A derivative UKF for tightly coupled INS/GPS integrated navigation

Brain-like position measurement method based on improved optical flow algorithm

In this paper, a brain-like navigation scheme based on fuzzy kernel C-means (FKCM) clustering assisted pyramid Lucas Kanade (LK) optical flow algorithm is developed to measure the position of vehicle. The Speed Cell and Place Cell in animals' brain are introduced to construct the brain-like navigation mechanism which involves the optical flow method and image template matching to imitate the cells above-mentioned separately. To eliminate the singular values during optical flow calculation, the output of pyramid LK algorithm is clustered by FKCM algorithm firstly. Then, the velocity is calculated and integrated to get the position of the vehicle, and the brain-like navigation scheme is introduced to correct the position measurement errors by eliminating the accumulated errors resulting from velocity integration. The prominent advantages of the presented method are: (i) a pure visual brain-like position measurement method based on the concept of speed cells and place cells is proposed, making visual navigation more accurate and intelligent; (ii) the FKCM algorithm is used to eliminate the singular value of the pyramid LK algorithm, which improves the calculated velocity accuracy. Also, experimental comparison with classical pyramid LK algorithm is given to illustrate the superiority of the proposed method in position measurement.

An Adaptive Fusion Attitude and Heading Measurement Method of MEMS/GNSS Based on Covariance Matching

Aimed at the problem of filter divergence caused by unknown noise statistical characteristics or variable noise characteristics in an MEMS/GNSS integrated navigation system in a dynamic environment, on the basis of revealing the parameter adjustment logic of covariance matching adaptive technology, a fusion adaptive filtering scheme combining innovation-based adaptive estimation (IAE) and the adaptive fading Kalman filter (AFKF) is proposed. By setting two system tuning parameters, for the process noise covariance adaptation loop and the measurement noise covariance adaptation loop, covariance matching is sped up and achieves an effective suppression of filter divergence. The vehicle-mounted experimental results show that the mean square error of the combined attitude error obtained based on the fusion filtering method proposed in this paper is better than 0.5°, and the mean square error of the heading error is better than 1.5°. The results can provide technical support for the continuous extraction of low-cost attitude information from mobile platforms.

An Improved System-Level Calibration Scheme for Rotational Inertial Navigation Systems

The system-level calibration technology of rotational inertial navigation is one of the main methods to improve the accuracy of inertial navigation, and the design of the calibration scheme is the key to calibration technology. By the establishment of the error model of inertial navigation system, a 30-position calibration scheme is designed in this study. Based on the 30-dimensional Kalman filter, the constant errors, scale factor errors and installation error of gyroscope and accelerometer are identified. Comparing the traditional schemes and the 30-position scheme with the simulation experiment, the observability of the 30-position scheme is higher, the residual error of the estimated sensor is smaller and the navigation positioning accuracy after the estimated inertial sensor error parameter compensation is higher, which verifies the feasibility of the 30-position scheme. Finally, the measured experiment uses the 30-position scheme to estimate the error of a certain type of IMU sensor, and the calibration curve of the error parameter is well converged before the end of the calibration experiment, so it has certain practical value.

GAN-FDSR: GAN-Based Fault Detection and System Reconfiguration Method

Fault detection and exclusion are essential to ensure the integrity and reliability of the tightly coupled global navigation satellite system (GNSS)/inertial navigation system (INS) integrated navigation system. A fault detection and system reconfiguration scheme based on generative adversarial networks (GAN-FDSR) for tightly coupled systems is proposed in this paper. The chaotic characteristics of pseudo-range data are analyzed, and the raw data are reconstructed in phase space to improve the learning ability of the models for non-linearity. The trained model is used to calculate generation and discrimination scores to construct fault detection functions and detection thresholds while retaining the generated data for subsequent system reconfiguration. The influence of satellites on positioning accuracy of the system under different environments is discussed, and the system reconfiguration scheme is dynamically selected by calculating the relative differential precision of positioning (RDPOP) of the faulty satellites. Simulation experiments are conducted using the field test data to assess fault detection performance and positioning accuracy. The results show that the proposed method greatly improves the detection sensitivity of the system for small-amplitude faults and gradual faults, and effectively reduces the positioning error during faults.

