Innovation Covariance Research Articles

A data-driven hybrid sensor fault detection/diagnosis method with flight test data

Fault diagnosis of multi-source signal systems is critical for the safe and reliable operation of modern industrial systems, and accurate fault diagnosis of systems based on multi-source signals remains challenging. This study proposes a data-driven hybrid fault detection/diagnosis method to identify sensor faults in complex systems through interactions between multiple sensors. Dynamic mode decomposition with control is used to obtain the approximate model of the investigated system from multi-source signals, extract the underlying physical mechanisms, combined with the Kalman filter observer to generate the residual between the observed data and the predicted data. Then the residual (moving innovation covariance matrix V k ) is input into the k-nearest neighbor classification algorithm for fault detection and diagnosis. The effectiveness of the proposed method was evaluated using the flight test braking system dataset. The results showed that the accuracy of the proposed method in fault detection and diagnosis (with accuracies of 100% and 100%, respectively) was significantly improved than that of using raw signal data (76.6% and 6.38%) or raw signal data and Vk (80.85% and 42.55%). The analysis of different parameters including fault severity, algorithm hyperparameter k , and sensor type showed that the proposed method has high robustness, generalization ability, and practicality.

Research on battery state of charge estimation based on variable window adaptive extended Kalman filter

Battery state of charge (SOC) estimation is one of the indispensable functions in the battery management system. Among them, the Kalman filter series of algorithms are widely used in the battery SOC estimation process. The adaptive extended Kalman filter uses the difference between the measured voltage and the estimated voltage (error innovation) as the innovative covariance matrix update noise in battery SOC estimation. However, the general adaptive Kalman filter does not consider the error innovation in the estimation process. The change. This will lead to inaccurate battery SOC estimation. In order to solve this problem, we proposes a variable window Kalman filter algorithm that takes into account the changes in the error innovation sequence. The algorithm updates the innovation covariance matrix according to the change of error innovation to improve the accuracy of SOC estimation. The results show that compared with the extended Kalman filter and the fixed window Kalman filter, its calculation efficiency is also improved while its accuracy is improved. Finally, its accuracy is verified under different initial parameters, and the study shows that the algorithm proposed in this article is robust.

An adaptive Kalman filtering algorithm based on maximum likelihood estimation

Traditional adaptive Kalman filtering algorithms based on innovation are often used to solve the problem of reduced or even divergent filtering estimation accuracy under abnormal measurement noise. However, these algorithms are usually characterized by difficulties in selecting window width and window weight, which cannot simultaneously take into account the filtering tracking sensitivity and filtering accuracy. In this paper, an adaptive Kalman filtering algorithm based on maximum likelihood estimation is proposed, which determines the window size and window weight size under the kth moment by designing a window adaptive selection function and a weight function to change the innovation covariance at the kth moment, which in turn changes the measurement noise covariance at the kth moment, so that the measurement noise covariance is no longer a fixed single value, but can better adapt to the changes in the environment, reflecting good adaptive characteristics. The simulation results based on GPS/SINS integrated navigation system demonstrate that the new filtering algorithm of this paper reflects higher filtering accuracy and stronger robustness under the carrier in multiple motion states and accompanied by time-varying measurement noise interference. Compared with the traditional adaptive Kalman filtering algorithm based on innovation, the accuracy of attitude angle estimation error under this method is improved by 119.97%; the accuracy of velocity estimation error is improved by 264.42%; the accuracy of position estimation error is improved by 156.69%.

Robust UKF Relative Positioning Approach for Tightly Coupled Vehicle Ad Hoc Networks Based on Adaptive M-Estimation

Huber M-estimation, as an estimation method based on mixed norm as cost function, provides an effective method for robust filtering to deal with measurement outliers. Based on statistical linear regression model approximating nonlinear measurement model, M-estimation algorithm is used to realize measurement update of states. However, when the measurement noise pollution rate is high, the filtering performance will be seriously degraded. In order to further improve the actual performance of data fusion under abnormal measurement noise, a vehicle cooperative positioning scheme based on adaptive M-estimation robust unscented Kalman filter (AMRUKF) was proposed. This algorithm combines Huber’s linear regression problem with covariance matching method, and calculates the adaptive matrix through the innovation covariance estimator based on fading memory index weighting to adaptively adjust the measurement noise covariance used in Huber M estimation method. The analytical and experimental results of tightly-coupled vehicle relative positioning show that the proposed AMRUKF method can effectively improve the robustness and accuracy of relative positioning and provide a practical control scheme for vehicle cooperative positioning.

Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. To address this issue, a computationally efficient multivariate Bayesian Circular Lattice Filter is developed, extending the usage of the TV-VAR model to a broader class of high-dimensional problems. The fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. The proposed estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. To illustrate the effectiveness of the proposed approach, a comprehensive comparison with other competing methods is conducted through simulation studies and finds that, in most cases, the proposed approach performs superior in terms of the average squared error between the estimated and true time-varying spectral density. Finally, the methodology is demonstrated through applications to quarterly Gross Domestic Product (GDP) data and Northern California wind data.

Robust Unscented Kalman Filter-Based Decentralized Multisensor Information Fusion for INS/GNSS/CNS Integration in Hypersonic Vehicle Navigation

INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integration is a favourable navigation mode for hypersonic vehicles. However, since the measurements from GNSS and CNS are easily interfered during highly dynamic maneuvers, this integration is very difficult to achieve optimal navigation solution with existing information fusion techniques. This paper proposes a new method of decentralized multi-sensor information fusion based on robust UKF (unscented Kalman filter) for INS/GNSS/CNS integration to solve the above issue. Firstly, a fault detection-based robust UKF is established for local state estimation, in which a hypothesis test is constructed via the Mahalanobis distance of innovation to detect abnormal measurements in GNSS and CNS; and subsequently, a scalar factor is determined and further introduced into the innovation covariance to decrease the Kalman gain to improve the UKF robustness against abnormal measurements. Secondly, the traditional multi-sensor optimal data fusion technique is extended to nonlinear systems by use of unscented transformation in the framework of minimum variance estimation to fuse the local state estimations from INS/GNSS and INS/CNS subsystems. The proposed information fusion method can achieve the globally optimal fusion estimation results against abnormal measurements for hypersonic vehicle navigation with INS/GNSS/CNS integration. Semi-physical simulations and comparison analysis have validated the superior performance of the proposed method.

Sensorless control of marine permanent magnet synchronous propulsion motor based on adaptive extended Kalman filter

Gross error interference or noise statistical deviation is the main factor that leads to the accuracy deterioration of extended Kalman filter (EKF) in estimating the speed and rotor position of ship propulsion permanent magnet synchronous motor (PMSM). In this paper, an adaptive extended Kalman filter (AEKF) algorithm based on innovation sequence is proposed. In the proposed method, gross error interference is first added to EKF to analyze its influence on the observation accuracy. Then, the weighting coefficient is set in the calculation of innovation covariance. By adjusting the weight of the innovation covariance matrix at the adjacent time, the innovation covariance difference is calculated and then used in the calculation of Kalman gain. The observation performance comparison between AEKF and EKF strategies is conducted with subject to gross error interference and noise statistics deviate. Simulation and experimental results demonstrate that the proposed AEKF has stronger robustness and higher prediction accuracy of speed and rotor position.

Achieving Adaptive Visual Multi-Object Tracking with Unscented Kalman Filter

As an essential part of intelligent monitoring, behavior recognition, automatic driving, and others, the challenge of multi-object tracking is still to ensure tracking accuracy and robustness, especially in complex occlusion environments. Aiming at the issues of the occlusion, background noise, and motion state violent change for multi-object in a complex scene, an improved DeepSORT algorithm based on YOLOv5 is proposed for multi-object tracking to enhance the speed and accuracy of tracking. Firstly, a general object motion model is devised, which is similar to the variable acceleration motion model, and a multi-object tracking framework with the general motion model is established. Then, the latest YOLOv5 algorithm, which has satisfactory detection accuracy, is utilized to obtain the object information as the input of multi-object tracking. An unscented Kalman filter (UKF) is proposed to estimate the motion state of multi-object to solve nonlinear errors. In addition, the adaptive factor is introduced to evaluate observation noise and detect abnormal observations so as to adaptively adjust the innovation covariance matrix. Finally, an improved DeepSORT algorithm for multi-object tracking is formed to promote robustness and accuracy. Extensive experiments are carried out on the MOT16 data set, and we compare the proposed algorithm with the DeepSORT algorithm. The results indicate that the speed and precision of the improved DeepSORT are increased by 4.75% and 2.30%, respectively. Especially in the MOT16 of the dynamic camera, the improved DeepSORT shows better performance.

