Robust Remaining Useful Life Estimation Based on an Improved Unscented Kalman Filtering Method

In the Prognostics and Health Management(PHM),remaining useful life(RUL)is very important and utilized to ensure the reliability and safety of the operation of complex mechanical systems.Recently,unscented Kalman filtering(UKF)has been applied widely in the RUL estimation.For a degradation system,the relationship between its monitored measurements and its degradation states is assumed to be nonlinear in the conventional UKF.However,in some special degradation systems,their monitored measurements have a linear relation with their degradation states.For these special problems,it may bring estimation errors to use the UKF method directly.Besides,many uncertain factors can result in the fluctuations of the estimated results,which may have a bad influence on the RUL estimation method.As a result,a robust RUL estimation approach is proposed in this paper to reduce the errors and randomness of estimation results for this kind of degradation problems.Firstly,an improved unscented Kalman filtering is established utilizing the Kalman filtering(KF)method and a linear adaptive strategy.The linear adaptive strategy is used to adjust its noise term adaptively.Then,the robust RUL estimation is realized by the improved UKF.At last,three problems are investigated to demonstrate the effectiveness of the proposed method.

Enhanced multi-baseline unscented Kalman filtering phase unwrapping algorithm

This paper presents an enhanced multi-baseline phase unwrapping algorithm by combining an unscented Kalman filter with an enhanced joint phase gradient estimator based on the amended matrix pencil model, and an optimal path-following strategy based on phase quality estimate function. The enhanced joint phase gradient estimator can accurately and effectively extract the phase gradient information of wrapped pixels from noisy interferograms, which greatly increases the performances of the proposed method. The optimal path-following strategy ensures that the proposed algorithm simultaneously performs noise suppression and phase unwrapping along the pixels with high-reliance to the pixels with low-reliance. Accordingly, the proposed algorithm can be predicted to obtain better results, with respect to some other algorithms, as will be demonstrated by the results obtained from synthetic data.

Unscented Kalman filter for a low-cost GNSS/IMU-based mobile mapping application under demanding conditions

For the last two decades,low-cost Global Navigation Satellite System(GNSS)receivers have been used in various applications.These receivers are mini-size,less expensive than geodetic-grade receivers,and in high demand.Irrespective of these outstanding features,low-cost GNSS receivers are potentially poorer hardwares with internal signal processing,resulting in lower quality.They typically come with low-cost GNSS antenna that has lower performance than their counterparts,particularly for multipath mitigation.Therefore,this research evaluated the low-cost GNSS device performance using a high-rate kinematic survey.For this purpose,these receivers were assembled with an Inertial Measurement Unit(IMU)sensor,which actively transmited data on acceleration and orientation rate during the observation.The position and navigation parameter data were obtained from the IMU readings,even without GNSS signals via the U-blox F9R GNSS/IMU device mounted on a vehicle.This research was conducted in an area with demanding conditions,such as an open sky area,an urban environment,and a shopping mall basement,to examine the device’s performance.The data were processed by two approaches:the Single Point Positioning-IMU(SPP/IMU)and the Differential GNSS-IMU(DGNSS/IMU).The Unscented Kalman Filter(UKF)was selected as a filtering algorithm due to its excellent performance in handling nonlinear system models.The result showed that integrating GNSS/IMU in SPP processing mode could increase the accuracy in eastward and northward components up to 68.28%and 66.64%.Integration of DGNSS/IMU increased the accuracy in eastward and northward components to 93.02%and 93.03%compared to the positioning of standalone GNSS.In addition,the positioning accuracy can be improved by reducing the IMU noise using low-pass and high-pass filters.This application could still not gain the expected position accuracy under signal outage conditions.

