Global Navigation Satellite System/Inertial Navigation System Research Articles

A Multi-Step Pseudo-Measurement Adaptive Kalman Filter Based on Filtering Performance Evaluation and Its Application in the INS/GNSS Navigation System

The objective of this paper is to tackle the issue of the degraded navigation accuracy of the inertial navigation system/global navigation satellite system (INS/GNSS) integrated navigation system in urban applications, especially under complex environments. This study utilizes historical state estimates and proposes a multi-step pseudo-measurement adaptive Kalman filter (MPKF) algorithm based on the filter performance evaluation. First, taking advantage of the independence between INS and GNSS, the enhanced second-order mutual difference (SOMD) algorithm is utilized for estimating the noise variance of the GNSS, which is decoupled from the estimate error of state and used as a module for filter performance evaluation. Then, the construction of the proposed method is presented, together with the analysis of the noise variance of multi-step pseudo-measurement. Ultimately, the efficacy of the MPKF is confirmed through a real-world vehicle experiment involving a tightly-coupled INS/GNSS integrated navigation application, demonstrating a noteworthy enhancement in navigation precision within densely wooded and built-up areas. Compared to the standard EKF and enhanced redundant measurement-based adaptive Kalman filter (ERMAKF), the proposed algorithm improves the positioning accuracy by 48% and 34%, velocity accuracy by 50% and 35%, and attitude accuracy by 38% and 48%, respectively, in the urban building segment.

A lightweight odometry network for GNSS/INS integration during GNSS outages

In challenging environments like urban canyons and tunnels, the Global Navigation Satellite System (GNSS) signal can be interrupted. When this happens, the integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) navigation system relies solely on INS, resulting in rapid dispersion of positioning accuracy over time. Incorporating odometer information into a filter algorithm is one potential solution for correcting INS errors and improving navigation accuracy. However, this approach increases the cost and power consumption of the system. To implement an odometer-assisted integrated navigation system without inflating cost and power consumption, we propose a lightweight odometer network, LONet. This network can emulate a wheeled odometer, determine the carrier’s forward velocity using Inertial Measurement Unit (IMU) output data, and utilize non-holonomic constraint (NHC) and zero velocity update (ZUPT) to maintain the system’s positioning accuracy. To evaluate the performance of our network, we conducted velocity estimate experiments across different velocity intervals. The results demonstrated that our network requires fewer parameters and produces lower errors in estimated velocity compared to state-of-the-art networks. Furthermore, we integrated LONet into the navigation system to mitigate the effects of GNSS signal outages. The results show that the LONet-assisted integrated navigation system achieved horizontal errors comparable to, and sometimes lower than, those obtained using a real wheeled odometer.

In Situ Calibration and Trajectory Enhancement of UAV and Backpack LiDAR Systems for Fine-Resolution Forest Inventory

Forest inventory has been relying on labor-intensive manual measurements. Using remote sensing modalities for forest inventory has gained increasing attention in the last few decades. However, tools for deriving accurate tree-level metrics are limited. This paper investigates the feasibility of using LiDAR units onboard uncrewed aerial vehicle (UAV) and Backpack mobile mapping systems (MMSs) equipped with an integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) to provide high-quality point clouds for accurate, fine-resolution forest inventory. To improve the quality of the acquired point clouds, a system-driven strategy for mounting parameters estimation and trajectory enhancement using terrain patches and tree trunks is proposed. By minimizing observed discrepancies among conjugate features captured at different timestamps from multiple tracks by single/multiple systems, while considering the absolute and relative positional/rotational information provided by the GNSS/INS trajectory, system calibration parameters and trajectory information can be refined. Furthermore, some forest inventory metrics, such as tree trunk radius and orientation, are derived in the process. To evaluate the performance of the proposed strategy, three UAV and two Backpack datasets covering young and mature plantations were used in this study. Through sequential system calibration and trajectory enhancement, the spatial accuracy of the UAV point clouds improved from 20 cm to 5 cm. For the Backpack datasets, when the initial trajectory was of reasonable quality, conducting trajectory enhancement significantly improved the relative alignment of the point cloud from 30 cm to 3 cm, and an absolute accuracy at the 10 cm level can be achieved. For a lower-quality trajectory, the initial 1 m misalignment of the Backpack point cloud was reduced to 6 cm through trajectory enhancement. However, to derive products with accurate absolute accuracy, UAV point cloud is required as a reference in the trajectory enhancement process of the Backpack dataset.

