Measurement Noise Uncertainty Research Articles

GNSS-assisted optimal alignment method for low-cost SINS motion of vehicle

Abstract To improve the alignment accuracy and environmental applicability of the micro-electromechanical system (MEMS)-based strapdown inertial navigation system (SINS), this study proposes a global navigation satellite system (GNSS)-assisted multi-vector determination of the attitude optimal indirect coarse alignment. Using the inertial information output from the inertial measurement unit and the velocity information from the GNSS, a simplified velocity observation vector is constructed and the velocity lever arm stemming from the mounting position inconsistencies of the GNSS and SINS is fed back into the velocity of the carrier system. When constructing the observation vectors, the integration interval is shortened by reconstructing the two-vector integration formula for reducing the cumulative error of the inertial device. The attitude matrix problem is defined as the Wahba problem, which is solved using the singular value decomposition method. Based on the relationship between gyro zero bias and misalignment angle, the corresponding state and measurement equations are designed. Furthermore, owing to the measurement noise uncertainty, the adaptive traceless Kalman filtering algorithm is introduced to realize the effective adaptation processing of the measurement noise. More accurate attitude matrix estimates are obtained by continuously correcting the carrier system transformation matrix. The running car experiment results show that the proposed method exhibits higher alignment accuracy and environmental applicability than the current MEMS strapdown inertial navigation coarse alignment method and the traditional optimization-based alignment method.

Performance enhancement of PPP/SINS tightly coupled navigation based on improved robust maximum correntropy kalman filtering

Extended kalman filter (EKF) is widely used to integrated navigation system of global navigation satellite system (GNSS) and strapdown inertial navigation system (SINS). However, non-Gaussian noise and the uncertainty of measurement noise can seriously reduce the performance of EKF, so it is difficult to obtain an optimal GNSS/INS integration solution. At present, non-Gaussian noise processing is still a difficult issue in filter research. In this paper, an adaptive and robust maximum correntropy extended kalman filter (MCEKF) method based on Cauchy kernel function is proposed to solve the above problem. Thanks to the excellent properties of Cauchy kernel function, the proposed method can effectively avoid filter faults and has better stability. However, the performance of MCEKF depends on the select of kernel bandwidth parameter, which is a difficult problem in the engineering application of MCEKF. In this paper, the switching kernel bandwidth algorithm is employed to adaptively estimate the kernel bandwidth parameter to solve the tradeoff between convergence rate and steady-state misalignment in the MCEKF algorithm under constant kernel bandwidth. Finally, the performance of the proposed algorithm is verified by two sets of vehicle-mounted precise point positioning (PPP) and SINS tightly coupled integration experiments in urban environment. The results show that compared with EKF, the proposed method can significantly improve the positioning accuracy, that is, the PPP/SINS positioning accuracy based on GE, GR and GRE system is improved by 25.1 %, 2.5 % and 17.0 % in D196 experiment, and 23.5 %, 16.5 % and 31.8 % in D107 experiment, respectively. The velocity and attitude accuracy of the two methods are similar. The velocity errors of all schemes can reach cm/s level. The roll, pitch and heading errors of navigation-grade inertial sensor are all less than 0.12 degree. The roll and pitch errors of MEMS are less than 1.0 degree, the heading error of the G, GE, GR, and GRE systems are 1.719, 1.464, 1.676, and 1.475 degree, respectively.

An Adaptive Cubature Kalman Filter Based on Resampling-Free Sigma-Point Update Framework and Improved Empirical Mode Decomposition for INS/CNS Navigation

For the degradation of the filtering performance of the INS/CNS navigation system under measurement noise uncertainty, an adaptive cubature Kalman filter (CKF) is proposed based on improved empirical mode decomposition (EMD) and a resampling-free sigma-point update framework (RSUF). The proposed algorithm innovatively integrates improved EMD and RSUF into CKF to estimate measurement noise covariance in real-time. Specifically, the improved EMD is used to reconstruct measurement noise, and the exponential decay weighting method is introduced to emphasize the use of new measurement noise while gradually discarding older data to estimate the measurement noise covariance. The estimated measurement noise covariance is then imported into RSUF to directly construct the posterior cubature points without a resampling step. Since the measurement noise covariance is updated in real-time and the prediction cubature points error is directly transformed to the posterior cubature points error, the proposed algorithm is less sensitive to the measurement noise uncertainty. The proposed algorithm is verified by simulations conducted on the INS/CNS-integrated navigation system. The experimental results indicate that the proposed algorithm achieves better performance for attitude angle.