Combining unscented Kalman filter and wavelet neural network for anti-slug

The stability of the subsea oil and gas production system is heavily influenced by slug flow. One successful method of managing slug flow is to use top valve control based on subsea pipeline pressure. However, the complexity of production makes it difficult to measure the pressure of subsea pipelines, and measured values are not always accessible in real-time. The research introduces a technique for integrating Unscented Kalman Filter (UKF) and Wavelet Neural Network (WNN) to estimate the state of subsea pipeline pressure using historical data and a state model. The proposed method treats multiphase flow transport as a nonlinear model, with a dynamic WNN serving as the state observer. To achieve real-time state estimation, the WNN is included into the UKF algorithm to create a WNN-based UKF state equation. Integrate WNN and UKF in a novel way to predict system state accurately. The simulated results show that the approach can efficiently predict the inlet pressure and manage the slug flow in real-time using the riser's top pressure, outlet flow and valve opening. This method of estimate can significantly increase the control effect.

Phase noise filtering and phase unwrapping method based on unscented Kalman filter

This paper presents a new phase unwrapping algorithm based on the unscented Kalman filter（UKF） for synthetic aperture radar（SAR） interferometry.This method is the result of combining an UKF with path-following strategy and an omni-directional local phase slope estimator.This technique performs simultaneously noise filtering and phase unwrapping along the high-quality region to the low-quality region,which is also able to avoid going directly through the noisy regions.In addition,phase slope is estimated directly from the sample frequency spectrum of the complex interferogram,by which the underestimation of phase slope is overcome.Simulation and real data processing results validate the effectiveness of the proposed method,and show a significant improvement with respect to the extended Kalman filtering（EKF） algorithm and some conventional phase unwrapping algorithms in some situations.

Interlaced optimal-REQUEST and unscented Kalman filtering for attitude determination

Aimed at low accuracy of attitude determination because of using low-cost components which may result in non-linearity in integrated attitude determination systems, a novel attitude determination algorithm using vector observations and gyro measurements is presented. The various features of the unscented Kalman filter （UKF） and optimal-REQUEST （quaternion estimator） algorithms are introduced for attitude determination. An interlaced filtering method is presented for the attitude determination of nano-spacecraft by setting the quaternion as the attitude representation, using the UKF and optimal-REQUEST to estimate the gyro drifts and the quaternion, respectively. The optimal-REQUEST and UKF are not isolated from each other. When the optimal-REQUEST algorithm estimates the attitude quaternion, the gyro drifts are estimated by the UKF algorithm synchronously by using the estimated attitude quaternion. Furthermore, the speed of attitude determination is improved by setting the state dimension to three. Experimental results show that the presented method has higher performance in attitude determination compared to the UKF algorithm and the traditional interlaced filtering method and can estimate the gyro drifts quickly.

Unscented extended Kalman filter for target tracking

A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of non- lineadty is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter （UKF）, however, the computational time of the UEKF is much less than that of the UKF.

Modified unscented Kalman filter using modified filter gain and variance scale factor for highly maneuvering target tracking

To improve the low tracking precision caused by lagged filter gain or imprecise state noise when the target highly maneuvers, a modified unscented Kalman filter algorithm based on the improved filter gain and adaptive scale factor of state noise is presented. In every filter process, the estimated scale factor is used to update the state noise covariance Qk, and the improved filter gain is obtained in the filter process of unscented Kalman filter （UKF） via predicted variance Pk｜k-1, which is similar to the standard Kalman filter. Simulation results show that the proposed algorithm provides better accuracy and ability to adapt to the highly maneuvering target compared with the standard UKF.

Adaptive unscented Kalman filter for parameter and state estimation of nonlinear high-speed objects

An adaptive unscented Kalman filter （AUKF） and an augmented state method are employed to estimate the timevarying parameters and states of a kind of nonlinear high-speed objects. A strong tracking filter is employed to improve the tracking ability and robustness of unscented Kalman filter （UKF） when the process noise is inaccuracy, and wavelet transform is used to improve the estimate accuracy by the variance of measurement noise. An augmented square-root framework is utilized to improve the numerical stability and accuracy of UKF. Monte Carlo simulations and applications in the rapid trajectory estimation of hypersonic artillery shells confirm the effectiveness of the proposed method.