Towards Predicting the Measurement Noise Covariance with a Transformer and Residual Denoising Autoencoder for GNSS/INS Tightly-Coupled Integrated Navigation

The tightly coupled navigation system is commonly used in UAV products and land vehicles. It adopts the Kalman filter to combine raw satellite observations, including the pseudorange, pseudorange rate and Doppler frequency, with the inertial measurements to achieve high navigational accuracy in GNSS-challenged environments. The accurate estimation of measurement noise covariance can ensure the quick convergence of the Kalman filter and the accuracy of the navigation results. Existing tightly coupled integrated navigation systems employ either constant noise covariance or simple noise covariance updating methods, which cannot accurately reflect the dynamic measurement noises. In this article, we propose an adaptive measurement noise estimation algorithm using a transformer and residual denoising autoencoder (RDAE), which can dynamically estimate the covariance of measurement noise. The residual module is used to solve the gradient degradation problem. The DAE is adopted to learn the essential characteristics from the noisy ephemeris data. By introducing the attention mechanism, the transformer can effectively learn the time and space dependency of long-term ephemeris data, and thus dynamically adjusts the noise covariance with the predicted factors. Extensive experimental results demonstrate that our method can achieve sub-meter positioning accuracy in the outdoor open environment. In a GNSS-degraded environment, our proposed method can still obtain about 3 m positioning accuracy. Another test on a new dataset also confirms that our proposed method has reasonable robustness and adaptability.

A 3D Range-Only SLAM Algorithm Based on Improved Derivative UKF

In this study, we constructed a 3D range-only (RO) localization algorithm based on improved unscented Kalman filtering (UKF). The algorithm can determine the location of unknown UWB nodes in a 3D environment through a moving node with low computational complexity, which can help agents to accurately identify feature points in 3D SLAM based only on the range. Specifically, we established an original UKF framework based the 3D RO localization algorithm, and developed a derivative UKF framework to reduce the computational complexity of the algorithm. We used singular value decomposition to compensate for the robustness of the algorithm. Next, we performed a theoretical analysis to show that our method reduces the computational burden without reducing the stability or accuracy of the system. Finally, we conducted numerical simulations and physical experiments to show the effectiveness of the developed 3D RO localization algorithm.

A Novel Adaptive Factor-Based H∞ Cubature Kalman Filter for Autonomous Underwater Vehicle

In the navigation of an autonomous underwater vehicle (AUV), the positioning accuracy and stability of the navigation system will decrease due to uncertainties such as mobility, inaccuracy of a priori process noise characteristic, and simplification of a dynamic model. In order to solve the above problems, a new, adaptive factor-based H∞ cubature Kalman filter based on a fading factor (AF-H∞CKF) is proposed in this paper. On the one hand, the H∞ game theory provides AF-H∞CKF good robustness in the worst case; on the other hand, the fading factor makes the innovation orthogonal and inflates the predicted error covariance and the Kalman gain, which avoids a decrease in estimation precision in the case of model uncertainty. The simulation and experiment results show that the AF-H∞CKF filter can deal with AUV navigation better than other existing algorithms in the presence of outliers and model uncertainty, which confirms its effectiveness and superiority.

Multi-model train state estimation based on multi-sensor parallel fusion filtering

Accurately determining a train's state is essential for passenger safety, operation efficiency, and maintenance. However, the actual operation state of a train is composed of a variety of modes and is disturbed by several known or unknown factors, for which an accurate estimator is required. Hence, in this paper, a train multi-mode model considering the actual operation environment is established, and a train state estimation method based on multi-sensor parallel fusion filter is proposed. In the parallel fusion filter, the current mode of train is determined by the proposed sliding window error and voting mechanism, and the global filter are constituted by the local filters, which are fused by linear-weighted summation. The simulation results demonstrate the effectiveness of our method in estimating the train's state. It is worth noting that even if monitoring data are missing or are abnormal, the state estimation accuracy of the proposed technique still meets the requirements of a real system, and the effectiveness and robustness of the method can be verified.

