tracking for a four wheeled omnidirectional robot is solved in the inertial fixed coordinate system. The solution relies on a reference model approach, where the resulting nonlinear error model is brought to a quasi-Linear Parameter Varying (LPV) form suitable for designing an LPV controller using Linear Matrix Inequalities (LMI)-based techniques. In particular, the controller is obtained within the switching LPV framework. The effectiveness of the proposed approach is shown through simulation results.

차량 전복 방지를 위한 정적 출력 피드백 제어기 설계

This paper presents static output feedback LQ and <TEX>$H_{\infty}$</TEX> controllers for rollover prevention. Linear quadratic static output feedback controllers have been proposed for rollover prevention in such a way to minimize the lateral acceleration and the roll angle. Rollover prevention capability can be enhanced if <TEX>$H_{\infty}$</TEX> controller is designed. To avoid full-state measurement for feedback requirement or sensitiveness of an observer to nonlinear model error, static output feedback is adopted. To design static output feedback controllers, Kosut's method is adopted because it is simple to calculate. Differential braking and active anti-roll bar are adopted as actuators that generate yaw and roll moments, respectively. The proposed method is shown to be effective in preventing rollover through the simulations on nonlinear multi-body dynamic simulation software, CarSim.

Fault Prediction for Nonlinear System Using Sliding ARMA Combined with Online LS-SVR

A robust online fault prediction method which combines sliding autoregressive moving average (ARMA) modeling with online least squares support vector regression (LS-SVR) compensation is presented for unknown nonlinear system. At first, we design an online LS-SVR algorithm for nonlinear time series prediction. Based on this, a combined time series prediction method is developed for nonlinear system prediction. The sliding ARMA model is used to approximate the nonlinear time series; meanwhile, the online LS-SVR is added to compensate for the nonlinear modeling error with external disturbance. As a result, the one-step-ahead prediction of the nonlinear time series is achieved and it can be extended ton-step-ahead prediction. The result of then-step-ahead prediction is then used to judge the fault based on an abnormity estimation algorithm only using normal data of system. Accordingly, the online fault prediction is implemented with less amount of calculation. Finally, the proposed method is applied to fault prediction of model-unknown fighter F-16. The experimental results show that the method can predict the fault of nonlinear system not only accurately but also quickly.

Iterative algorithm for weighted total least squares adjustment

In this contribution, an iterative algorithm is developed for parameter estimation in a nonlinear measurement error model y−e = (A−EA)x, which is based on the complete description of the variance–covariance matrices of the observation errors e and of the coefficient matrix errors EA without any restriction, e.g. in the case that there are correlations among observations. This paper derives the weighted total least squares solution without applying Lagrange multipliers in a straightforward manner. The algorithm is simple in the concept, easy in the implementation, and fast in the convergence. The final exact solution can be achieved through iteration. Based on the similarity between the proposed algorithm and the ordinary least squares method, the estimate for the covariance matrix of the unknown parameters can be analogously computed by using the error propagation law. The efficacy of the proposed WTLS algorithm is demonstrated by solving three WTLS problems, i.e. a linear regression model, a planar similarity transformation and two-dimensional affine transformation in the case of diagonal and fully populated covariance matrices in both start and transformed coordinate systems.

Airborne Earth Observation Positioning and Orientation by SINS/GPS Integration Using CD R-T-S Smoothing

This paper addresses the issue of state estimation in the integration of a Strapdown Inertial Navigation System (SINS) and Global Positioning System (GPS), which is used for airborne earth observation positioning and orientation. For a nonlinear system, especially with large initial attitude errors, the performance of linear estimation approaches will degrade. In this paper a nonlinear error model based on angle errors is built, and a nonlinear estimation algorithm called the Central Difference Rauch-Tung-Striebel (R-T-S) Smoother (CDRTSS) is utilized in SINS/GPS integration post-processing. In this algorithm, the measurements are first processed by the forward Central Difference Kalman filter (CDKF) and then a separate backward smoothing pass is used to obtain the improved solution. The performance of this algorithm is compared with a similar smoother based on an extended Kalman filter known as ERTSS through Monte Carlo simulations and flight tests with a loaded SINS/GPS integrated system. Furthermore, a digital camera was used to verify the precision of practical applications in a check field with numerous reference points. All these validity checks demonstrate that CDRTSS is a better method and the work of this paper will offer a new approach for SINS/GPS integration for Synthetic Aperture Radar (SAR) and other airborne earth observation tasks.

