Robust Kalman Filter Research Articles

Robust Variational Inference for LPV Dual-Rate Systems With Randomly Delayed Outputs

This article proposes a variational Bayesian (VB) approach for the identification of linear parameter-varying (LPV) dual-rate systems when the measured data are contaminated with varying time delays and outliers. By treating all the unknown parameters as hidden variables and imposing suitable priors, the full Bayesian model for the identification problem can be established. A modified robust Kalman filter is adopted to estimate the missing outputs required in the regressor, and the VB algorithm is employed to simultaneously estimate the LPV model parameters with their uncertainties, time delays with their significances, and noise-free process outputs. One additional advantage of the proposed method is that the optimal interval of time delays can be determined automatically with the insignificant time delays suppressed. The validity of the developed approach is illustrated through a numerical study and the electronic bandpass filter benchmark.

An Improved Long-Period Precise Time-Relative Positioning Method Based on RTS Data.

The high precision positioning can be easily achieved by using real-time kinematic (RTK) and precise point positioning (PPP) or their augmented techniques, such as network RTK (NRTK) and PPP-RTK, even if they also have their own shortfalls. A reference station and datalink are required for RTK or NRTK. Though the PPP technique can provide high accuracy position data, it needs an initialisation time of 10–30 min. The time-relative positioning method estimates the difference between positions at two epochs by means of a single receiver, which can overcome these issues within short period to some degree. The positioning error significantly increases for long-period precise positioning as consequence of the variation of various errors in GNSS (Global Navigation Satellite System) measurements over time. Furthermore, the accuracy of traditional time-relative positioning is very sensitive to the initial positioning error. In order to overcome these issues, an improved time-relative positioning algorithm is proposed in this paper. The improved time-relative positioning method employs PPP model to estimate the parameters of current epoch including position vector, float ionosphere-free (IF) ambiguities, so that these estimated float IF ambiguities are used as a constraint of the base epoch. Thus, the position of the base epoch can be estimated by means of a robust Kalman filter, so that the position of the current epoch with reference to the base epoch can be obtained by differencing the position vectors between the base epoch and the current one. The numerical results obtained during static and dynamic tests show that the proposed positioning algorithm can achieve a positioning accuracy of a few centimetres in one hour. As expected, the positioning accuracy is highly improved by combining GPS, BeiDou and Galileo as a consequence of a higher amount of used satellites and a more uniform geometrical distribution of the satellites themselves. Furthermore, the positioning accuracy achieved by using the positioning algorithm here described is not affected by the initial positioning error, because there is no approximation similar to that of the traditional time-relative positioning. The improved time-relative positioning method can be used to provide long-period high precision positioning by using a single dual-frequency (L1/L2) satellite receiver.

Robust tracking of moving objects using thermal camera and speeded up robust features descriptor

SummaryRobust methods based on nonlinear influence functions are often used to remove outliers from data. The article describes the design of an algorithm for tracking a moving object in a thermal image using a SURF descriptor and robust Kalman filter. However, given that the main shortfall of robust methods is reduced efficiency, tunable parameters of the robust influence function are used to achieve a balance between robustness and efficiency. The parameters adapt to the observed scene's current conditions, while their estimation is based on the calculated data outlier contamination factor. The outliers that contaminate the data are generally a result of various types of occlusions. The results show that the proposed solution achieves better performance than the standard Kalman filter or fixed‐parameter robust Kalman filter.

Amplifying power quality and diminishing harmonic distortion in MG VIA adaptive MPC-based robust EKF through IPSO-SHE

The objective of micro grid (MG) is to generate, regulate and distribute the electricity to the utility grid. Any faults occur in the MG can cause deviations on the voltage, frequency and voltage sag/swell, which affects the power quality. In order to overcome these issues in this paper we proposed to design an adaptive model predictive control (MPC)-based robust extended Kalman filter (REKF) with improved particle swarm optimised selective harmonic elimination (IPSO-SHE) control system. This fetches the importance of power quality improvement. The utilisation of adaptive MPC with robust EKF express the harmonic signatures produced in the system which can be used to detect islanding. An IPSO-SHE is finally employed to reduce the harmonics which significantly improves the quality of power delivered to the load. Our proposed control system has been implemented in the working platform of MATLAB/Simulink and tested with certain load conditions. The simulation results of the proposed control system and comparison with existing control systems shows the significance of the proposed work.

A robust in-motion attitude alignment method for odometer-aided strapdown inertial navigation system.

