NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP

In order to achieve precise,robust autonomous guidance and control of a tracked vehicle,a kinematic model with longitudinal and lateral slip is established,Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly.The first filter is the well-known extended Kalman filter.The second filter is an unscented version of the Kalman filter.The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution.The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies.The four different approaches have different complexities,behavior and advantages that are surveyed and compared.

Estimation Performance for the Cubature Particle Filter under Nonlinear/Non-Gaussian Environments

This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle lter(CPF),which is an estimation algorithm that combines the cubature Kalman lter(CKF)and the particle lter(PF).The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution.It is benecial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems.Based on the spherical-radial transformation to generate an even number of equally weighted cubature points,the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function(pdf)to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’rule.It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system,and thus the importance density function can be used to approximate the true posterior density distribution.In Bayesian ltering,the nonlinear lter performs well when all conditional densities are assumed Gaussian.When applied to the nonlinear/non-Gaussian distribution systems,the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle lterbased approaches,such as the extended particle lter(EPF),and unscented particle lter(UPF),and also the Kalman lter(KF)-type approaches,such as the extended Kalman lter(EKF),unscented Kalman lter(UKF)and CKF.Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

A gain-varying UIO approach with adaptive threshold for FDI of nonlinear F16 systems

A discrete gain-varying unknown input observer （UIO） method is presented for actuator fault detection and isolation （FDI） problems in this paper. A novel residual scheme together with a moving horizon threshold is proposed. This design methodology is applied to a nonlinear F16 system with polynomial aerodynamics coefficient expressions, where the coefficient expressions for the F16 system and UIOs may be slightly different. The simulation results illustrate that a satisfactory FDI performance can be achieved even when the F16 system is under the environment of model uncertainties, exogenous noise and measurement errors.

A new extended H_∞ filter for discrete nonlinear systems

Nonlinear estimation problem is investigated in this paper. By extension of a linear H_∞estimation with corrector-predictor form to nonlinear cases, a new extended H_∞filter is proposed for time-varying discrete-time nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H_∞bound performs better than the EKF.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

Real time remaining useful life prediction based on nonlinear Wiener based degradation processes with measurement errors

Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item's individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.

Hellinger distance based probability distribution approach to performance monitoring of nonlinear control systems

Control performance monitoring has attracted great attention in both academia and industry over the past two decades. However, most research efforts have been devoted to the performance monitoring of linear control systems, without considering the pervasive nonlinearities(e.g. valve stiction) present in most industrial control systems. In this work, a novel probability distribution distance based index is proposed to monitor the performance of non-linear control systems. The proposed method uses Hellinger distance to evaluate change of control system performance. Several simulation examples are given to illustrate the effectiveness of the proposed method.

An Approximate High Gain Observer for Speed-sensorless Estimation of Induction Motors

Rotor speed estimation for induction motors is a key problem in speed-sensorless motor drives. This paper performs nonlinear high gain observer design based on the full-order model of the induction motor. Such an effort appears nontrivial due to the fact that the full-model at best admits locally a non-triangular observable form(NTOF), and its analytical representation in the NTOF can not be obtained. This paper proposes an approximate high gain estimation algorithm, which enjoys a constructive design, ease of tuning, and improved speed estimation and tracking performance. Experiments demonstrate the effectiveness of the proposed algorithm.

Fitting V F Converter*ss Output Using High Order Neural Networks

A new method is presented in this paper for fitting VFC*ss (voltage to frequency converter) output functions by using high order neural networks. The nonlinear estimation is implemented when the VFC110 is used at a full scale output frequency of 4 MHz. Two kinds of on line dynamic calibrating circuits are designed to improve the sampling precision. This method can also be applied to different industrial applications.

Generalized cubature quadrature Kalman filters:derivations and extensions

A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the QR decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.