Standardized hierarchical adaptive Lp regression for noise robust focal epilepsy source reconstructions

ObjectiveTo investigate the ability of standardization to reduce source localization errors and measurement noise uncertainties for hierarchical Bayesian algorithms with L1- and L2-norms as priors in electroencephalography and magnetoencephalography of focal epilepsy. MethodsDescription of the standardization methodology relying on the Hierarchical Bayesian framework, referred to as the Standardized Hierarchical Adaptive Lp-norm Regularization (SHALpR).The performance was tested using real data from two focal epilepsy patients. Simulated data that resembled the available real data was constructed for further localization and noise robustness investigation. ResultsThe proposed algorithms were compared to their non-standardized counterparts, Standardized low-resolution brain electromagnetic tomography, Standardized Shrinking LORETA-FOCUSS, and Dynamic statistical parametric maps. Based on the simulations, the standardized Hierarchical adaptive algorithm using L2-norm was noise robust for 10 dB signal-to-noise ratio (SNR), whereas the L1-norm prior worked robustly also with 5 dB SNR. The accuracy of the standardized L1-normed methodology to localize focal activity was under 1 cm for both patients. ConclusionsNumerical results of the proposed methodology display improved localization and noise robustness. The proposed methodology also outperformed the compared methods when dealing with real data. SignificanceThe proposed standardized methodology, especially when employing the L1-norm, could serve as a valuable assessment tool in surgical decision-making.

A novel Bayesian-based INS/GNSS integrated positioning method with both adaptability and robustness in urban environments

Achieving higher accuracy positioning results in urban environments at a lower cost has been an important pursuit in areas such as autonomous driving and intelligent transportation. Low-cost Inertial Navigation System and Global Navigation Satellite System (INS/GNSS) integrated navigation systems have been an important means of fulfilling the above quest due to the complementary error characteristics between INS and GNSS. The complex urban driving environment requires the system sufficiently adaptive to keep up with the time-varying measurement noise and sufficiently robust to cope with measurement outliers and prior uncertainties. However, many efforts lack a balance between adaptability and robustness. In this paper, a novel positioning method with both adaptability and robustness is proposed by coupling the Mahalanobis distance method, the Variational Bayesian method and the student’s t-distribution in one process (M-VBt method). This method is robust against non-Gaussian noise and priori uncertainties, plus adaptive against measurement noise uncertainty and time-varying noise. The field test results show that the M-VBt method (especially the Mahalanobis distance part) has significantly improved the system performance in the complex urban driving environment.

Bayesian uncertainty quantification of tristructural isotropic particle fuel silver release: Decomposing model inadequacy plus experimental noise and parametric uncertainties

Tristructural isotropic (TRISO) particle fuel is one of the most promising fuel concepts enabling high temperature and high burnup reactor operation. One dominant source of radioactivity released from the TRISO particles is silver (Ag), which is subject to a high release fraction and long decay life compared to other fission products. Previous modeling efforts using the fuel performance code BISON indicated nonnegligible uncertainties in modeling the diffusion process of fission products in TRISO compared to the Advanced Gas Reactor experiments. The overall uncertainties observed when modeling the fission product diffusion can result from uncertainties in model parameters, noisy experimental measurements, and deficiencies in the developed models. The three types of underlying uncertainties have not yet been properly quantified in open literature. This paper presents the Bayesian uncertainty quantification (UQ) using massively parallelizable Markov chain Monte Carlo samplers. The uncertainties due to model parameters, model inadequacy, and experimental measurement noise are quantified, with the σ term used to represent the sum of the model inadequacy and measurement noise uncertainties. It is worth noting that this is the first time the σ term is inferred for nuclear fuel experiments, as compared to using prescribed values for uncertainty quantification in previous work. The parallelizable Markov chain Monte Carlo samplers efficiently infer the model parameters and the σ term, giving insight into physical parameters like diffusion coefficients and the combined model discrepancy and measurement noise. A subsequent forward uncertainty quantification (UQ) is also performed based on the calibration results to generate more accurate predictions of the Ag release. The model inadequacy plus experimental noise is the most dominant source of uncertainty compared to the parametric uncertainty. All the UQ analyses presented in this work are based on the second series of the irradiation experiments in the Advanced Gas Reactor program.