IN-SITU CALIBRATION AND TRAJECTORY ENHANCEMENT OF UAV AND BACKPACK LIDAR SYSTEMS FOR HIGH-RESOLUTION FOREST INVENTORY

Abstract. Using remote sensing modalities for forest inventory has gained increasing attention in the last few decades. However, tools for deriving accurate tree-level metrics are limited. This paper investigates the feasibility of using LiDAR units onboard uncrewed aerial vehicle (UAV) and Backpack mobile mapping systems (MMS) equipped with an integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) to provide high quality point clouds for accurate, high-resolution forest inventory. To improve the quality of acquired point clouds, a system-driven strategy for mounting parameters refinement and trajectory enhancement using terrain patches and tree trunks is proposed. To evaluate the performance of the proposed strategy, two UAV and one Backpack datasets covering a forest plantation are used in this study. Through sequential system calibration and trajectory enhancement, the spatial accuracy of the UAV point clouds improves from 20 cm to 5 cm. For the Backpack dataset, when the initial trajectory is of reasonable accuracy, conducting trajectory enhancement significantly improves the alignment of the point cloud from 30 cm to 3cm. For a lower-quality trajectory, using the UAV data as a reference, the misalignment is reduced from 1 m to 3 cm.

A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS/GNSS Integration

The resolution accuracy of the inertial navigation system/global navigation satellite system (INS/GNSS) integrated system would be degraded in challenging areas. This paper proposed a novel algorithm, which combines the second-order mutual difference method with the maximum correntropy criteria extended Kalman filter to address the following problems (1) the GNSS measurement noise estimation cannot be isolated from the state estimation and suffers from the auto-correlated statistic sequences, and (2) the performance of EKF would be degraded under the non-Gaussian condition. In detail, the proposed algorithm determines the possible distribution of the measurement noise by a kernel density function detection, then depending on the detection result, either the difference sequences–based method or an autoregressive correction algorithm’s result is utilized for calculating the noise covariance. Then, the obtained measurement noise covariance is used in MCEKF instead of EKF to enhance filter adaptiveness. Meanwhile, to enhance the numerical stability of the MCEKF, we adopted the Cholesky decomposition to calculate the matrix inverse in the kernel function. The road experiment verified that our proposed method could achieve more accurate navigation resolutions than the compared ones.

UAV-Based Remote Sensing for Detection and Visualization of Partially-Exposed Underground Structures in Complex Archaeological Sites

The utilization of remote sensing technologies for archaeology was motivated by their ability to map large areas within a short time at a reasonable cost. With recent advances in platform and sensing technologies, uncrewed aerial vehicles (UAV) equipped with imaging and Light Detection and Ranging (LiDAR) systems have emerged as a promising tool due to their low cost, ease of deployment/operation, and ability to provide high-resolution geospatial data. In some cases, archaeological sites might be covered with vegetation, which makes the identification of below-canopy structures quite challenging. The ability of LiDAR energy to travel through gaps within vegetation allows for the derivation of returns from hidden structures below the canopy. This study deals with the development and deployment of a UAV system equipped with imaging and LiDAR sensing technologies assisted by an integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) for the archaeological mapping of Dana Island, Turkey. Data processing strategies are also introduced for the detection and visualization of underground structures. More specifically, a strategy has been developed for the robust identification of ground/terrain surface in a site characterized by steep slopes and dense vegetation, as well as the presence of numerous underground structures. The derived terrain surface is then used for the automated detection/localization of underground structures, which are then visualized through a web portal. The proposed strategy has shown a promising detection ability with an F1-score of approximately 92%.