An improved adaptive FastSLAM algorithm with time‐varying noise estimator

AbstractIn this study, an adaptive FastSLAM (AFastSLAM) algorithm, which is obtained by estimating the time‐varying noise statistics and improving FastSLAM algorithm, is proposed. This improvement was accomplished by using maximum likelihood estimation and expectation maximization criterion and a one‐step smoothing algorithm in importance sampling. In addition, innovation covariance estimation (ICE) method was used to prevent loss of positive definiteness of the process and measurement noise covariance matrices. The proposed method was compared with FastSLAM by calculating the root mean square error (RMSE) using different particle numbers at varying initial process and measurement noise values. Simulation studies have shown that AFastSLAM provides much more accurate, consistent, and successful estimates than FastSLAM for both robot and landmark positions.

The Strong Tracking Innovation Filter

Sliding innovation filter (SIF) has recently been introduced as a robust strategy for estimation of linear systems. The SIF has been extended to nonlinear systems via analytical linearization. However, as the performance of the extended SIF (ESIF) degrades in the presence of severe nonlinearities, this article has initially developed a derivative-free cubature SIF (CSIF) that uses statistical linearization for the error propagation. In addition, the SIF gain has been reformed to incorporate the innovation covariance matrix, thus reducing the estimation error. Furthermore, the adaptive fading factor has been employed to strengthen the robustness and convergence properties of the CSIF against abrupt changes of state variables. Simulation results of the proposed estimation algorithm named the strong tracking innovation filter (STIF) have been compared to those of the ESIF and the CSIF in different conditions of the modeling error in the dynamic system and statistical characteristics of the system inputs. This comparison has demonstrated the superior performance of the STIF in terms of the convergence rate, estimation accuracy, and the chattering elimination. Integration of the STIF into a sliding mode controller for the concurrent estimation and control of a Mars lander has reconfirmed the robustness and accuracy of the proposed STIF.

A novel maximum likelihood and moving weighted average based adaptive Kalman filter

For the state estimation with inaccurate noise statistics, the existing adaptive Kalman filters (AKFs) usually have substantial computational complexity or are not easy to estimate online. Inspired by the fact, a new computationally efficient AKF based on maximum likelihood and moving weighted average (MMAKF) is proposed. Firstly, to reduce computational complexity, instead of estimating the noise covariance matrixes, the maximum likelihood principle is introduced to directly estimate the prediction error covariance matrix and innovation covariance matrix. Subsequently, a new moving weighted average algorithm is designed to optimize the estimated results. Then, a computationally efficient AKF is derived, and its convergence performance and application are discussed. Simulation results for the target tracking example illustrate that the proposed AKF can effectively reduce error caused by inaccurate noise statistics and basically keep simplicity and elegance of the classical KF.

Integrated Navigation Algorithm Based on Multiple Fading Factors Kalman Filter.

An integrated navigation algorithm based on a multiple fading factors Kalman filter (MFKF) is proposed to solve the problems that the Kalman filtering (KF) algorithm easily brings about diffusion when the model becomes a mismatched or noisy, and the MFKF accuracy is reduced when the fading factor is overused. Based on the innovation covariance theory, the algorithm designs an improved basis for judging filtering anomalies and makes the timing of the introduction of the fading factor more reasonable by switching the filtering state. Different from the traditional basis of filter abnormality judgment, the improved judgment basis adopts a recursive way to continuously update the estimated value of the innovation covariance to improve the estimation accuracy of the innovation covariance, and an empirical reserve factor for the judgment basis is introduced to adapt to practical engineering applications. By establishing an inertial navigation system (INS)/global navigation satellite system (GNSS) integrated navigation model, the results show that the average positioning accuracy of the proposed algorithm is improved by 26.52% and 7.48%, respectively, compared with the KF and MFKF, and shows better robustness and self-adaptability.

