A new method for compensating the errors of integrated navigation systems using artificial neural networks

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.

Special approaches are required to integrate low-cost MEMS-based inertial navigation system (MEMS-INS) with global navigation satellite system (GNSS). This article proposes a robust GNSS/MEMS-strapdown inertial navigation system (SINS), the tightly coupled navigation approach aided by non-holonomic constraint (NHC). The tight integration model is adopted to overcome the accuracy degradation caused by changing satellite geometry and frequent GNSS outages in urban areas. The innovation-based test statistic is devised to enhance the filtering with the resistance to GNSS outliers. To further improve the stand-alone accuracy during relatively long GNSS outages, the virtual measurement is also introduced using the NHC condition that land vehicle does not slip and always remain in contact with the ground. The field test results with continuous GNSS aiding indicate that the proposed algorithm can improve overall accuracy in position, velocity, and attitude by about 16, 43, and 19% with immunity from GNSS outliers, compared with the traditional loosely coupled (LC) method. Even during 60-s GNSS outages, the proposed algorithm can effectively compensate MEMS-SINS errors, accomplishing the overall accuracy improvements by about 46% (position), 35% (velocity), and 15% (attitude), compared with the traditional LC counterpart.

Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student’s t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student’s t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student’s t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively.

Publication in the conference proceedings of EUSIPCO, Glasgow, Scotland, 2009

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.

Regardless of whether the global navigation satellite system (GNSS)/inertial navigation system (INS) is integrated or the INS operates independently during GNSS outages, the stochastic error of the inertial sensor has an important impact on the navigation performance. The structure of stochastic error in low-cost inertial sensors is quite complex; therefore, it is difficult to identify and separate errors in the spectral domain using classical stochastic error methods such as the Allan variance (AV) method and power spectral density (PSD) analysis. However, a recently proposed estimation, based on generalized wavelet moment estimation (GMWM), is applied to the stochastic error modeling of inertial sensors, giving significant advantages. Focusing on the online implementation of GMWM and its integration within a general navigation filter, this paper proposes an algorithm for online stochastic error calibration of inertial sensors in urban cities. We further develop the autonomous stochastic error model by constructing a complete stochastic error model and determining model ranking criterion. Then, a detecting module is designed to work together with the autonomous stochastic error model as feedback for the INS/GNSS integration. Finally, two experiments are conducted to compare the positioning performance of this algorithm with other classical methods. The results validate the capability of this algorithm to improve navigation accuracy and achieve the online realization of complex stochastic models.

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

Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) are the most commonly used navigation systems. They both have unique advantages and disadvantages. GNSS is capable of generating precise navigation solutions while enough satellites are in view. However, the GNSS signals are sensitive to the environment. While the signals is attenuated, the GNSS receiver will fail to provide reliable navigation solutions. INS is an advanced navigation system built based on Newton's law. Due to the random noises contained in the Inertial Measurement Unit (IMU), the INS navigation solutions errors diverge over time. Therefore, effective integration of the two common systems can obtain better navigation results than any individual system. In this paper, for enhancing the GNSS/INS tightly integration system with low cost, multiple receivers were employed in the tight integration. Pseudo-range and Pseudo-range rates from the multiple receivers were employed to compose the measurement vector of the integration filter. In order to reduce the computation load, a measurement difference method was proposed. The state vector dimension could be reduced with the measurement difference scheme. Both simulation and field test were carried out for evaluating the performance of the proposed method. Since it was hard to obtain GNSS raw measurements from commercial receivers, self-developed DSP+FPGA (Digital Signal Processor, DSP; Field Programmable Gate Array, FPGA) based GNSS receivers were employed in the field test. The statistical analysis of the results showed that the positioning errors decreased with the receiver's amount increasing. In addition, a measurement difference method was proposed to reduce the state vector dimension for saving the computation load with the identical navigation solutions accuracy.

<h3>Abstract</h3> Aiming to improve the position and velocity precision of the INS/GNSS system during GNSS outages, a novel system that combines unscented Kalman filter (UKF) and nonlinear autoregressive neural networks with external inputs (NARX) is proposed. The NARX-based module is utilized to predict the measurement updates of UKF during GNSS outages. A new offline approach for selecting the optimal inputs of NARX networks is suggested and tested. This approach is based on mutual information (MI) theory for identifying the inputs that influence each of the outputs (the measurement updates of UKF) and lag-space estimation (LSE) for investigating the dependency of these outputs on the past values of the inputs and the outputs. The performance of the proposed system is verified experimentally using a real dataset. The comparison results indicate that the NARX-aided UKF outperforms other methods that use different input configurations for neural networks.