A Hypothesis Test-Constrained Robust Kalman Filter for INS/GNSS Integration With Abnormal Measurement

This paper presents a hypothesis test-constrained robust Kalman filter for INS/GNSS (inertial navigation system/global navigation satellite system) integrated navigation in the presence of measurement outliers. This method estimates measurement noise covariance by combining hypothesis test with the maximum likelihood theory to handle measurement outliers. A chi square test and an improved sequential probability ratio test are established to characterize abrupt and slow-growing measurement outliers, respectively. Subsequently, these two hypothesis tests are used to constrain the maximum likelihood estimation of measurement noise covariance to accommodate measurement outliers. Based on the hypothesis test-constrained maximum likelihood estimation of measurement noise covariance, a robust Kalman filter is developed for INS/GNSS integrated navigation in the presence of measurement outliers. Simulation and experimental results demonstrate that the proposed method can effectively deal with measurement outliers. The resultant navigation accuracy is about 46% and 30% higher than that of the Kalman filter and maximum likelihood-based robust Kalman filter for INS/GNSS integrated navigation.

Cubature Kalman filter with closed-loop covariance feedback control for integrated INS/GNSS navigation

Cubature Kalman Filter (CKF) offers a promising solution to handle the data fusion of integrated nonlinear INS/GNSS (Inertial Navigation System/Global Navigation Satellite System) navigation. However, its accuracy is degraded by inaccurate kinematic noise statistics which originate from disturbances of system dynamics. This paper develops a method of closed-loop feedback covariance control to address the above problem of CKF. In this method, the posterior state and its covariance are fed back to the filtering process to constitute a closed-loop structure for CKF covariance propagation. Subsequently, based on the maximum likelihood principle, a control scheme of the prior state covariance is established by using the feedback state and covariance within an estimation window and further adopting a proportional coefficient to amplify the feedback terms in recent time steps for the full use of new information to reflect actual system characteristics. Since it does not directly use kinematic noise covariance, the proposed method can effectively avoid the adverse impact of inaccurate kinematic noise statistics on filtering solutions. Further, it can also guarantee the prior state covariance to be positive semi-definite without involving extra measures. The efficacy of the proposed method is validated by simulations and experiments for integrated INS/GNSS navigation.

OdoNet: Untethered Speed Aiding for Vehicle Navigation Without Hardware Wheeled Odometer

Odometer has been proven to significantly improve the robustness and accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integrated vehicle navigation in GNSS-denied environments. However, odometer is inaccessible in many applications, especially for aftermarket devices and smartphones. To apply forward speed aiding without hardware wheeled odometer, we propose OdoNet, an untethered one-dimensional Convolution Neural Network (CNN)-based pseudo-odometer model learning from a single Inertial Measurement Unit (IMU). Dedicated experiments have been conducted to verify the generalization capability and the precision of the OdoNet. The results indicate that the IMU individuality, the vehicle loads, and the road conditions have little impact on the robustness and precision of the OdoNet, while the IMU biases and the mounting angles may notably ruin the OdoNet. Hence, a data-cleaning procedure is adopted to effectively mitigate the impacts of the IMU biases and the mounting angles. Compared to the processing mode using only non-holonomic constraint (NHC), by employing the pseudo-odometer, the positioning error is reduced by around 68%, while the percentage is around 74% for the hardware wheeled odometer. In conclusion, the proposed OdoNet can be employed as an untethered pseudo-odometer for vehicle navigation.

An Effective Integrity Monitoring Scheme for GNSS/INS/Vision Integration Based on Error State EKF Model

It is well-known that the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) /Vision integration has been increasingly used for safety-critical applications like self-driving cars. However, the performance of the GNSS/INS/Vision integration degrades due to unknown faults. Therefore, it is essential to develop integrity monitoring algorithms for the integrated navigation system. A new protection level (PL) formula to ensure the integrity of the state estimation of the GNSS/INS/Vision integration is proposed, which can be calculated by the relation between the filter estimation error and faults. An integrity risk allocation tree is developed for each sensor fault hypothesis including the nominal hypothesis, and the specific PL is given in the case of GNSS, INS and visual measurement faults. In addition, the performance of the proposed PL is comprehensively evaluated. A field vehicular test was conducted to evaluate the performance of the integrity monitoring algorithm for the GNSS/INS/Vision integration. The results demonstrate that the proposed PL for the GNSS/INS/Vision integration can fit the position error against six different fault modes.