A Robust Tracking Algorithm Based on Modified Generalized Probability Data Association for Wireless Sensor Network

Wireless sensor network (WSN) is composed of many micro sensor nodes, and the localization technology is one of the most important applications of the WSN technology. At present, many positioning algorithms have high positioning accuracy in line-of-sight environment, but poor positioning accuracy in non-line-of-sight (NLOS) environment. In this article, we propose a modified generalized probability data association algorithm based on arrival of time. We divided the range measurements into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> different groups, and each group obtained the corresponding position estimation, model probabilities, and covariance matrix of the mobile node through IMM-EKF. We used model probability and hypothesis test to perform NLOS identification for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> groups, in which the model probability provided by each group was used for the first NLOS identification, and the innovation and innovation covariance matrix were used for the second NLOS identification in the hypothesis test. Position estimation contaminated by NLOS error is discarded. The correct position estimation is weighted with the corresponding association probability. The simulation and experimental results show that the proposed algorithm can mitigate the influence of NLOS errors and achieve higher localization accuracy when compared with the existing methods.

A Projection Method for the Estimation of Error Covariance Matrices for Variational Data Assimilation in Ocean Modelling

Data assimilation methods are an invaluable tool for operational ocean models. These methods are often based on a variational approach and require the knowledge of the spatial covariances of the background errors (differences between the numerical model and the true values) and the observation errors (differences between true and measured values). Since the true values are never known in practice, the error covariance matrices containing values of the covariance functions at different locations, are estimated approximately. Several methods have been devised to compute these matrices, one of the most widely used is the one developed by Hollingsworth and Lönnberg (H-L). This method requires to bin (combine) the data points separated by similar distances, compute covariances in each bin and then to find a best fit covariance function. While being a helpful tool, the H-L method has its limitations. We have developed a new mathematical method for computing the background and observation error covariance functions and therefore the error covariance matrices. The method uses functional analysis which allows to overcome some shortcomings of the H-L method, for example, the assumption of statistical isotropy. It also eliminates the intermediate steps used in the H-L method such as binning the innovations (differences between observations and the model), and the computation of innovation covariances for each bin, before the best-fit curve can be found. We show that the new method works in situations where the standard H-L method experiences difficulties, especially when observations are scarce. It gives a better estimate than the H-L in a synthetic idealised case where the true covariance function is known. We also demonstrate that in many cases the new method allows to use the separable convolution mathematical algorithm to increase the computational speed significantly, up to an order of magnitude. The Projection Method (PROM) also allows computing 2D and 3D covariance functions in addition to the standard 1D case.

Extended Kalman filter for online soft tissue characterization based on Hunt-Crossley contact model

Real-time soft tissue characterization is significant to robotic assisted minimally invasive surgery for achieving precise haptic control of robotic surgical tasks and providing realistic force feedback to the operator. This paper presents a nonlinear methodology for online soft tissue characterization. An extended Kalman filter (EKF) is developed based on dynamic linearization of the nonlinear H–C contact model in terms of system state for online characterization of soft tissue parameters. To handle the resultant linearization modelling error, an innovation orthogonal EKF is further developed by incorporating an adaptive factor in the EKF filtering to adaptively adjust the innovation covariance according to the principle of innovation orthogonality. Simulation and experimental results as well as comparison analysis demonstrate that the proposed methodology can effectively characterize soft tissue parameters, leading to dramatically improved accuracy comparing to recursive least square estimation. Further, the proposed methodology also requires a smaller computational load and can achieve the real-time performance for soft tissue characterization.