Interacting Multiple Model Filter with a Maximum Correntropy Criterion for GPS Navigation Processing

In order to deal with the uncertainty of measurement noise, particularly for outlier types of multipath interference and non-line of sight (NLOS) reception, this paper proposes a novel method for processing the navigation states of the Global Positioning System (GPS) that combines the maximum correntropy criterion (MCC) and the interacting multiple model (IMM), with an extended Kalman Filter (EKF). Multipath mitigation is essential for increased positioning accuracy since multipath interference is one of the primary sources of errors. Nonlinear filtering with IMM configuration uses filter structural adaptation. In processing time-varying satellite signal standards for GPS navigation, it offers an alternative for creating the adaptive filter. A collection of switching models built on a method of multiple model estimation can be used to characterize the uncertainty of the noise. Even though most noise in real life is non-Gaussian, time-varying, and of fluctuating strength, the standard EKF operates effectively when the noise is Gaussian. The performance of EKF will drastically decline if the signals appear non-Gaussian. The underlying system disrupted by heavy-tailed, non-Gaussian impulsive sounds could be better since the EKF employs second-order statistical information. The MCC is a method for comparing two random variables based on higher-order signal statistics. The maximum correntropy-extended Kalman filter (MCEKF), which uses the MCC rather than the minimal mean square error (MMSE) as the optimization criterion, is used to enhance performance in non-Gaussian situations. Finally, a performance evaluation will be conducted to compare the effectiveness of the suggested strategy in improving positioning to alternative system designs.

Characterization of rotational symmetry and noise in multifocal contact lens power maps

AbstractPurpose: Spherical multifocal contact lenses are typically designed with a rotationally symmetrical power profile. Imperfections in the raw material, manufacturing and measurement process can break this symmetry, altering the intended lens design. The purpose of this work is to develop a method to separate the intended symmetric design profile from the asymmetries and to give the spatial distribution of the measurement noise uncertainty in diopters.Methods: NIMO TR1504 (Lambda‐X) version V.2.13.2 has been used to measure the local power map of various multifocal contact lenses. From the map, a set of radial power profiles is obtained for different angles (0°, 180°), (0°, 360°). A symmetrical lens should show a constant radial profile for different angles, while asymmetries manifest as differences in the set of radial power profiles. They are analysed using a Principal Components Method (PCA) implemented in MATLAB.Results: The method displays a map of the symmetric radial profile of the lens, another map of the deviations with spatial structure indicating the angles where the deviations are stronger (rotational asymmetries), and noise with three separated components (spatially random variations). Asymmetries of the order of 0.17D (with maximums of 0.4D), and random noise values of 0.12D were found in some lenses.Conclusions: The characterization of multifocal contact lens prescription is important in visual optics. The prescription perceived by the patient depends on the distribution of the radial power profile on the pupil. That is the reason why asymmetries and imperfections estimation is important. The method developed in this work allows to calculate a diopter equivalent number for them.

3D Lightning Location Method Based on Range Difference Space Projection

Most lightning location networks obtain the position results by optimizing the goodness of fit to determine that all combinatorial time differences of arrivals (TDOAs) are due to a common discharge. This paper proposes a three-dimensional (3D) lightning location method based on range difference (RD) space projection. The proposed method projects all the measurements into the RD space, which has the space-invariant feature of the equivalence cell and can be partitioned soundly. Aiming at the problem of computational cost of the procedure of the projection, the hierarchical strategy is proposed to improve computational efficiency. The performance of the RD space projection based on the hierarchical strategy is analyzed via Monte-Carlo simulations. The results show that the proposed method can locate lightning sources in real time with high accuracy. The results also show that the location accuracy is limited by the level of the inherent time uncertainty, the layout, and the size of the receiver network. Under the fixed layout and size of the receiver network, and the fixed measurement noise uncertainty, the positioning precision cannot be improved more even if the grid step is small enough or the number of receivers is large enough.

GNSS-5G Hybrid Positioning Based on Multi-Rate Measurements Fusion and Proactive Measurement Uncertainty Prediction

The fifth-generation (5G) network can be used jointly with a global navigation satellite system (GNSS) to help relieve the problem of having few visible satellites in urban environments and achieve highly accurate localization. The 5G base stations (BSs) can provide range and angle measurements at a much higher rate than GNSS. However, this benefit has not been fully employed by existing GNSS-5G hybrid methods. In addition, the near–far effect of 5G BS causes a large dynamic range of the measurement noise uncertainty. This challenge has not been well dealt with by the existing adaptive noise estimation methods, resulting in the decline of positioning accuracy and system convergence. This work proposes a multiple-rate adaptive Kalman filter (MRAKF) for GNSS-5G hybrid positioning with a hybrid sequential fusing scheme. It supports the fusion of GNSS and 5G measurements at different data rates to better employ the high-rate 5G measurements. A distance-dependent model is derived to quantitatively characterize the effect of BS-user equipment (UE) distance over the measurement noise covariance, leading to a proactive measurement uncertainty prediction algorithm to adaptively adjust the observation noise covariance matrix. Furthermore, a switchover strategy is proposed to switch its positioning mode to avoid the impact of variation of available line of sight (LOS) BSs. Both simulations and a real driving test were carried out. Results show that the proposed MRAKF method significantly improves the positioning accuracy compared with the other four adaptive noise estimation methods and the standard EKF. It requires the lowest computation complexity among all adaptive methods in this work.