A significant issue of land vehicle navigation is in-motion attitude alignment of the odometer (OD)-aided strapdown inertial navigation system (SINS). The consecutive OD outliers can occur due to sudden wheel slipping and skidding while vehicle maneuvering. They seriously reduce the robustness and precision of attitude alignment. In this paper, we investigate a robust in-motion attitude alignment method for the OD-aided SINS. The method consists of in-motion coarse alignment and in-motion fine alignment. In the in-motion coarse alignment process, we developed Huber's M-estimation and integral formula based robust Kalman filter (HRKF/IF-CA), which can restrain the interference of consecutive OD outliers on reconstructed observation vectors. Thus, HRKF/IF-CA can contribute to better coarse attitude results. The next process is in-motion fine alignment. Under the popular repeated backtracking scheme, we investigate HRKF based fine alignment (HRKF-FA) with the SINS/OD summed measurement model. HRKF-FA can refine attitude alignment and restrain the interference of consecutive OD outliers simultaneously. Finally, the proposed method is evaluated by simulation and vehicle test. The attitude alignment results show that this method can achieve reasonable attitude results, and the interference of consecutive OD outliers caused by sudden wheel slipping and skidding can be greatly restrained.

Real-time GNSS precise point positioning using improved robust adaptive Kalman filter

Multi-constellation GNSS precise point positioning (PPP) typically uses the extended Kalman filter (EKF) for kinematic applications. Unfortunately, the obtained positioning accuracy in this approach is prone to errors caused by measurement outliers and the system’s dynamic model. An adaptive robust Kalman filter (RKF) was recently developed to mitigate these errors. However, RKF uses empirical values as detection thresholds for the outliers, which requires the measurements to be from the same constellation and of equal precision to obtain an optimal PPP solution. The classification robust adaptive Kalman filter (CAKF) has subsequently been developed to deal with measurements of different precisions, namely pseudorange and carrier-phase measurements. This paper proposes a real-time GPS/Galileo PPP system, which employs a modified version of CAKF called the Improved Robust adaptive Kalman Filter (IRKF). The positioning performance of GPS/Galileo PPP through the IRKF is initially verified in comparison with those obtained through the EKF, RKF, and CAKF using the Centre for Orbit Determination in Europe (CODE) final orbit and clock products in both of static and kinematic modes. The real-time GPS/Galileo PPP solution through the IRKF is then assessed in comparison with its near-real-time counterpart. The results indicate that when the IRKF approach is utilised, the positioning accuracy is significantly improved and the convergence behaviour is enhanced compared with results from EKF, conventional RKF, and CAKF. In the real-time mode, centimeter-level horizontal positioning accuracy is achieved under an open sky environment, while decimeter-level horizontal positioning accuracy is achieved under a challenging environment. On the other hand, decimeter-level accuracy is achieved for the vertical positioning component under all environmental scenarios. Moreover, the positioning accuracy of the real-time solution is comparable to the near-real-time counterpart.

Robust Kalman Filter with Fading Factor Under State Transition Model Mismatch and Outliers Interference

In practical applications, due to the complexity of the system, the process equation of the state space model is difficult to match the actual state transition model. In addition, the unreliability of the sensor will cause the measurement to be accompanied by outliers. In this paper, a novel robust Kalman filter with fading factor is proposed to improve the accuracy of state estimation for the linear system under state transition model mismatch and outliers interference. Firstly, in order to modify the state transition model, this filter introduces a fading factor which is modelled as the inverse gamma distribution to update the state prediction covariance. Then, aiming at the phenomenon that the measurement noise does not follow the Gaussian distribution and has nonzero mean characteristics due to outliers interference, the measurement noise is modelled as the generalized hyperbolic skew Student’s t distribution. Finally, the state estimation is realized by using the variational Bayesian. The simulation results show that the estimation accuracy of the proposed filter is higher than that of the Kalman filter and the strong tracking filter.

Study on Multi-GNSS Precise Point Positioning Performance with Adverse Effects of Satellite Signals on Android Smartphone.