Maximum correntropy delay Kalman filter for SINS/USBL integrated navigation

Communication delay and non-Gaussian noise are challenging issues for underwater navigation and positioning. This study proposes a filtering algorithm for strapdown inertial navigation system/ultra-short baseline (SINS/USBL) integrated navigation to deal with time-varying delay in underwater acoustic communication and cope with non-Gaussian noise induced by outliers and measurement noises. Considering the influence of platform error angle, the measurement equation of SINS/USBL is derived. According to the distance-related time delay characteristics of USBL acoustic communication, the delay system model is obtained based on state inversion. A linear recursive model based on a delay system model is constructed to update the posterior estimation and covariance matrix by combining it with the maximum correntropy criterion. The algorithm solves the problems of communication delay and non-Gaussian noise and greatly reduces the computational complexity due to its adaptive adjustment function. Simulation and experimental results verify the filter's improved accuracy and robustness.

Dual-Satellite Alternate Switching Ranging/INS Integrated Navigation Algorithm for Broadband LEO Constellation Independent of Altimeter and Continuous Observation

In challenging environments such as forests, valleys and higher latitude areas, there are usually fewer than four visible satellites. For cases with only two visible satellites, we propose a dual-satellite alternate switching ranging integrated navigation algorithm based on the broadband low earth orbit (LEO) constellation, which integrates communication and navigation (ICN) technology. It is different from the traditional dual-satellite integrated navigation algorithm: the difference is that it can complete precise real-time navigation and positioning without an altimeter and continuous observation. First, we give the principle of our algorithm. Second, with the help of an unscented Kalman filter (UKF), we give the observation equation and state equation of our algorithm, and establish the mathematical model of multipath/non-line of sight (NLOS) and noise interference. Finally, based on the SpaceX constellation, for various scenarios, we analyze the performance of our algorithm through simulation. The results show that: our algorithm can effectively suppress the divergence of the inertial navigation system (INS), in the face of different multipath/NLOS interference and various noise environments it still keeps good robustness, and also has great advantages in various indicators compared with the traditional dual-satellite positioning algorithms and some existing 3-satellite advanced positioning algorithms. These results show that our algorithm can meet the real-time location service requirements in harsh and challenging environments, and provides a new navigation and positioning method when there are only two visible satellites.

An IMU/ODM/UWB Joint Localization System Based on Modified Cubature Kalman Filtering

In this article, a multisensor joint localization system is proposed based on modified cubature Kalman filtering, which aims to improve the accuracy of state estimation under a moderate computational burden in the presence of high process noise. Specifically, first, the covariance of process noise is matched based on adaptive filtering. The inertial measurement unit (IMU), odometer (ODM), and ultra-wideband (UWB) information acquired by the associated sensors is then employed to augment the system state and are fused to lower the influence of process noise. In the presented localization setting, all sensors (IMU/ODM/UWB) are set to work in parallel under the federated Kalman filter (FKF) framework, which can correct the cumulative error of the internal sensor and and can improve the computational efficiency. Two sets of numerical simulations were performed to show that the proposed method can obtain accurate state estimation with a slightly increased computational burden.

Fault Diagnosis of Brake Train Based on Multi-Sensor Data Fusion

In this paper, a fault diagnosis method is proposed based on multi-sensor fusion information for a single fault and composite fault of train braking systems. Firstly, the single mass model of the train brake is established based on operating environment. Then, the pre-allocation and linear-weighted summation criterion are proposed to fuse the monitoring data. Finally, based on the improved expectation maximization, the braking modes and braking parameters are identified, and the braking faults are diagnosed in real time. The simulation results show that the braking parameters of systems can be effectively identified, and the braking faults can be diagnosed accurately based on the identification results. Even if the monitoring data are missing or abnormal, compared with the maximum fusion, the accuracies of parameter identifications and fault diagnoses can still meet the needs of the actual systems, and the effectiveness and robustness of the method can be verified.