Square-Root Cubature Kalman Filter Based on H∞ Filter for Attitude Measurement of High-Spinning Aircraft

A novel H∞ filter called square-root cubature H∞ Kalman filter is proposed for attitude measurement of high-spinning aircraft. In this method, a combined measurement model of three-axis geomagnetic sensor and gyroscope is used, and the Euler angle algorithm model is used to reduce the state dimension and linearize the state equation, which can reduce the amount of calculation. Simultaneously, the method can be applied to the case of measurement noise uncertainty. By continuously modifying the error limiting parameters to update the measurement noise estimation, the filtering accuracy and robustness can be improved. The square-root forms enjoy a consistently improved numerical stability because all the resulting covariance matrices by QR decomposition are guaranteed to stay positive semidefinite. The algorithm is applied to the simulation experiment of attitude measurement with the combination of geomagnetic sensor and gyroscope and compared with the results of Unscented Kalman filter, cubature Kalman filter, square root cubature Kalman filter, and singular value decomposition cubature Kalman filter, which proves the effectiveness and superiority of the algorithm.

Reverse harmonic load flow analysis using an evolutionary technique

In the present paper, a new approach to estimate the harmonic distortions is proposed by considering the existence of harmonic sources in the power system. The algorithm employs a differential evolution technique by formulating the reverse harmonic load flow problem for each harmonic order and by considering a limited number of phasor measurement units (PMUs) deployed across the power system. The technique utilizes the measured voltage and current harmonics obtained using synchronized PMUs with known transmission network as input data. The proposed technique estimates the harmonic voltage phasors at the unmonitored buses of the power system with reasonable accuracy. The effectiveness and efficiency of the proposed method is validated by applying it to five bus and IEEE 14-bus test systems by considering uncertainty in measurement noise. It is shown that the proposed approach yields optimum solution and provides reliable and accurate harmonic state estimates.

Fault detection method in subsea power distribution systems using statistical optimisation

Developing automation solutions that enable remote communications, monitoring and control for subsea applications are key steps in designing subsea power distribution systems. These systems require fast local control to protect the multiple electrical loads and the capability of transferring prompt real-time trip signals. This study introduces a data-driven distributed fault detection and identification algorithm to monitor multiple subsea loads. The proposed scheme is divided into three steps. First, a stochastic hidden-Markov model (HMM) is developed to model the dynamic evolution of different potential conditions of multiple subsea loads. Simultaneously, the second step computes a model of the transition probability between the current operating condition and the potential response of an individual load. In the third step, using real-time measurements, the HMM is updated to predict an unobserved degradation of the load's current condition. This is achieved through an integrated perturbation analysis and sequential quadratic programming method. An assessment of case studies on subsea AC power system is presented, which includes different subsea motor loads for compressors and pumps. Results show robustness against uncertainty in measurement noise and changes in equipment mean time between failures, providing enhanced reliability.

Navigation Performance Enhancement Using IMM Filtering for Time Varying Satellite Signal Quality

A novel scheme using fuzzy logic based interacting multiple model (IMM) unscented Kalman filter (UKF) is employed in which the Fuzzy Logic Adaptive System (FLAS) is utilized to address uncertainty of measurement noise, especially for the outlier types of multipath errors for the Global Positioning System (GPS) navigation processing. Multipath is known to be one of the dominant error sources, and multipath mitigation is crucial for improvement of the positioning accuracy. It is not an easy task to establish precise statistical characteristics of measurement noise in practical engineering applications. Based on the filter structural adaptation, the IMM nonlinear filtering provides an alternative for designing the adaptive filter in the GPS navigation processing for time varying satellite signal quality. The uncertainty of the noise can be described by a set of switching models using the multiple model estimation. An UKF employs a set of sigma points by deterministic sampling, which avoids the error caused by linearization as in an extended Kalman filter (EKF). For enhancing further system flexibility, the fuzzy logic system is introduced. The use of IMM with FLAS enables tuning of appropriate values for the measurement noise covariance so as to obtain improved estimation accuracy. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