Improving GNSS/INS Tightly Coupled Positioning by Using BDS-3 Four-Frequency Observations in Urban Environments

Vehicular positioning in urban environments has become a research hotspot in recent years, and global navigation satellite system/inertial navigation system (GNSS/INS) tightly coupled positioning is a commonly used method. With the broadcast of BDS-3 and Galileo four-frequency signals, the multi-frequency and multi-system tightly coupled positioning method provides more possibilities for vehicular positioning in urban environments. At present, most of the studies on multi-frequency and multi-system mainly focus on static or baseline solutions, and there are few studies on the urban dynamic environment. In this paper, based on the triple-frequency GPS/BDS-2/INS tightly coupled positioning model, the BDS-3 four-frequency observation is introduced to conduct a preliminary study on the performance of GPS/BDS-2/BDS-3/INS tightly coupled positioning. Taking into account the positioning accuracy and calculation efficiency of the tightly coupled positioning, single epoch extra-wide-lane/wide-lane (EWL/WL) observation is used to participate in the modeling of tightly coupled positioning. The EWL/WL ambiguity is solved by the geometry-free (GF) method, in which triple-frequency carrier ambiguity resolution (TCAR) and four-frequency carrier ambiguity resolution (FCAR) are used for triple-frequency and four-frequency observations, respectively. Finally, the positioning performance of the tightly coupled method in this paper is evaluated through vehicular experiment. The experimental results show that in the urban dynamic environment, due to the higher quality of the linear combination of BDS-3 four-frequency, the positioning accuracy of the BDS-3/INS tightly coupled was slightly better than that of the triple-frequency BDS-2/INS. Compared with GPS/BDS-2/INS, the GPS/BDS-2/BDS-3/INS tightly coupled positioning accuracy increased by 29.1% and 58.7% in horizontal and vertical directions, respectively, which can realize decimeter positioning accuracy in urban environments.

Tightly Coupled GNSS/INS Integration Spoofing Detection Algorithm Based on Innovation Rate Optimization and Robust Estimation

The spoofing detection algorithm for a global navigation satellite system/inertial navigation system (GNSS/INS) integrated navigation system based on the innovation rate and robust estimation has limitations such as extensive or invalid detection times, high missed detection rates, and false alarm rates. This study addresses these limitations by proposing a tightly coupled GNSS/INS integration spoofing detection algorithm based on innovation rate optimization and robust estimation. The proposed algorithm improved the normalized innovation of a small step or slow-growing ramp, thereby optimizing its innovation rate test statistics. The proposed approach also reduces the spoofing effect on the innovation rate by adaptively adjusting a gain matrix using robust estimation, thus improving the detection ability further. The simulation results show that the detection time of the proposed algorithm is reduced by 51.9% on average when dealing with small step or slow-growing ramp spoofing. Moreover, the missed detection rate decreases by 58% on average, and the false alarm rate remains at approximately zero. The proposed algorithm is suitable for spoofing detection in unmanned aerial vehicle applications of GNSS/INS integrated navigation systems with the advantages of fast detection and good performance.