Multi-sensor federated unscented Kalman filtering algorithm in intermittent observations

Aiming at the adverse effect caused by limited detecting probability of sensors on filtering preci- sion of a nonlinear system state, a novel muhi-sensor federated unscented Kalman filtering algorithm is proposed. Firstly, combined with the residual detection strategy, effective observations are cor- rectly identified. Secondly, according to the missing characteristic of observations and the structural feature of unscented Kalman filter, the iterative process of the single-sensor unscented Kalman filter in intermittent observations is given. The key idea is that the state estimation and its error covariance matrix are replaced by the state one-step prediction and its error covariance matrix, when the phe- nomenon of observations missing occurs. Finally, based on the realization mechanism of federated filter, a new fusion framework of state estimation from each local node is designed. And the filtering precision of system state is improved further by the effective management of observations missing and the rational utilization of redundancy and complementary information among multi-sensor observa- tions. The theory analysis and simulation results show the feasibility and effectiveness of the pro- posed algorithm.

Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB 3 p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.

A new model for predicting the total tree height for stems cut-to-length by harvesters in Pinus radiata plantations

A new model for predicting the total tree height for harvested stems from cut-to-length(CTL)harvester data was constructed for Pinus radiata(D.Don)following a conceptual analysis of relative stem profi les,comparisons of candidate models forms and extensive selections of predictor variables.Stem profi les of more than 3000 trees in a taper data set were each processed 6 times through simulated log cutting to generate the data required for this purpose.The CTL simulations not only mimicked but also covered the full range of cutting patterns of nearly 0.45×106 stems harvested during both thinning and harvesting operations.The single-equation model was estimated through the multipleequation generalized method of moments estimator to obtain effi cient and consistent parameter estimates in the presence of error correlation and heteroscedasticity that were inherent to the systematic structure of the data.The predictive performances of our new model in its linear and nonlinear form were evaluated through a leave-one-tree-out cross validation process and compared against that of the only such existing model.The evaluations and comparisons were made through benchmarking statistics both globally over the entire data space and locally within specifi c subdivisions of the data space.These statistics indicated that the nonlinear form of our model was the best and its linear form ranked second.The prediction accuracy of our nonlinear model improved when the total log length represented more than 20%of the total tree height.The poorer performance of the existing model was partly attributed to the high degree of multicollinearity among its predictor variables,which led to highly variable and unstable parameter estimates.Our new model will facilitate and widen the utilization of harvester data far beyond the current limited use for monitoring and reporting log productions in P.radiata plantations.It will also facilitate the estimation of bark thickness and help make harvester data a potential source of taper data to reduce the intensity and cost of the conventional destructive taper sampling in the fi eld.Although developed for P.radiata,the mathematical form of our new model will be applicable to other tree species for which CTL harvester data are routinely captured during thinning and harvesting operations.

Genetic programming-based chaotic time series modeling

This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values, To provide highly precise data for estimating nonlinear param- eters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine （WCFM_SVM）. Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young＇s modulus and Poisson＇s ratio to avoid solving compli- cated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg-Marquardt （LM） algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH LONG MEMORY DATA

This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.

Modified Levenberg-Marquardt algorithm for source localization using AOAs in the presence of sensor location errors

In this paper,by utilizing the angle of arrivals(AOAs) and imprecise positions of the sensors,a novel modified Levenberg-Marquardt algorithm to solve the source localization problem is proposed.Conventional source localization algorithms,like Gauss-Newton algorithm and Conjugate gradient algorithm are subjected to the problems of local minima and good initial guess.This paper presents a new optimization technique to find the descent directions to avoid divergence,and a trust region method is introduced to accelerate the convergence rate.Compared with conventional methods,the new algorithm offers increased stability and is more robust,allowing for stronger non-linearity and wider convergence field to be identified.Simulation results demonstrate that the proposed algorithm improves the typical methods in both speed and robustness,and is able to avoid local minima.

Existence of Multiple Equilibrium Points in Global Attractor for the Strongly Damped Wave Equations

The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.