An efficient tuning framework for Kalman filter parameter optimization using design of experiments and genetic algorithms

Tightly-coupled (TC) fusion of Inertial Measurement Units (IMUs) with Global Navigation Satellite Systems (GNSSs) is a common technique that provides high-rate positioning even under GNSS interruptions. In order to provide accurate positioning, errors of IMU and GNSS must be modelled and estimated by filtering techniques such as Extended Kalman Filter (EKF). Due to nonlinearity and stochastic characteristics of IMU and GNSS system and measurement models, robust filter design has been a challenge. Conventional design techniques use mission-specific fixed models and trial-and-error noise parameter tuning to design IMU/GNSS filters. These conventional techniques are inflexible and do not always lead to accurate designs as there are no ways to verify the filter ability to estimate sensors errors accurately. To address this challenge, this paper presents a flexible design framework and a systematic procedure for TC IMU/GNSS fusion. The framework utilizes symbolic engines to represent and linearize system and measurement models. Symbolic engines are flexible in new models and fusion algorithms development. In order to evaluate the estimation of sensors errors, an Inverse-Kinematics module is developed to generate error-free sensors measurements which can be contaminated by known errors. The filter parameters are tuned using Genetic Algorithms and the performance is evaluated based on the accuracy of estimating all states including the added known errors. The framework has been used to develop a quaternion-based EKF design and verified on real raw IMU/GNSS data. The results showed that the developed framework greatly reduces efforts to design robust and accurate fusion systems for TC IMU/GNSS integration.

Abstract. Multisensor systems are essential for autonomous navigation applications to achieve reliable accuracy. Integrating the Global Navigation Satellite System (GNSS) and the Inertial Navigation System (INS) is the most common integration scheme. However, this integration is unreliable in different scenarios since the GNSS signal may deteriorate in downtown areas or suffer from a blockage in underground and indoor areas. Therefore, other sensors are integrated with INS to compensate for GNSS outages. This paper proposes a novel algorithm for radar/INS tightly-coupled integration for autonomous navigation applications. This algorithm is applied in multiple steps. Radar data analysis is the first and most crucial step to remove the noisy data and the outliers and keep the useful objects. Then, data association is done to match the detected objects between radar frames. The tightly-coupled integration is performed at the measurement level through an Extended Kalman Filter (EKF), where the distance between the INS and the detected objects can be predicted from the INS and measured from the radar. Real data was collected from four Frequency Modulated Continuous Wave (FMCW) radar units in Calgary's suburban areas and Toronto's downtown area. The proposed algorithm was tested and assessed by introducing simulated GNSS single outages with different durations. The results show an enhancement in the vehicle's position by about 94% to 96%.

Now a days, Unmanned Aerial Vehicles (UAVs) have been exploited in numerous civil and military aspects such as disaster management and border monitoring. Although most of these UAVs are equipped with Global Navigation Satellite System (GNSS) / Inertial Navigation System (INS) reliable integrated system for localization proposes, they are susceptible to lose their GNSS signals under some environmental and artificial challenging circumstances such as, flying in urban areas, jamming, and spoofing. In such complicated scenarios, the navigation solution will degrade rapidly due to the accumulated INS drift errors. Although various aiding sensors such as cameras, and radar are employed to mitigate the INS drift errors, their estimated positioning accuracy is still affected by some factors. This paper presents a nested optimal filter approach (G-H filter, Extended Kalman Filter (EKF)) for UAVs in GNSS denied environment, to enhance the estimated positioning accuracy by integrating the Radar Odometry (RO)/INS/MAG to sustain a reliable navigation solution during GNSS outage. First, the UAV relative velocity is calculated based on image processing approach from the radar range doppler map, then the G-H filter is deployed to improve the accuracy of the vehicle estimated forward velocities based on the vehicle dynamic characteristics to reduce the effect of unrealistic velocity estimate from the radar. These improved velocities are then fused with the Inertial Measurement Unit (IMU), magnetometer, and barometer via EKF to mitigate the positioning RMS errors during the GNSS signals outages. The experimental results demonstrate the proposed system's ability to notably enhance the 3D positioning accuracy during the GNSS signal outage by more than 99% when compared to a stand-alone IMU dead reckoning solution.

Path-following control systems for ships can be designed using both heading and course angle autopilots in conjunction with a proportional line-of-sight (LOS) guidance law. Ships are usually equipped with a gyrocompass from a safety perspective since magnetic compasses are susceptible to magnetic disturbances. Unfortunately, the gyrocompass is an expensive device, and smaller vessels and boats cannot afford to use this as the primary device for steering. An alternative solution is to compute the course over ground (COG) and speed over ground (SOG) from global navigation satellite systems (GNSS) and use these signals for feedback control. This article presents course autopilot design for path following and a five-state extended Kalman filter (EKF) to estimate the COG and SOG efficiently. Even though many algorithms exist for computation of the COG and SOG, it is advantageous to design an EKF since a state estimator can be extended to include other sensory systems such as Doppler Velocity Log (DVL), radar, attitude rate sensors, computer vision systems, etc. This is in contrast to proprietary systems that do not allow the user to modify the software. The convergence and accuracy of the EKF are significantly improved by using target-tracking models in combination with kinematic equations. A high-fidelity model of a MARINER class cargo ship is used in the path-following case study. From the simulation study, it can be concluded that the EKF successfully estimates the COG and the SOG from GNSS measurements during path following. The solution is remarkably robust and accurate, and when combined with a course autopilot, the need for a compass is eliminated during path following.