A Novel Method of Fault Detection and Identification in a Tightly Coupled, INS/GNSS-Integrated System

Fault detection and identification are vital for guaranteeing the precision and reliability of tightly coupled inertial navigation system (INS)/global navigation satellite system (GNSS)-integrated navigation systems. A variance shift outlier model (VSOM) was employed to detect faults in the raw pseudo-range data in this paper. The measurements were partially excluded or included in the estimation process depending on the size of the associated shift in the variance. As an objective measure, likelihood ratio and score test statistics were used to determine whether the measurements inflated variance and were deemed to be faulty. The VSOM is appealing because the down-weighting of faulty measurements with the proper weighting factors in the analysis automatically becomes part of the estimation procedure instead of deletion. A parametric bootstrap procedure for significance assessment and multiple testing to identify faults in the VSOM is proposed. The results show that VSOM was validated through field tests, and it works well when single or multiple faults exist in GNSS measurements.

Unscented Particle Filter Algorithm Based on Divide-and-Conquer Sampling for Target Tracking

Unscented particle filter (UPF) struggles to completely cover the target state space when handling the maneuvering target tracing problem, and the tracking performance can be affected by the low sample diversity and algorithm redundancy. In order to solve this problem, the method of divide-and-conquer sampling is applied to the UPF tracking algorithm. By decomposing the state space, the descending dimension processing of the target maneuver is realized. When dealing with the maneuvering target, particles are sampled separately in each subspace, which directly prevents particles from degeneracy. Experiments and a comparative analysis were carried out to comprehensively analyze the performance of the divide-and-conquer sampling unscented particle filter (DCS-UPF). The simulation result demonstrates that the proposed algorithm can improve the diversity of particles and obtain higher tracking accuracy in less time than the particle swarm algorithm and intelligent adaptive filtering algorithm. This algorithm can be used in complex maneuvering conditions.

Adaptive H-infinite kalman filter based on multiple fading factors and its application in unmanned underwater vehicle

Aiming at the problem that the navigation performances of unmanned underwater vehicle (UUV) may be affected by inaccurate prior navigation information and external environmental interference, which may make the accuracy and reliability of strapdown inertial navigation system (SINS) and global position system (GPS) integrated navigation results worse, positioning divergent and system even invalid, an adaptive H-infinite kalman filtering algorithm based on multiple fading factors (MAHKF) is proposed in this paper. Firstly, the time-varying adaptive fading factor is used to modify the filter parameters on-line to make the initial error of navigation filter converge quickly. Secondly, the H-infinite kalman filter of the SINS/GPS system is built on combining the advantages of robust control, which improved the system robustness under extreme external environment. Further, the adaptive thresholdγ of the H-infinite kalman filter is introduced to make the filter adaptive to the environment change. Results of the simulation and experiment demonstrate that the initial error is converged at the beginning stage of navigation process, and the interference from external uncertainty inputs to the integrated navigation system are suppressed effectively with the proposed algorithm. Compared with the conventional kalman filter algorithm (KF), the position errors in three directions of the UUV are reduced by 66.57%,67.98% and 64.51% respectively with the proposed MAHKF.

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.

Multi-Sensor Combined Measurement While Drilling Based on the Improved Adaptive Fading Square Root Unscented Kalman Filter

In the process of the attitude measurement for a steering drilling system, the measurement of the attitude parameters may be uncertain and unpredictable due to the influence of server vibration on bits. In order to eliminate the interference caused by vibration on the measurement and quickly obtain the accurate attitude parameters of the steering drilling tool, a new method for multi-sensor dynamic attitude combined measurement is presented. Firstly, by using a triaxial accelerometer and triaxial magnetometer measurement system, the nonlinear model based on the quaternion is established. Then, an improved adaptive fading square root unscented Kalman filter is proposed for eliminating the vibration disturbance signal. In this algorithm, the square root of the state covariance matrix is used to replace the covariance matrix in the classical unscented Kalman filter (UKF) to avoid the filter divergence caused by the negative definite state covariance matrix. The fading factor is introduced into UKF to adjust the filter gain in real-time and improve the adaptive ability of the algorithm to mutation state. Finally, the computational method of the fading factor is optimized to ensure the self-adaptability of the algorithm and reduce the computational complexity. The results of the laboratory test and the field-drilling data show that the proposed method can filter out the interference noise in the attitude measurement sensor effectively, improve the solution accuracy of attitude parameters of drilling tools in the case of abrupt changes in the measuring environment, and thus ensuring the dynamic stability of the well trajectory.