Identifying Shocks via Time-Varying Volatility

Abstract I propose to identify an SVAR, up to shock ordering, using the autocovariance structure of the squared innovations implied by an arbitrary stochastic process for the shock variances. These higher moments are available without parametric assumptions on the variance process. In contrast, previous approaches exploiting heteroskedasticity rely on the path of innovation covariances, which can only be recovered from the data under specific parametric assumptions on the variance process. The conditions for identification are testable. I compare the identification scheme to existing approaches in simulations and provide guidance for estimation and inference. I use the methodology to estimate fiscal multipliers peaking at 0.86 for tax cuts and 0.75 for government spending. I find that tax shocks explain more variation in output at longer horizons. The empirical implications of my estimates are more consistent with theory and the narrative record than those based on some leading approaches.

State-of-charge estimation of lithium-ion battery pack by using an adaptive extended Kalman filter for electric vehicles

State-of-charge (SOC) estimation is an important aspect for modern battery management systems. Extended Kalman filter (EKF) has been extensively used in battery SOC estimation. However, EKF cannot obtain accurate estimation results when the model parameters have strong uncertainty or/and the accurate initial value of noise covariance matrix is unknown. To overcome these defects, the parameters of Lithium-ion battery model on the basis of the second-order resistor–capacitor (RC) equivalent model are identified, and then an improved adaptive EKF (IAEKF) of SOC estimation method for Lithium-ion battery pack is proposed for enhancing estimation accurate and robustness. In IAEKF, the statistical characteristics of measurement noise is adaptively corrected using a forgetting factor, namely, Sage–Husa EKF (SHEKF), and the error covariance matrix is adaptively corrected in accordance with the innovation, in which the calculation of the actual innovation covariance matrix adopts the variable sliding window length. Results of numerical simulation and experiment show that the proposed SOC estimation method can accurately estimate SOC under complex driven condition and has strong robustness to the uncertainty of model parameters and the initial value of the noise covariance matrix.

Multiple fading factors-based strong tracking variational Bayesian adaptive Kalman filter

If the system model or the statistical characteristics of noise are inaccurate, the past measurements will directly affect the accuracy of current state estimation or even lead to filtering divergence. To overcome above difficulties, a multiple fading factors-based strong tracking variational Bayesian adaptive Kalman filter is proposed. Firstly, the inverse Wishart distribution is adopted to model the measurement noise covariance matrix. Secondly, the remodified measurement noise covariance matrix and the innovation covariance matrix estimated by exponential weighting method are employed to construct the scalar fading factor. Next, the multiple fading factors are calculated to correct the predicted error covariance matrix. Finally, the local optimal estimations of measurement noise covariance matrix and state are obtained by variational Bayesian approach. The target tracking simulations verify that the proposed algorithm has better tracking ability for the predicted error covariance matrix and the measurement noise covariance matrix compared with the existing filters.

Identifiability of structural singular vector autoregressive models

We generalize well‐known results on structural identifiability of vector autoregressive (VAR) models to the case where the innovation covariance matrix has reduced rank. Singular structural VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and we provide a rank condition for identifiability of the noise parameters. Since the Yule–Walker equations may have multiple solutions, we analyse the effect of restricting system parameters on over‐ and underidentification in detail and provide easily verifiable conditions.

Adaptively Robust Square-Root Cubature Kalman Filter Based on Amending

To solve the problem of decreased filtering accuracy and even filter divergence for the case that the model errors and measurement outliers exist simultaneously, an adaptively robust square-root cubature Kalman filter (SRCKF) based on amending is proposed in this paper. Based on the error analysis, the judgment criterion and the amending criterion related to the innovation are set. Then the filter could overcome the influence of the measurement outliers with the robust amendment of the measurement noise covariance matrix based on the principle of the innovation covariance matching. To further deal with model errors, the new method of the adaptive amendment of the predicted state based on the innovation is developed and combined. Finally, the proposed algorithm can balance the effect of the prior predicted value and the posterior feedback measurement value on the filtering process and reduce the state estimation error. The simulation results show that the proposed algorithm can effectively suppress the negative impact of the model errors and the measurement outliers and can obtain better estimation performance and obviously decreasing running time compared with the adaptively robust unscented Kalman filter (ARUKF) and the robust multiple fading factors cubature Kalman filter (RMCKF).