The Trajectory Tracking Problem of Quadrotor UAV: Global Stability Analysis and Control Design Based on the Cascade Theory

AbstractThis paper deals with the trajectory tracking problem of a six‐degree of freedom (6‐DOF) quadrotor unmanned aerial vehicle (UAV). The problem of simplified kinematics based on Euler angles is analyzed and the modified Rodrigues parameters (MRPs) technique is introduced to model the rotational dynamics of the rigid body. A nonlinear system error model is established based on the trajectory tracking problem, and, due to the coupling property between the translational and rotational dynamics, we divide the complete closed‐loop system into two reduced‐order subsystems and a coupling term. The Rodrigues theorem is applied to analyze the internal connections between the coupling term and MRPs. Therefore, the global stability conclusions, by which the trajectory tracking controller of the quadrotor UAV could be designed based on the subsystem directly in future works, are proved based on several assumptions of the subsystems. Thereafter, the controllers, using the backstepping approach and nonlinear disturbance observer/sliding mode control approach, which stabilize the quadrotor UAV globally ‐exponentially and globally uniformly bounded, are proposed based on the stability theorem proofs mentioned above. Numerical simulations are provided to show that the theoretical conclusions and the controller proposed are effective.

A Novel Scheme for DVL-Aided SINS In-Motion Alignment Using UKF Techniques

In-motion alignment of Strapdown Inertial Navigation Systems (SINS) without any geodetic-frame observations is one of the toughest challenges for Autonomous Underwater Vehicles (AUV). This paper presents a novel scheme for Doppler Velocity Log (DVL) aided SINS alignment using Unscented Kalman Filter (UKF) which allows large initial misalignments. With the proposed mechanism, a nonlinear SINS error model is presented and the measurement model is derived under the assumption that large misalignments may exist. Since a priori knowledge of the measurement noise covariance is of great importance to robustness of the UKF, the covariance-matching methods widely used in the Adaptive KF (AKF) are extended for use in Adaptive UKF (AUKF). Experimental results show that the proposed DVL-aided alignment model is effective with any initial heading errors. The performances of the adaptive filtering methods are evaluated with regards to their parameter estimation stability. Furthermore, it is clearly shown that the measurement noise covariance can be estimated reliably by the adaptive UKF methods and hence improve the performance of the alignment.

Application of Neural Network for Nonlinear Predictive Control

A novel model predictive control method was proposed for a class of dynamic processes with modest nonlinearities in this paper. In this method, a diagonal recurrent neural network (DRNN) is used to compensate nonlinear modeling error that is caused because linear model is regarded as prediction model of nonlinear process. It is aimed at offsetting the effect of model mismatch on the control performance, strengthening the robustness of predictive control and the stability of control system. Under a certain assumption condition, linear model predictive control method is extended to nonlinear process, which doesn’t need solve nonlinear optimization problem. Consequently, the computational efforts are reduced drastically. The simulation example shows that the proposed method is an effective control strategy with excellent tracing characteristics and strong robustness.

A stabilized optimal nonlinear feedback control for satellite attitude tracking

An optimal nonlinear feedback control law with asymptotic stabilization is proposed for the satellite attitude tracking problem. With regard to the large angle or high angular rate task, the full nonlinear tracking error model is built in the form of modified Rodrigues parameters. Based on the optimality of the kinematics, the tracking error model is treated as a high-gain system and analyzed with the perturbation method, and eventually the tracking system is proved to be feedback equivalent to the Jurdjevic–Quinn type system. Then, a Lyapunov function satisfying the asymptotic stability and the Hamilton–Jacobi–Bellman equation simultaneously is used to design the feedback control profile which minimizes a performance index containing penalties on both the state and the control effort. The numerical results show the asymptotic stability and torque penalty features of the control law with the parameters of the control regulation carefully selected.