H-infinity adaptive observer enhancements for vehicle chassis dynamics-based navigation sensor fault construction

The issues of chassis dynamics-based navigation sensor fault and state estimation in land vehicles are specialized in this study. Owing to the essential attributes of robust theory-based observers, an H-infinity adaptive observer is proposed to implement the fault reconstructions of faulty sensors, offering a reference to vehicles for further favorable control decision-making. This observer fuses a linear matrix inequality convex optimization strategy, with the dynamics of land vehicles established mathematically, the consequent problems associated with augmented descriptor system state-space model, Lyapunov stability and linear matrix inequality convex optimization are discussed in detail. The numerical simulations on vehicular systems that suffered with single-existing deadlocking, gain scheduling, and constant deflection sensor fault are conducted. The results indicate, the fault channel outputs fairly reflect the variations of real faults under severe step-type fault input circumstances, so that the applicability of the fault observer against sensor failures is guaranteed. The proposed sensor fault construction idea is further extended to a loosely coupled inertial measurement units/global positioning system (GPS) illustration with GPS unavailable in its north velocity channel. After reconstructing the priori system state for “State one-step prediction” of Kalman filter, the compensated navigation parameters by state estimator exhibit consistent with the references as expected, the vehicle chassis dynamics-based sensor fault construction method, therefore, may be recognized as an effective measure to a class of integrated navigation systems experiencing some unknown sensor failures.

Set-Membership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty

This paper presents a new set-membership based hybrid Kalman filter (SM-HKF) by combining the Kalman filtering (KF) framework with the set-membership concept for nonlinear state estimation under systematic uncertainty consisted of both stochastic error and unknown but bounded (UBB) error. Upon the linearization of the nonlinear system model via a Taylor series expansion, this method introduces a new UBB error term by combining the linearization error with systematic UBB error through the Minkowski sum. Subsequently, an optimal Kalman gain is derived to minimize the mean squared error of the state estimate in the KF framework by taking both stochastic and UBB errors into account. The proposed SM-HKF handles the systematic UBB error, stochastic error as well as the linearization error simultaneously, thus overcoming the limitations of the extended Kalman filter (EKF). The effectiveness and superiority of the proposed SM-HKF have been verified through simulations and comparison analysis with EKF. It is shown that the SM-HKF outperforms EKF for nonlinear state estimation with systematic UBB error and stochastic error.

A Robust Cubature Kalman Filter with Abnormal Observations Identification Using the Mahalanobis Distance Criterion for Vehicular INS/GNSS Integration

INS/GNSS (inertial navigation system/global navigation satellite system) integration is a promising solution of vehicle navigation for intelligent transportation systems. However, the observation of GNSS inevitably involves uncertainty due to the vulnerability to signal blockage in many urban/suburban areas, leading to the degraded navigation performance for INS/GNSS integration. This paper develops a novel robust CKF with scaling factor by combining the emerging cubature Kalman filter (CKF) with the concept of Mahalanobis distance criterion to address the above problem involved in nonlinear INS/GNSS integration. It establishes a theory of abnormal observations identification using the Mahalanobis distance criterion. Subsequently, a robust factor (scaling factor), which is calculated via the Mahalanobis distance criterion, is introduced into the standard CKF to inflate the observation noise covariance, resulting in a decreased filtering gain in the presence of abnormal observations. The proposed robust CKF can effectively resist the influence of abnormal observations on navigation solution and thus improves the robustness of CKF for vehicular INS/GNSS integration. Simulation and experimental results have demonstrated the effectiveness of the proposed robust CKF for vehicular navigation with INS/GNSS integration.

An Ultra-Short Baseline Positioning Model Based on Rotating Array & Reusing Elements and Its Error Analysis

The USBL (Ultra-Short Base Line) positioning system is widely used in underwater acoustic positioning systems due to its small size and ease of use. The traditional USBL positioning system is based on ‘slant range and azimuth’. The positioning error is an increasing function with the increase in distance and the positioning accuracy depends on the ranging accuracy of the underwater target. This method is not suitable for long-distance underwater positioning operations. This paper proposes a USBL positioning calculation model based on depth information for ‘rotating array and reusing elements’. This method does not need to measure the distance between the USBL acoustic array and target, so it can completely eliminate the influence of long-distance ranging errors in USBL positioning. The theoretical analysis and simulation experiments show that the new USBL positioning model based on ‘rotating array and reusing elements’ can completely eliminate the influence of the wavelength error and spacing error of underwater acoustic signals on the positioning accuracy of USBL. The positioning accuracy can be improved by approximately 90%, and the horizontal positioning error within a positioning distance of 1000 m is less than 1.2 m. The positioning method has high precision performance in the long distance, and provides a new idea for the engineering design of a USBL underwater positioning system.