LiDAR-sensed tree canopy correction in uneven terrain conditions using a sensor fusion approach for precision sprayers

Precision spraying is one of the most promising techniques to produce healthy and sustainably profitable crops. However, accurate canopy density measurements for precision spraying decisions are still a challenging endeavor, especially in orchards with uneven terrain conditions. A sensor fusion-based canopy point correction system was developed with a 3D light detection and ranging (LiDAR) sensor and an inertial navigation system-global navigation satellite system (INS-GNSS) for accurate tree canopy density measurement. The LiDAR sensor was used to acquire the tree canopy architectures, while the INS-GNSS sensor was to evaluate the terrain slopes and the tree georeferenced locations. A mathematical model was developed to perform the simulation for correction of canopy points based on given changes in the roll, pitch, and yaw angles. A sensor fusion algorithm was developed to process the canopy point corrections for the tree fruit orchards with three different sloping conditions, including longitudinal, lateral, and combination of both slopes. Simulation results reported that the developed model established the correction of tree canopy points with varying roll, pitch, and yaw angles. Field evaluation results suggested that the developed system could be used for correcting canopy points at any sloping conditions in various terrains. The measured tree canopy density from the corrected canopy points reported a possible of off-target chemical reduction up to 13.87%, 5.19%, and 15.45% in orchard sites 1, 2 and 3, respectively. With the accurate tree canopy density measurement, it is anticipated that the developed system could be used to reduce the off-target deposition for precision spraying applications in uneven tree fruit orchards.

Vehicle Location Algorithm Based on Federated Learning and Smart Phone in GNSS Low Sampling Rate Scene

In the existing vehicle positioning system based on Global Navigation Satellite System/Inertial Navigation System (GNSS/INS), when the GNSS signal is lost, the error accumulated by using only the INS will damage the positioning accuracy. In order to improve the accuracy, this paper proposed a positioning method based on data-driven and learning models, which utilized distributed data sets to collaboratively construct accurate positioning models through federated fusion algorithms without sacrificing user privacy. In the field scenarios of IID and Non-IID types, this paper compared the performance of INS and the existing two typical methods, DeepSense and PVAUA, it is verified that the two federated learning algorithm models constructed had higher positioning accuracy in different scenarios and different GNSS signal loss durations. The results were analyzed.

Polar Region Integrated Navigation Method Based on Covariance Transformation

Aircraft flying the trans-arctic routes usually apply inertial navigation mechanization in two different navigation frames, e.g., the local geographic frame and the grid frame. However, this change of navigation frame will cause filter overshoot and error discontinuity. To solve this problem, taking the inertial navigation system/global navigation satellite system (INS/GNSS) integrated navigation system as an example, an integrated navigation method based on covariance transformation is proposed. The relationship of the system error state between different navigation frames is deduced as a means to accurately convert the Kalman filter’s covariance matrix. The experiment and semi-physical simulation results show that the presented covariance transformation algorithm can effectively solve the filter overshoot and error discontinuity caused by the change of navigation frame. Compared with non-covariance transformation, the system state error is thereby reduced significantly.

System Calibration Including Time Delay Estimation for GNSS/INS-Assisted Pushbroom Scanners Onboard UAV Platforms

Unmanned aerial vehicles (UAVs ) equipped with imaging sensors and integrated global navigation satellite system/inertial navigation system (GNSS/INS ) units are used for numerous applications. Deriving reliable 3D coordinates from such UAVs is contingent on accurate geometric calibration, which encompasses the estimation of mounting parameters and synchronization errors. Through a rigorous impact analysis of such systematic errors, this article proposes a direct approach for spatial and temporal calibration (estimating system parameters through a bundle adjustment procedure) of a GNSS/INS -assisted pushbroom scanner onboard a UAV platform. The calibration results show that the horizontal and vertical accuracies are within the ground sampling distance of the sensor. Unlike for frame camera systems, this article also shows that the indirect approach is not a feasible solution for pushbroom scanners due to their limited ability for decoupling system parameters. This finding provides further support that the direct approach is recommended for spatial and temporal calibration of UAV pushbroom scanner systems.