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.

Machine learning (ML) frameworks are investigated for use in simultaneous tracking and navigation (STAN) with low Earth orbit (LEO) satellites. STAN is a navigation paradigm that utilizes specialized LEO receivers to extract navigation observables (e.g., pseudorange and Doppler) from LEO satellite signals. Two neural network architectures are compared: Feed Forward Neural Network (FFNN) and Recurrent Neural Network (RNN). Additionally, two ML-based orbit determination frameworks are compared: ephemeris propagation and residual error propagation. The objective of the comparison is to select an approach with the lowest open-loop propagation error as well as computational cost. Based on simulation results, a nonlinear autoregressive neural network with exogenous inputs (NARX) embedded within the residual error modeling framework is selected as the best ML approach among the compared candidates. Experimental results are presented demonstrating a ground vehicle navigating for a total of 258 seconds, while receiving signals from two Orbcomm LEO satellites. Global navigation satellite system (GNSS) signals were artificially cut off for the last 30 seconds, during which the vehicle traversed a trajectory of 871 m. Two navigation frameworks are compared to estimate the vehicle’s trajectory: (i) LEO signal-aided inertial navigation system (INS) STAN framework using Simplified General Perturbation (SGP4) as its propagator and (ii) the proposed LEO signal-aided INS STAN framework using ML as its propagator. The STAN with SGP4 achieved a three-dimensional (3-D) position root-mean squared error (RMSE) of 30 m. In contrast, the proposed STAN with SGP4+NARX framework achieved a 3-D position RMSE of 3.6 m.

Nowadays, unmanned aerial vehicles (UAVs) play a vital role in many applications and have been successfully employed in a wide variety of applications such as road surveying, precision agriculture, landslide monitoring, cultural heritage mapping, and pipeline monitoring. All of these applications require accurate and stable navigation system. Currently, most of the commercially available UAVs rely on the integration of the Global Satellite Navigation Systems (GNSS) and Inertial Navigation Systems (INS) to estimate the position, velocity, and attitude. The small form factor of modern UAVs allowed them to operate in more challenging environments such as urban and natural canyons. In these environments, the GNSS availability cannot be guaranteed, and hence the navigation solution will deteriorate dramatically during these GNSS signal outages due to the drift exhibited by the inertial navigation solution. Using other aiding sensors is crucial to limit the accumulated errors associated with INS measurements. Onboard cameras can offer a useful clue to support the navigation solution during the GNSS signal outage periods. Varieties of monocular visual odometry based on photogrammetric and Structure from Motion (SfM) approaches have been proposed to assist the navigation estimation process. The main problem of using the monocular VO technique is the loss of scale if neither external measurement nor a priori knowledge about the surrounding environment are available. Moreover, the estimated camera pose from VO is prone to drift with time. This paper introduces a novel approach for estimating the navigation states of an Unmanned Aerial Vehicle (UAV) by integrating the visual information that obtained from a monocular camera with the Inertial Measurement Unit (IMU) observations via an Extended Kalman Filter (EKF). Most of the current monocular VO algorithms rely on a calibrated camera model and apply the conventional photogrammetric and SfM approaches. While these approaches can help towards estimating the relative rotation and translation by tracking image features and applying geometrical constraints, they cannot estimate the motion scale using only the image visual features.