A misalignment angle error calibration method of underwater acoustic array in strapdown inertial navigation system/ultrashort baseline integrated navigation system based on single transponder mode

The angle misalignment error of a USBL (Ultrashort Baseline) acoustic array is one of the major error sources of the strapdown inertial navigation system/USBL positioning system, which will directly affect the positioning accuracy of the USBL positioning system. For the traditional calibration method cannot accurately estimate the angle misalignment error due to its strict trajectory requirements in the field experiment and the high-precision layout of the transceiver array elements, a new method for estimating the angle misalignment error of a USBL acoustic array based on single transponder and dual-vector reconstruction is studied in this paper. The precondition of USBL misalignment calibration is to locate the underwater transponder accurately. In this paper, the single transponder segmentation iterative long baseline method is used to locate the underwater target transponder. The dual-vector reconstruction method is studied to control the estimation accuracy of USBL misalignment error calibration based on the traditional single transponder method, which provides a theoretical basis for the determination of the iteration times to the USBL angle misalignment error estimation module. The underwater experiment results show that the positioning error could be reduced to less than 1 m after the angle misalignment error compensation. The underwater transponder positioning and the angle misalignment error estimation of USBL could be accomplished in a circle sailing. It is a new method with good performance of high estimation accuracy, simple operation, and easy realization.

Estimation of the Solow-Cobb-Douglas economic growth model with a Kalman filter: An observability-based approach

This work presents a novel approach for estimating the Solow-Cobb-Douglas economic growth model. In this case, an Extended Kalman Filter is used for estimating, at the same time, the time-varying parameters of the model and the system state, from subsets of partially available economic data measurements. Different from traditional econometric techniques, the proposed EKF approach is applied directly to a state-space representation of the original nonlinear model, where all the model parameters are treated as time-varying parameters. An extensive nonlinear observability analysis was carried out in order to investigate the different subsets of measurements that can be used for estimating the state of the system, and also, in order to find out theoretically necessary conditions to achieve the observability system property. Experiments with real macroeconomic data are presented in order to validate the proposed approach. While the observability analysis offer theoretically conditions for system observability, the experimental results suggest that between the subsets of available economic data, some specific economic data are more relevant than others for better estimating the model.

A calibration method of ultra-short baseline installation error with large misalignment based on variational Bayesian unscented Kalman filter

The ultrashort baseline system is widely used in ships and underwater navigation and positioning. The misalignment and level arm with the inertial measurement unit are the two sources of positioning inaccuracy. The accuracy of calibration is usually affected by measurement noise and linearization of the observation equation. In order to improve the calibration accuracy, the variational Bayesian unscented Kalman filter (VBUKF) method is proposed for the calibration of the ultrashort baseline installation error in the paper. The detailed derivation of VBUKF for the calibration is presented in the paper. Simulation experiments and field experiments were carried out, respectively, to verify the algorithm. The simulation results show that the proposed method can calibrate the installation error of the sensors in real time on line. The field experiment verified that the algorithm improves the calibration accuracy of the installation error under the large misalignment. The positioning accuracy is also improved compared with the traditional method.

Incorporating delayed measurements in an improved high-degree cubature Kalman filter for the nonlinear state estimation of chemical processes

The on-line estimation of process quality variables has a large impact on the advanced monitoring and control techniques of chemical processes. The present study offers an improved high-degree cubature Kalman filter (HCKF) to solve the nonlinear state estimation problem of high-dimensional chemical processes. We substituted the Cholesky decomposition in the HCKF filter with a diagonalization transformation of the matrix. In addition, we enhanced numerical stability and estimation accuracy. On this basis, we present one nonlinear state estimation method based on the sample-state augmentation and improved HCKF to handle issues with delayed measurements. Finally, we used the nonlinear state estimation experiments for the polymerization process to validate the proposed method. The numerical results indicated the achievement of state estimation with higher accuracy and better stability following the effective utilization of the delayed measurements for nonlinear chemical processes.