Airship aerodynamic model estimation using unscented Kalman filter

An airship model is made-up of aerostatic,aerodynamic,dynamic,and propulsive forces and torques.Besides others,the computation of aerodynamic forces and torques is difficult.Usually,wind tunnel experimentation and potential flow theory are used for their calculations.However,the limitations of these methods pose difficulties in their accurate calculation.In this work,an online estimation scheme based on unscented Kalman filter(UKF)is proposed for their calculation.The proposed method introduces six auxiliary states for the complete aerodynamic model.UKF uses an extended model and provides an estimate of a complete state vector along with auxiliary states.The proposed method uses the minimum auxiliary state variables for the approximation of the complete aerodynamic model that makes it computationally less intensive.UKF estimation performance is evaluated by developing a nonlinear simulation environment for University of Engineering and Technology,Taxila(UETT)airship.Estimator performance is validated by performing the error analysis based on estimation error and 2-σ uncertainty bound.For the same problem,the extended Kalman filter(EKF)is also implemented and its results are compared with UKF.The simulation results show that UKF successfully estimates the forces and torques due to the aerodynamic model with small estimation error and the comparative analysis with EKF shows that UKF improves the estimation results and also it is more suitable for the under-consideration problem.

A new real-time eye tracking based on nonlinear unscented Kalman filter for monitoring driver fatigue

A new scheme for driver fatigue detection is presented, which is based on the nonlinear unscented Kalman filter and eye tracking. Assuming a probability distribution than to approximate an arbitrary nonlinear function or transformation, eye nonlinear tracking can be achieved using an unscented transformation (UT), which adopts a set of deterministic sigma points to match the posterior probability density function of the eye movement. Driver fatigue can be detected using the percentage of eye closure (PERCLOS) framework in a realistic driving condition after the eye nonlinear tracking. This system was tested adequately in realistic driving environments with subjects of different genders, with/without glasses, in day/night driving, being commercial/noncommercial drivers, in continuous driving time, and under different road conditions. The last experimental results show that the proposed method not only improves the robustness for nonlinear eye tracking, but also can provide more accurate estimation than the traditional Kalman filter.

MLP training in a self-organizing state space model using unscented Kalman particle filter

Many Bayesian learning approaches to the multi-layer perceptron （MLP） parameter optimization have been proposed such as the extended Kalman filter （EKF）. This paper uses the unscented Kalman particle filter （UPF） to train the MLP in a self- organizing state space （SOSS） model. This involves forming augmented state vectors consisting of all parameters （the weights of the MLP） and outputs. The UPF is used to sequentially update the true system states and high dimensional parameters that are inherent to the SOSS moder for the MLP simultaneously. Simulation results show that the new method performs better than traditional optimization methods.

Sampling strong tracking nonlinear unscented Kalman filter and its application in eye tracking

The unscented Kalman filter is a developed well-known method for nonlinear motion estimation and tracking. However, the standard unscented Kalman filter has the inherent drawbacks, such as numerical instability and much more time spent on calculation in practical applications. In this paper, we present a novel sampling strong tracking nonlinear unscented Kalman filter, aiming to overcome the difficulty in nonlinear eye tracking. In the above proposed filter, the simplified unscented transform sampling strategy with n＋ 2 sigma points leads to the computational efficiency, and suboptimal fading factor of strong tracking filtering is introduced to improve robustness and accuracy of eye tracking. Compared with the related unscented Kalman filter for eye tracking, the proposed filter has potential advantages in robustness, convergence speed, and tracking accuracy. The final experimental results show the validity of our method for eye tracking under realistic conditions.

Stochastic stability of the derivative unscented Kalman filter

This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime system with linear system state equation. The first paper established a derivative unscented Kalman filter（DUKF） to eliminate the redundant computational load of the unscented Kalman filter（UKF） due to the use of unscented transformation（UT） in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique.

Control of epileptiform spikes based on nonlinear unscented Kalman filter

A new control strategy based on nonlinear unscented Kalman filter （UKF） is proposed for a neural mass model that serves as a model for simulating real epileptiform stereo-electroeneephalographic （SEEG） signals. The UKF is used as an observer to estimate the state from the noisy measurement because it has been proved to be effective for state estimation of nonlinear systems. A UKF controller is constructed via the estimated state and is illustrated to be effective for epileptiform spikes suppression of aforementioned model by numerical simulations.