SARSA in extended Kalman Filter for complex urban environments positioning

Nowadays, the Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) integrated navigation system is widely used in many applications. The extended Kalman Filter (EKF) is a popular data fusion method for the INS/GNSS integrated navigation system. However, the process and measurement noise covariance matrices of the EKF cannot be modelled accurately due to varied scenes and complicated GNSS signal errors in urban environments, which undermines or deteriorates the EKF's performance. To mitigate noise covariance uncertainties' influence, this paper proposes an adaptive EKF algorithm named SARSA EKF, which enables the State-Action-Reward-State-Action (SARSA) method in EKF to realise the autonomous selection of the noise covariance matrices based on the Q-value. Meanwhile, a pruning algorithm is designed to remove inappropriate selections of noise covariance matrices and enhance the performance. The simulation and field test results indicate that the positioning accuracy of the SARSA EKF is better than the traditional EKF and the Q-learning EKF (QLEKF). The positioning accuracy's mean error of the SARSA EKF decreases by 34.32% and 25.95% compared with the traditional EKF and the QLEKF, respectively. And the positioning accuracy's standard deviation of the SARSA EKF decreases by 41.74% and 32.99% compared with the traditional EKF and the QLEKF, respectively.

Covariance transformation method for polar integrated navigation

The aircraft flying the trans-arctic routes faces the problem that the changes of navigation frames will affect the navigation accuracy. To solve this problem, taking Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) integrated navigation system as an example, an integrated navigation method based on covariance transformation is proposed. This method aims at finding the transformation relationship of the system error state and the covariance between different navigation frames. The experiment and semi-physical simulation results show that the covariance transformation algorithm can effectively solve the filtering instability caused by the changes of the navigation frame. Compared with the non-covariance transformation, the system state error is reduced by an order of magnitude.

Cubature Kalman Filter With Both Adaptability and Robustness for Tightly-Coupled GNSS/INS Integration

Tightly-coupled GNSS/INS (Global Navigation Satellite System/Inertial Navigation System) integration is of importance to vehicle positioning. However, this integration technology has difficulty in achieving optimal positioning solutions for the dynamic systems involving strong nonlinearity and systematic modelling error. This paper proposes a new methodology to address the problem of tightly-coupled GNSS/INS integration. This methodology rigorously derives a novel adaptive CKF (Cubature Kalman Filter) with fading memory for kinematic modelling error and a new robust CKF with emerging memory for observation modelling error, using the concept of Mahalanobis distance without involving artificial empiricism. Based on this, a new CKF with both adaptability and robustness is further developed by fusing the results of the standard CKF, adaptive CKF and robust CKF via the principle of interacting multiple model (IMM). Simulation and experiment results together with comparison analysis prove that the proposed methodology can curb the interferences of both kinematic and observation modelling errors on state estimation, leading to improved positioning accuracy for vehicle positioning via tightly-coupled GNSS/INS integration.

Optical and Mass Flow Sensors for Aiding Vehicle Navigation in GNSS Denied Environment.

Nowadays, autonomous vehicles have achieved a lot of research interest regarding the navigation, the surrounding environmental perception, and control. Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) is one of the significant components of any vehicle navigation system. However, GNSS has limitations in some operating scenarios such as urban regions and indoor environments where the GNSS signal suffers from multipath or outage. On the other hand, INS standalone navigation solution degrades over time due to the INS errors. Therefore, a modern vehicle navigation system depends on integration between different sensors to aid INS for mitigating its drift during GNSS signal outage. However, there are some challenges for the aiding sensors related to their high price, high computational costs, and environmental and weather effects. This paper proposes an integrated aiding navigation system for vehicles in an indoor environment (e.g., underground parking). This proposed system is based on optical flow and multiple mass flow sensors integrations to aid the low-cost INS by providing the navigation extended Kalman filter (EKF) with forward velocity and change of heading updates to enhance the vehicle navigation. The optical flow is computed for frames taken using a consumer portable device (CPD) camera mounted in the upward-looking direction to avoid moving objects in front of the camera and to exploit the typical features of the underground parking or tunnels such as ducts and pipes. On the other hand, the multiple mass flow sensors measurements are modeled to provide forward velocity information. Moreover, a mass flow differential odometry is proposed where the vehicle change of heading is estimated from the multiple mass flow sensors measurements. This integrated aiding system can be used for unmanned aerial vehicles (UAV) and land vehicle navigations. However, the experimental results are implemented for land vehicles through the integration of CPD with mass flow sensors to aid the navigation system.