Constrained Unscented Particle Filter for SINS/GNSS/ADS Integrated Airship Navigation in the Presence of Wind Field Disturbance

Due to the disturbance of wind field, it is difficult to achieve precise airship positioning and navigation in the stratosphere. This paper presents a new constrained unscented particle filter (UPF) for SINS/GNSS/ADS (inertial navigation system/global navigation satellite system/atmosphere data system) integrated airship navigation. This approach constructs a wind speed model to describe the relationship between airship velocity and wind speed using the information output from ADS, and further establishes a mathematical model for SINS/GNSS/ADS integrated navigation. Based on these models, it also develops a constrained UPF to obtain system state estimation for SINS/GNSS/ADS integration. The proposed constrained UPF uses the wind speed model to constrain the UPF filtering process to effectively resist the influence of wind field on the navigation solution. Simulations and comparison analysis demonstrate that the proposed approach can achieve optimal state estimation for SINS/GNSS/ADS integrated airship navigation in the presence of wind field disturbance.

An Autonomous Vehicle Navigation System Based on Inertial and Visual Sensors

The strapdown inertial navigation system (SINS) is widely used in autonomous vehicles. However, the random drift error of gyroscope leads to serious accumulated navigation errors during long continuous operation of SINS alone. In this paper, we propose to combine the Inertial Measurement Unit (IMU) data with the line feature parameters from a camera to improve the navigation accuracy. The proposed method can also maintain the autonomy of the navigation system. Experimental results show that the proposed inertial-visual navigation system can mitigate the SINS drift and improve the accuracy, stability, and reliability of the navigation system.

Robust Adaptive Cubature Kalman Filter and Its Application to Ultra-Tightly Coupled SINS/GPS Navigation System

In this paper, we propose a robust adaptive cubature Kalman filter (CKF) to deal with the problem of an inaccurately known system model and noise statistics. In order to overcome the kinematic model error, we introduce an adaptive factor to adjust the covariance matrix of state prediction, and process the influence introduced by dynamic disturbance error. Aiming at overcoming the abnormality error, we propose the robust estimation theory to adjust the CKF algorithm online. The proposed adaptive CKF can detect the degree of gross error and subsequently process it, so the influence produced by the abnormality error can be solved. The paper also studies a typical application system for the proposed method, which is the ultra-tightly coupled navigation system of a hypersonic vehicle. Highly dynamical scene experimental results show that the proposed method can effectively process errors aroused by the abnormality data and inaccurate model, and has better tracking performance than UKF and CKF tracking methods. Simultaneously, the proposed method is superior to the tracing method based on a single-modulating loop in the tracking performance. Thus, the stable and high-precision tracking for GPS satellite signals are preferably achieved and the applicability of the system is promoted under the circumstance of high dynamics and weak signals. The effectiveness of the proposed method is verified by a highly dynamical scene experiment.

Adaptive Square-Root Unscented Particle Filtering Algorithm for Dynamic Navigation

This paper presents a new adaptive square-root unscented particle filtering algorithm by combining the adaptive filtering and square-root filtering into the unscented particle filter to inhibit the disturbance of kinematic model noise and the instability of filtering data in the process of nonlinear filtering. To prevent particles from degeneracy, the proposed algorithm adaptively adjusts the adaptive factor, which is constructed from predicted residuals, to refrain from the disturbance of abnormal observation and the kinematic model noise. Cholesky factorization is also applied to suppress the negative definiteness of the covariance matrices of the predicted state vector and observation vector. Experiments and comparison analysis were conducted to comprehensively evaluate the performance of the proposed algorithm. The results demonstrate that the proposed algorithm exhibits a strong overall performance for integrated navigation systems.