The emergence of dual frequency global navigation satellite system (GNSS) chip actively promotes the progress of precise point positioning (PPP) technology in Android smartphones. However, some characteristics of GNSS signals on current smartphones still adversely affect the positioning accuracy of multi-GNSS PPP. In order to reduce the adverse effects on positioning, this paper takes Huawei Mate30 as the experimental object and presents the analysis of multi-GNSS observations from the aspects of carrier-to-noise ratio, cycle slip, gradual accumulation of phase error, and pseudorange residual. Accordingly, we establish a multi-GNSS PPP mathematical model that is more suitable for GNSS observations from a smartphone. The stochastic model is composed of GNSS step function variances depending on carrier-to-noise ratio, and the robust Kalman filter is applied to parameter estimation. The multi-GNSS experimental results show that the proposed PPP method can significantly reduce the effect of poor satellite signal quality on positioning accuracy. Compared with the conventional PPP model, the root mean square (RMS) of GPS/BeiDou (BDS)/GLONASS static PPP horizontal and vertical errors in the initial 10 min decreased by 23.71% and 62.06%, respectively, and the horizontal positioning accuracy reached 10 cm within 100 min. Meanwhile, the kinematic PPP maximum three-dimensional positioning error of GPS/BDS/GLONASS decreased from 16.543 to 10.317 m.

A Robust INS/SRS/CNS Integrated Navigation System with the Chi-Square Test-Based Robust Kalman Filter.

In order to achieve a highly autonomous and reliable navigation system for aerial vehicles that involves the spectral redshift navigation system (SRS), the inertial navigation (INS)/spectral redshift navigation (SRS)/celestial navigation (CNS) integrated system is designed and the spectral-redshift-based velocity measurement equation in the INS/SRS/CNS system is derived. Furthermore, a new chi-square test-based robust Kalman filter (CSTRKF) is also proposed in order to improve the robustness of the INS/SRS/CNS navigation system. In the CSTRKF, the chi-square test (CST) not only detects measurements with outliers and in non-Gaussian distributions, but also estimates the statistical characteristics of measurement noise. Finally, the results of our simulations indicate that the INS/SRS/CNS integrated navigation system with the CSTRKF possesses strong robustness and high reliability.

Integration of variance component estimation with robust Kalman filter for single-frequency multi-GNSS positioning

Although the emergence of new satellite systems offers considerable opportunities, the integration of Global Navigation Satellite System (GNSS) multi-constellation entails more complicated approaches, especially for stochastic modeling. This study proposes a filtering approach that combines robust Kalman filtering and variance component estimation to specify the weights of multi-GNSS observations in single-frequency positioning. In this approach, robust Kalman filter resists the impact of unexpected outliers by introducing the equivalent covariance matrix, while multi-GNSS observation variances are determined adaptively in each epoch by using variance component estimation. The study demonstrated that the proposed filtering approach determines the variances of multi-GNSS observations more rigorously as a result of the assessment of the observation residuals. The results also showed that the positioning accuracy of single-frequency multi-GNSS positioning that depends on the conventional weighting approaches is improved by 18.5% on average with the employment of the proposed filtering approach and its improvement ratio can exceed 30% in some stations.

Robust Square-Root Cubature FastSLAM with Genetic Operators

SUMMARYAn improved FastSLAM based on the robust square-root cubature Kalman filter (RSRCKF) with partial genetic resampling is proposed in this paper. In the proposed method, RSRCKF is used to design the proposal distribution of FastSLAM and to estimate environment landmarks. The proposed method does not require a priori knowledge of the noise statistics. In addition, to increase diversity, it uses the genetic operators-based strategy to further improve the particle diversity. In fact, a partial genetic resampling operation is carried out to maintain the diversity of particles. The proposed method is compared with other methods via simulation and experimental data. It can be seen from the results that the proposed method provides significantly more accurate and robust estimation results compared with other methods even with fewer particles and unknown a priori. In addition, the consistency of the proposed method is better than that of other methods.

A Novel Heavy-Tailed Mixture Distribution Based Robust Kalman Filter for Cooperative Localization

In cooperative localization for autonomous underwater vehicles (AUVs), the practical stochastic noise may be heavy-tailed, and nonstationary distributed because of acoustic speed variation, multipath effect of acoustic channel, and changeable underwater environment. To address such noise, a novel heavy-tailed mixture (HTM) distribution is first proposed in this article, and then expressed as a hierarchical Gaussian form by employing a categorical distributed auxiliary vector. Based on that, a novel HTM distribution based robust Kalman filter is proposed, where the one-step prediction, and measurement likelihood probability density functions are, respectively, modeled as an HTM distribution, and a Normal-Gamma-inverse Wishart distribution. The proposed filter is verified by a lake experiment about cooperative localization for AUVs. Compared with the cutting-edge filter, the proposed filter has been improved by 50.27% in localization error but no more than twice computational time is required.