Adaptive Huber-based Kalman filtering for spacecraft attitude estimation

An adaptive Huber-based Kalman filter (AHF) is presented to deal with model error and unknown measurement noise in this article. The adaptive method for model error is obtained using an upper bound for the predicted state error covariance matrix. The measurement noise uncertainty is tackled at each time step by minimizing a criterion function that is original from the Huber technique. A recursive algorithm is also provided to solve the criterion function. The proposed AHF algorithm has been tested in an attitude estimation problem using a gyroscope and star tracker sensors for a single spacecraft in flight simulations in the presence of both model error and non-Gaussian random measurement errors. Simulation results demonstrate the superior performance of the proposed filter compared with the previous filter algorithms. The main contribution of this work can be considered the new application of an existing method.

In-Flight Alignment UsingH∞Filter for Strapdown INS on Aircraft

In-flight alignment is an effective way to improve the accuracy and speed of initial alignment for strapdown inertial navigation system (INS). During the aircraft flight, strapdown INS alignment was disturbed by lineal and angular movements of the aircraft. To deal with the disturbances in dynamic initial alignment, a novel alignment method for SINS is investigated in this paper. In this method, an initial alignment error model of SINS in the inertial frame is established. The observability of the system is discussed by piece-wise constant system (PWCS) theory and observable degree is computed by the singular value decomposition (SVD) theory. It is demonstrated that the system is completely observable, and all the system state parameters can be estimated by optimal filter. Then a H ∞ filter was designed to resolve the uncertainty of measurement noise. The simulation results demonstrate that the proposed algorithm can reach a better accuracy under the dynamic disturbance condition.

Adaptive robust Kalman filter for relative navigation using global position system

An adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty. The adaptive algorithm estimates process noise covariance based on the recursive minimisation of the difference between residual covariance matrix given by the filter and that calculated from time-averaging of the residual sequence generated by the filter at each time step. A recursive algorithm is proposed based on both Massachusetts Institute of Technology (MIT) rule and typical non-linear extended Kalman filter equations for minimising the difference. The measurement update using a robust technique to minimise a criterion function originated from Huber filter. The proposed adaptive robust Kalman filter has been successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors. The numerical simulation results indicate that the proposed adaptive robust filter can provide better relative navigation performance in terms of accuracy and robustness as compared with previous filter algorithms.

A Probabilistic Damage Identification Approach for Structures under Unknown Excitation and with Measurement Uncertainties

Recently, an innovative algorithm has been proposed by the authors for the identification of structural damage under unknown external excitations. However, identification accuracy of this proposed deterministic algorithm decreases under high level of measurement noise. A probabilistic approach is therefore proposed in this paper for damage identification considering measurement noise uncertainties. Based on the former deterministic algorithm, the statistical values of the identified structural parameters are estimated using the statistical theory and a damage index is defined. The probability of identified structural damage is further derived based on the reliability theory. The unknown external excitations to the structure are also identified by statistical evaluation. A numerical example of the identification of structural damage of a multistory shear-type building and its unknown excitation shows that the proposed probabilistic approach can accurately identify structural damage and the unknown excitations using only partial measurements of structural acceleration responses contaminated by intensive measurement noises.

Optimal Scalar Quantization for Motion Tracking via Boolean Compressive Infrared Sampling

The recently emerged compressive sensing framework aims to acqure signals at reduced sample rates compared to the classical Shannon-Nyquist rate. This paper is concerned with the optimization problem of motion tracking driven by a sort of passive infrared sampling paradigm which springs from compressive sensing framework. In particular, a structured implementation with binary passive infrared sensor node is proposed to acquire the sparse presence state of human motion with resolution of some small cells. To calibrate the cells, a functional scalar quantizer is employed. Its optimization is used to adjust the design of sampling model to reduce the uncertainty of measurement noise. Simulation results show that the proposed optimization method benefits tracking accuracy to a certain degree.

Improved adaptive Huber filter for relative navigation using global position system

An improved adaptive Huber filter algorithm is presented to model error and measurement noise uncertainty. The adaptive algorithm for model error is obtained using an upper bound for the state prediction covariance matrix. The measurement noise is estimated at each filter step by minimizing a criterion function which was original from adaptive Huber filter. A recursive algorithm is provided for solving the criterion function. The proposed adaptive filter algorithm was successfully implemented in relative navigation using global position system for spacecraft formation flying in high earth orbits with real orbit perturbations and non-Gaussian random measurement error. Simulation results indicated that the proposed adaptive filter performed better in robustness and accuracy compared with previous adaptive algorithms.