A SINS/SRS/GNS Autonomous Integrated Navigation System Based on Spectral Redshift Velocity Measurements

In order to meet the requirements of autonomy and reliability for the navigation system, combined with the method of measuring speed by using the spectral redshift information of the natural celestial bodies, a new scheme, consisting of Strapdown Inertial Navigation System (SINS)/Spectral Redshift (SRS)/Geomagnetic Navigation System (GNS), is designed for autonomous integrated navigation systems. The principle of this SINS/SRS/GNS autonomous integrated navigation system is explored, and the corresponding mathematical model is established. Furthermore, a robust adaptive central difference particle filtering algorithm is proposed for this autonomous integrated navigation system. The simulation experiments are conducted and the results show that the designed SINS/SRS/GNS autonomous integrated navigation system possesses good autonomy, strong robustness and high reliability, thus providing a new solution for autonomous navigation technology.

Multi-Sensor Optimal Data Fusion Based on the Adaptive Fading Unscented Kalman Filter

This paper presents a new optimal data fusion methodology based on the adaptive fading unscented Kalman filter for multi-sensor nonlinear stochastic systems. This methodology has a two-level fusion structure: at the bottom level, an adaptive fading unscented Kalman filter based on the Mahalanobis distance is developed and serves as local filters to improve the adaptability and robustness of local state estimations against process-modeling error; at the top level, an unscented transformation-based multi-sensor optimal data fusion for the case of N local filters is established according to the principle of linear minimum variance to calculate globally optimal state estimation by fusion of local estimations. The proposed methodology effectively refrains from the influence of process-modeling error on the fusion solution, leading to improved adaptability and robustness of data fusion for multi-sensor nonlinear stochastic systems. It also achieves globally optimal fusion results based on the principle of linear minimum variance. Simulation and experimental results demonstrate the efficacy of the proposed methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integrated navigation.

High accuracy navigation information estimation for inertial system using the multi-model EKF fusing adams explicit formula applied to underwater gliders

The underwater navigation system, mainly consisting of MEMS inertial sensors, is a key technology for the wide application of underwater gliders and plays an important role in achieving high accuracy navigation and positioning for a long time of period. However, the navigation errors will accumulate over time because of the inherent errors of inertial sensors, especially for MEMS grade IMU (Inertial Measurement Unit) generally used in gliders. The dead reckoning module is added to compensate the errors. In the complicated underwater environment, the performance of MEMS sensors is degraded sharply and the errors will become much larger. It is difficult to establish the accurate and fixed error model for the inertial sensor. Therefore, it is very hard to improve the accuracy of navigation information calculated by sensors. In order to solve the problem mentioned, the more suitable filter which integrates the multi-model method with an EKF approach can be designed according to different error models to give the optimal estimation for the state. The key parameters of error models can be used to determine the corresponding filter. The Adams explicit formula which has an advantage of high precision prediction is simultaneously fused into the above filter to achieve the much more improvement in attitudes estimation accuracy. The proposed algorithm has been proved through theory analyses and has been tested by both vehicle experiments and lake trials. Results show that the proposed method has better accuracy and effectiveness in terms of attitudes estimation compared with other methods mentioned in the paper for inertial navigation applied to underwater gliders.

Visual-based quadrotor control by means of fuzzy cognitive maps

By applying an image-based visual servoing (IBVS) method, the intelligent image-based controlling of a quadrotor type unmanned aerial vehicle (UAV) tracking a moving target is studied in this paper. A fuzzy cognitive map (FCM) is a soft computing method which is classified as a fuzzy neural system and exploits the main aspects of fuzzy logic and neural network systems; so it seems to be a suitable choice for implementing a vision-based intelligent technique. An FCM has been employed in implementing an IBVS scheme on a quadrotor UAV, so that the UAV can track a moving target on the ground. For this purpose, by properly combining the perspective image moments, some features with the desired characteristics for controlling the translational and yaw motions of a UAV have been presented. In designing a vision-based control method for a UAV quadrotor, there are some challenges, including the target mobility and not knowing the height of UAV above the target. Also, no sensor has been installed on the moving object and the changes of its yaw angle are not available. Despite all the stated challenges, the proposed method, which uses an FCM in controlling the translational motion and the yaw rotation of a UAV, adequately enables the quadrotor to follow the moving target. The simulation results for different paths show the satisfactory performance of the designed controller.