Comparison of linear and nonlinear aerodynamic parameter estimation approaches for an unmanned aerial vehicle using unscented Kalman filter

Aerodynamic parameter estimation provides an effective way for aerospace system modeling using measured data from flight tests, especially for the purpose of developing elaborate simulation environments and designing control systems of unmanned aerial vehicle （UAV） with short design cycles and reduced cost. However, parameter identification of airplane dynamics by nonlinear mod- els is complicated because of the noisy and biased sensor measurements. Using linear models for system identification is an alternative way if the fidelity can be guaranteed, as control design procedures are better established in linear systems. This paper considers the application and comparison of linear as well as nonlinear aerodynamic parameter estimation approaches of an UAV using unscented Kalman filter （UKF）. It also highlights the degree of deterioration of the linear model in the UKF identification process. The results show that both the linear and nonlinear methodologies can accurately estimate the control system design. Furthermore, considering loss of accuracy to be negligible, the linear model can be employed for control design of the UAV as presented here.

Fault tolerant navigation method for satellite based on information fusion and unscented Kalman filter

An effective autonomous navigation system for the integration of star sensor,infrared horizon sensor,magnetometer,radar altimeter and ultraviolet sensor is developed.The requirements of the integrated navigation system manager make optimum use of the various navigation sensors and allow rapid fault detection,isolation and recovery.The normal full fusion feedback method of federated unscented Kalman filter（UKF） cannot meet the needs of it.So a no-reset feedback federated Kalman filter architecture is developed and used in the autonomous navigation system.The minimal skew sigma points are chosen to improve the calculation speed.Simulation results are presented to demonstrate the advantages of the algorithm.These advantages include improved failure detection and correction,improved computational efficiency,and reliability.Additionally,its＇ accuracy is higher than that of the full fusion feedback method.

Scaling parameters selection principle for the scaled unscented Kalman filter

The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

Instantaneous spectrum estimation of earthquake ground motions based on unscented Kalman filter method

Representing earthquake ground： motion as time varying ARMA model, the instantaneous spectrum can only be determined by the time varying coefficients of the corresponding ARMA model. In this paper, unscented Kalman filter is applied to estimate the time varying coefficients. The comparison between the estimation results of unscented Kalman filter and Kalman filter methods shows that unscented Kalman filter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter, and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity or abruptness. Moreover, the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former studies has great effect on the estimation precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.

Maximum Correntropy Criterion-Based UKF for Loosely Coupling INS and UWB in Indoor Localization

Indoor positioning is a key technology in today’s intelligent environments,and it plays a crucial role in many application areas.This paper proposed an unscented Kalman filter(UKF)based on the maximum correntropy criterion(MCC)instead of the minimummean square error criterion(MMSE).This innovative approach is applied to the loose coupling of the Inertial Navigation System(INS)and Ultra-Wideband(UWB).By introducing the maximum correntropy criterion,the MCCUKF algorithm dynamically adjusts the covariance matrices of the system noise and the measurement noise,thus enhancing its adaptability to diverse environmental localization requirements.Particularly in the presence of non-Gaussian noise,especially heavy-tailed noise,the MCCUKF exhibits superior accuracy and robustness compared to the traditional UKF.The method initially generates an estimate of the predicted state and covariance matrix through the unscented transform(UT)and then recharacterizes the measurement information using a nonlinear regression method at the cost of theMCC.Subsequently,the state and covariance matrices of the filter are updated by employing the unscented transformation on the measurement equations.Moreover,to mitigate the influence of non-line-of-sight(NLOS)errors positioning accuracy,this paper proposes a k-medoid clustering algorithm based on bisection k-means(Bikmeans).This algorithm preprocesses the UWB distance measurements to yield a more precise position estimation.Simulation results demonstrate that MCCUKF is robust to the uncertainty of UWB and realizes stable integration of INS and UWB systems.