We describe an integrated navigation system based on Global Navigation Satellite Systems (GNSS), an Inertial Navigation System (INS) and terrestrial ranging technologies that can support accurate and seamless indoor-outdoor positioning. To overcome severe multipath disturbance in indoor environments, Locata technology is used in this navigation system. Such a “Locata-augmented” navigation system can operate in different positioning modes in both indoor and outdoor environments. In environments where GNSS is unavailable, e.g. indoors, the proposed system is designed to operate in the Locata/INS “loosely-integrated” mode. On the other hand, in outdoor environments, all GNSS, Locata and INS measurements are available, and all useful information can be fused via a decentralised Federated Kalman filter. To evaluate the proposed system for seamless indoor-outdoor positioning, an indoor-outdoor test was conducted at a metal-clad warehouse. The test results confirmed that the proposed navigation system can provide continuous and reliable position and attitude solutions, with the positioning accuracy being better than five centimetres.

Accuracy assessment of integrated GNSS measurements with LIDAR mobile mapping data in urban environments

The performance of navigation can be significantly enhanced by coupling the Global Navigation Satellite System (GNSS) and the Inertial Navigation System (INS) because the characteristics of these two systems complement each other. Among those structures of coupling, Ultra-Tight Coupling (UTC) fully uses the information of both systems, therefore has attracted much attention of researchers. To do researches of UTC, it is reasonable that the simulation platform should be built first. Although there have been several open source simulation platforms for the researches of Tight Coupling (TC), which have become important tools for the analysis of TC, the researches about designing simulation platform of UTC is rare, and the standard of simulation has not been settled either, becoming a barrier of the development of UTC. In this paper, a Software Defined Receiver (SDR) for UTC simulation is proposed. The SDR is derived from the open source code of TC SDR with many modules added, including the GNSS signal generation, transmitting, acquisition, and tracking. The tracking results of receiver are transformed to the errors of pseudo-range, and then used in the Extended Kalman Filter (EKF) for coupling. The output of EKF on the other hand adjusts the INS and the loop of GNSS as feedback. The design of SDR for UTC does not need to simulate the navigation data, hence is easy to be realized. The simulation results are also presented to show the validity of the designed SDR.

Abstract. Typically, in situations where Global Navigation Satellite System (GNSS) signals are unavailable, navigation systems rely on integrating GNSS and inertial navigation system (INS) data. While such integration can provide accurate positioning during short GNSS signal outages, it cannot sustain prolonged GNSS outages. The reason for this is that the system's performance depends solely on the INS and can result in significant errors over time. To address this issue, additional onboard sensors are necessary. This study proposes a navigation system that integrates INS and LiDAR simultaneous localization and mapping (SLAM) using an extended Kalman filter (EKF). The system was tested using the raw KITTI dataset in various outdoor driving scenarios without GNSS signals. It is shown that the proposed system significantly outperformed the INS-only system, with an average RMSE improvement of around 93% and 58% in the horizontal and the up directions, respectively.

Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) integration requires accurate modelling of both INS deterministic and stochastic errors. The Allan Variance (AV) analysis on INS static data is one method of determining INS stochastic errors. However, it is known that INS errors can vary depending on a vehicle’s motion and environment, and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic. In order to overcome this limitation, this paper proposes the use of Dynamic Allan Variance (DAV). The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV. The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV, applied on a kinematic dataset compared to the AV, applied on a static laboratory dataset.

The possible applications and benefits of autonomous Unmanned Aerial Vehicle (UAV) use in urban areas are gaining considerable attention. Before these possibilities can be realized, it is essential that UAVs be able to navigate reliably and precisely in urban environments. The most common means of determining the location of a UAV is to utilize position measurements from Global Navigation Satellite Systems (GNSS). In urban environments, however, GNSS measurements are significantly degraded due to occlusions and multipath. This research analyzes the use of camera Line-of-Sight (LOS) measurements to self-describing fiducials as a replacement for conventional GNSS measurements. An extended Kalman filter (EKF) is developed and validated for the purpose of combining continuous measurements from an Inertial Measurement Unit (IMU) with the discrete LOS measurements to accurately estimate the states of a UAV. The sensitivity of the estimation error covariance to various system parameters is assessed, including IMU grade, fiducial placement, vehicle altitude, and image processing frequency.