Kalman Filter Based on Multiple Scaled Multivariate Skew Normal Variance Mean Mixture Distributions With Application to Target Tracking

In this brief, we first propose a multiple scaled multivariate skew normal variance-mean mixture (MSMSNVMM) distribution to model heavy-tailed and/or skew measurement noises (HTSMN) whose each dimension has different tail and skewness behaviors. The MSMSNVMM distribution has more flexible tail behaviors and richer skewness features than Gaussian scale mixture (GScM) distribution, generalized Gaussian scale mixture (GGScM) distribution and scale mixtures of skew normal (SMSN) distribution. Furthermore, we derive a robust Kalman filter based on variational Bayesian (VB) method. The superiority of the new filter is demonstrated in a maneuvering target tracking example.

A Novel Mixture Distributions-Based Robust Kalman Filter for Cooperative Localization

In cooperative localization for autonomous underwater vehicles (AUVs), the practical state and measurement noises may be non-stationary non-Gaussian distributed because of sensor outliers, multi-path effect of acoustic channel, and changeable underwater environment. In this paper, a couple of novel mixture distributions, i.e., the Gaussian-Slash mixture distribution and the Gaussian-generalized hyperbolic skew Student's t mixture distribution, are proposed to model such state and measurement noises, respectively. By introducing two Bernoulli distributed random variables, both the proposed mixture distributions can be expressed as hierarchically Gaussian forms. Based on this, a novel mixture distributions based robust Kalman filter (MDRKF) is derived by exploiting the variational Bayesian inference. A lake experiment about the cooperative localization for AUVs demonstrated that the proposed MDRKF has better localization accuracy but higher computational complexity than the existing state-of-the-art filtering algorithms.

UMoDT: an unobtrusive multi-occupant detection and tracking using robust Kalman filter for real-time activity recognition

Human activity recognition (HAR) is an important branch of human-centered research. Advances in wearable and unobtrusive technologies offer many opportunities for HAR. While much progress has been made in HAR using wearable technology, it still remains a challenging task using unobtrusive (non-wearable) sensors. This paper investigates detection and tracking of multi-occupant HAR in a smart-home environment, using a novel low-resolution Thermal Vision Sensor (TVS). Specifically, the research presents the development and implementation of a two-step framework, consisting of a Computer Vision-based method to detect and track multiple occupants combined with Convolutional Neural Network (CNN)-based HAR. The proposed algorithm uses frame difference over consecutive frames for occupant detection, a set of morphological operations to refine identified objects, and features are extracted before applying a Kalman filter for tracking. Laterally, a 19-layer CNN architecture is used for HAR and afterward the results from both methods are fused using time interval-based sliding window. This approach is evaluated through a series of experiments based on benchmark Thermal Infrared datasets (VOT-TIR2016) and multi-occupant data collected from TVS. Results demonstrate that the proposed framework is capable of detecting and tracking 88.46% of multi-occupants with a classification accuracy of 90.99% for HAR.

ANN-assisted robust GPS/INS information fusion to bridge GPS outage

Inertial navigation is an edge computing-based method for determining the position and orientation of a moving vehicle that operates according to Newton’s laws of motion on which all the computations are performed at the edge level without need to other far resources. One of the most crucial struggles in Global Positioning System (GPS) and Inertial Navigation System (INS) fusion algorithms is that the accuracy of the algorithm is reduced during GPS interruptions. In this paper, a low-cost method for GPS/INS fusion and error compensation of the GPS/INS fusion algorithm during GPS interruption is proposed. To further enhance the reliability and performance of the GPS/INS fusion algorithm, a Robust Kalman Filter (RKF) is used to compensate the influence of gross error from INS observations. When GPS data is interrupted, Kalman filter observations will not be updated, and the accuracy of the position will continuously decrease over time. To bridge GPS data interruption, an artificial neural network-based fusion method is proposed to provide missing position information. A well-trained neural network is used to predict and compensate the interrupted position signal error. Finally, to evaluate the effectiveness of the proposed method, an outdoor test using a custom-designed hardware, GPS, and INS sensors is employed. The results indicate that the accuracy of the positioning has improved by 67% in each axis during an interruption. The proposed algorithm can enhance the accuracy of the GPS/INS integrated system in the required navigation performance.