This paper explores the pervasive challenges of pedestrian positioning using smartphones in densely populated urban environments where Global Navigation Satellite System (GNSS) signals are inaccessible, for example, in indoor areas. Existing sensor-based positioning methods, such as inertial navigation systems (INS), GNSS, and visual-inertial odometry (VIO), suffer from inherent restrictions that compromise the accuracy and reliability of the positioning performance. An approach based on machine learning is proposed to address these limitations, employing the Support Vector Machine (SVM) algorithm to accurately distinguish indoor/outdoor (IO) based on the measurement of GNSS. The proposed approach in this study seamlessly incorporates 3D mapping aided (3DMA) GNSS measurements and localized estimations derived by VIO via factor graph optimization (FGO), complemented by an IO detection switch, to achieve accurate pose estimation and effectively eliminate global drift. The system's effectiveness and robustness are rigorously assessed through comprehensive extensive real-life experiments, with an average reduction of 4 meters, leading to noteworthy and statistically significant findings. Received: 1 April 2024 | Revised: 13 September 2024 | Accepted: 26 October 2024 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement The source code that supports the findings of this study is openly available in 3DMAGNSSVINS-IOFGO at https://github.com/queenie-ho/3DMAGNSSVINS-IOFGO. Author Contribution Statement Hiu-Yi Ho and Hoi-Fung Ng: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Weisong Wen: Conceptualization, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition. Yanlei Gu: Resources, Writing - review & editing, Writing - review & editing. Li-Ta Hsu: Conceptualization, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition.

This paper investigates into the feasibility of a combined use of Ultra-wideband (UWB) and Global Navigation Satellite System (GNSS) / Inertial Navigation System (INS) for integrated navigation in GNSS challenged environments. The performance of the original integrated GNSS/INS navigation system deteriorated rapidly due to the GNSS signal outages. The position information provided by UWB is used as the observation quantity of Extend Kalman Filter (EKF) to make up for the influence of GNSS signal loss. Considering the positioning service performance provided by UWB is closely related to the geometric distribution of base station of UWB, an optimization searching based on maximum convex-hull (OSMC) method is adopted to establish the optimal base station layout scheme. The features of navigation have been investigated in vehicle test with the results showing clear evidence that the method can resist the impact of GNSS outages effectively and the positioning information are stable and reliable.

Genetic algorithm (GA) is applied in this paper to optimize parameters of the extended Kalman filter (EKF) in a speed-senserless field-oriented controller (FOC) system. The main parameters of EKF are the covariance matrics Q and R, which are bound respectively to the state and measurement noises. As for speed-sensorless FOC system, the convergence and precision of both rotor speed and flux estimation depend on the accuracy of the models of system noise and measurement noise, i.e. Q and R. A GA training simulation system of optimum parameters of EKF is given and the simulation results show the efficiency and rationality of the algorithm.

Adaptive Kalman filters (AKF) have been widely applied to the inertial navigation system (INS)/global navigation satellite system (GNSS) integrated navigation system. However, the traditional AKF methods suffer from the problems of filtering instability or covariance underestimation, especially when the GNSS measurement disturbances occur. In this paper, an enhanced redundant measurement-based AKF is developed to improve the filtering performance. The scheme is based on the mutual difference sequence derived from the redundant measurement of INS. By using the mutual difference sequence, the measurement noise covariance can be estimated without being affected by the inaccuracy estimates, hence avoiding the risk of filtering divergence. In addition, the kernel density estimation is used to estimate the GNSS measurement noise’s probability density to detect whether the Gaussian properties of the measurement noise are maintained. When the noise statistics are far from Gaussian distribution, the difference sequence will be modeled as an autoregressive process using the Burg’s method. The real variance of the difference sequence can then be updated relying on the autoregressive model in order to avoid the covariance underestimation. A field experiment was carried out to evaluate the performance of the proposed method. The test results demonstrate that the proposed method can effectively mitigate the GNSS measurement disturbances and improve the accuracy of the navigation solution.

The dominant navigation system for low-cost, mass-market Unmanned Aerial Vehicles (UAVs) is based on an Inertial Navigation System (INS) coupled with a Global Navigation Satellite System (GNSS). However, problems tend to arise during periods of GNSS outage where the navigation solution degrades rapidly. Therefore, this paper details a model-based integration approach for fixed wing UAVs, using the Vehicle Dynamics Model (VDM) as the main process model aided by low-cost Micro-Electro-Mechanical Systems (MEMS) inertial sensors and GNSS measurements with moment of inertia calibration using an Unscented Kalman Filter (UKF). Results show that the position error does not exceed 14.5 m in all directions after 140 s of GNSS outage. Roll and pitch errors are bounded to 0.06 degrees and the error in yaw grows slowly to 0.65 degrees after 140 s of GNSS outage. The filter is able to estimate model parameters and even the moment of inertia terms even with significant coupling between them. Pitch and yaw moment coefficient terms present significant cross coupling while roll moment terms seem to be decorrelated from all of the other terms, whilst more dynamic manoeuvres could help to improve the overall observability of the parameters.