A Fast Robust In-Motion Alignment Method for SINS With DVL Aided

In this paper, a fast robust in-motion alignment method is proposed for the strapdown inertial navigation system (SINS) with DVL aided. The proposed method is divided into two procedures, which are coarse alignment procedure and fine alignment procedure. In the coarse alignment procedure, an apparent velocity modeling method is investigated. Building upon this model, a robust Kalman filter (RKF) is designed for parameter estimation, then an optimal observation vector, in which the outliers of the Doppler Velocity Log (DVL) outputs are eliminated, is reconstructed. As compared with the existing method, in the proposed method, the robustness of coarse alignment procedure is enhanced. To improve the accuracy of the coarse alignment method, a fine alignment method is designed. Different from the traditional fine alignment method, the error model of the proposed fine alignment method is constructed in n 0-frame. With this advantage, the time-varying error attitude estimation for the traditional method has transformed into a time-invariant error attitude estimation. Thus, the raw data and intermediate data, which are collected in the coarse alignment procedure, can be reused in the fine alignment procedure. Take advantage of the high performance of the navigational computer, the forward-forward data processing can be carried on repeatedly, the one cycle of the forward-forward procedure consumes about 0.3 s in the real-time system. Simulation and field tests showed that the proposed method can obtain a high-accuracy initial alignment results and suppress the interference of the outliers of the DVL outputs.

Robust Initial Alignment for SINS/DVL Based on Reconstructed Observation Vectors

Misalignment angle will result in a considerable error for the integration of Doppler velocity log (DVL) and of Strapdown Inertial Navigation System (SINS). In this article, a robust initial alignment method for SINS/DVL is proposed to solve a practical applicable issue, which is that the outputs of DVL are often corrupted by the outliers. First, the alignment principle for SINS/DVL is summarized. Second, based on the principle of this alignment method, the apparent velocity model is investigated, and the parameters expression of the apparent velocity model are derived detailed. Using the apparent velocity model, the unknown parameters of the apparent velocity model are estimated by the developed robust Kalman filter, then the reconstructed observation vector, where the outliers are detected and isolated, is reconstructed by the estimated parameters. Based on the reconstructed observation vectors, the initial attitude is determined. Finally, the simulation and field tests are carried out to verify the performance of the proposed method. The test results are shown that the proposed method can detect and isolate the outliers effectively and get better performance than the previous work.

GNSS DOPPLER VELOCITY BASED ON ADAPTIVE ROBUST KALMAN FILTERING

Abstract. The main factors affecting the error of Doppler velocity measurement mainly come from the measurement errors of GNSS data, influence of different motion states on GNSS velocity measurement and the noise of different receiver types. To improve the precision of GNSS velocity estimation, an algorithm of adaptive robust Kalman filter based on the PDOP was put forward. PDOP value as well as the number of satellite in each epoch are used as a criterion in the velocity processing. While the PDOP value is greater than the threshold value, which means the observation accuracy is low, then the robust Kalman filter based on IGG – III scheme is introduced. While the PDOP value is between the threshold values, which means the observation precision is normal, adaptive factor could be determined normally, and the single-factor three-stage adaptive model is applied for Kalman filtering. If the above two conditions are not consistent, it indicates that the prediction accuracy of the local epoch satellite is high, and Kalman filtering can be directly used. Through the experiment of shipborne GNSS velocity measurement, it was proved that comparing with conventional least square, the algorithm based on the adaptive robust Kalman filtering can improve the accuracy and stability of the GNSS velocity determination.

Two-Stage Kalman Filter for Fault Tolerant Estimation of Wind Speed and UAV Flight Parameters

Abstract In this study, an estimation algorithm based on a two-stage Kalman filter (TSKF) was developed for wind speed and Unmanned Aerial Vehicle (UAV) motion parameters. In the first stage, the wind speed estimation algorithm is used with the help of the Global Positioning System (GPS) and dynamic pressure measurements. Extended Kalman Filter (EKF) is applied to the system. The state vector is composed of the wind speed components and the pitot scale factor. In the second stage, in order to estimate the state parameters of the UAV, GPS, and Inertial Measurement Unit (IMU) measurements are considered in a Linear Kalman filter. The second stage filter uses the first stage EKF estimates of the wind speed values. Between these two stages, a sensor fault detection algorithm is placed. The sensor fault detection algorithm is based on the first stage EKF innovation process. After detecting the fault on the sensor measurements, the state parameters of the UAV are estimated via robust Kalman filter (RKF) against sensor faults. The robust Kalman filter algorithm, which brings the fault tolerance feature to the filter, secures accurate estimation results in case of a faulty measurement without affecting the remaining good estimation characteristics. In simulations, noise increment and bias type of sensor faults are considered.