To address the critical technical challenge of positioning failure in unmanned mining trucks induced by global navigation satellite system (GNSS) signal attenuation in complex open-pit coal mine environments, particularly the significant trajectory oscillation during cornering in IMU-LiDAR integrated navigation under the simulated GNSS outage condition (with a focus on the challenging scenario of GNSS outage), this study proposes a collaborative positioning method integrating inertial measurement unit (IMU) and LiDAR based on the extended Kalman filter (EKF). A nonlinear system fusion positioning model was established, where IMU high-frequency motion estimation serves as the prediction equation and LiDAR point cloud matching (adopting the normal distribution transformation, NDT, algorithm) acts as the observation equation. The EKF algorithm performs optimal estimation on both the position estimation results of IMU and the pose information of LiDAR obtained via NDT, effectively suppressing the cumulative errors of IMU and the matching jitter of LiDAR under feature degradation scenarios. To verify the algorithm's performance comprehensively, a standardized experimental vehicle platform was constructed, and tests were conducted under multi-route, multi-speed, and repeated trial conditions. To simulate a representative and controllable weak-GNSS condition, the GNSS signal was programmatically blocked to emulate a complete outage scenario. Results indicate that while individual positioning algorithms exhibit significant tracking jitter in curved sections, the proposed IMU-LiDAR fusion trajectory closely matches the preset path. Compared to standalone IMU/LiDAR algorithms, the fusion method reduces average offset by up to 24.51% and standard deviation by up to 34.15%; when compared with mainstream open-source integrated navigation algorithms such as FAST-LIO2 and LIO-SAM, it also demonstrates superior positioning accuracy and trajectory stability. These research findings provide reliable technical support for intelligent construction in open-pit coal mines.

Global Navigation Satellite Systems (GNSS) has been the primary positioning solution for Unmanned Aerial Vehicles (UAVs) due to their worldwide coverage, high precision and lightweight receivers. However, GNSS is prone to electromagnetic interference and malicious assaults, including jamming or spoofing because of its low signal-to-noise ratio (SNR). To ensure the continuity and protection of UAV operations, using redundant navigation systems is essential. In recent years, the phased array radio system (PARS) has established itself as a local navigation solution. PARS is robust towards malicious assaults because of an much higher SNR than GNSS regarding directed and encrypted transmission. An essential factor of PARS is that the orientation of the radio antenna at a ground station needs to be precisely determined to obtain the correct positioning of UAVs. This paper presents a method for extending a previously proposed calibration algorithm to estimate the ground antenna orientation with an inertial navigation system (INS) aided by redundant positioning sensors (GNSS, PARS or barometer) using a multiplicative extended Kalman filter (MEKF) so that the calibration can be activated during flights whenever GNSS is available. In other words, the proposed navigation system is essentially an aided-INS which switches between two modes depending on the availability of GNSS: calibration and GNSS aiding mode when GNSS is available (Mode 1) and PARS and barometer aiding mode when GNSS is unavailable (Mode 2). Considering that the navigation system needs to include the effect of Earth’s curvature for a long-distance flight, PARS horizontal measurement and the barometer measurement were treated independently, and the navigation equations were propagated in Earth Centred Earth Fixed (ECEF) frame. The independent treatment of barometer measurement, and the propagation in ECEF frame were also beneficial when using multiple ground antennas to have a common reference point and reference frame. The proposed method was validated using data (Inertial Measurement Unit (IMU), GNSS, PARS, Pixhawk autopilot (including barometer) measurements) collected during a field test. In the validation, GNSS was made available at the middle of the flight and the calibration mode was activated for 200s. The proposed navigation system successfully estimated the precise orientation of multiple ground antennas and the navigation solutions were verified using GNSS and Pixhawk autopilot solutions as ground truth.

The Global Navigation Satellite Systems (GNSS) such as Global Positioning System (GPS) are the prime land and autonomous vehicles navigation information source. However, urban canyons high rise buildings block the GPS signal. Therefore, the Inertial Navigation System (INS) or the Reduced Inertial Sensor System (RISS) are utilized as an alternative source of the navigation information. The RISS is able to produce a full navigation solution using less number of sensors and calculations. Dramatically, the RISS solution drifts over time as the INS system. The integration between the GPS and the RISS is mitigating each system drawbacks. However, during the GPS outage periods, the navigation system is only depending on the inertial measurements. The RISS is utilizing the odometer/speedometer to measure the vehicle's forward speed. Many types of error affect the odometer measurements. These errors are either due to the vehicle's specifications as the differences in wheel diameters, and/or inefficient wheelbase or the road nature as wheel slips, uneven road surfaces, and/or skidding. In this paper, a Radar-based RISS system is introduced to take place the traditional RISS or INS systems. The radar unit is an essential part of the adaptive cruise control (ACC) system. Furthermore, it is capable of measuring the relative velocity and distance between the carrying and the in front vehicle to reduce collisions and increase the safety of driving. In addition, the radar measurements are not affected by the error sources that affect the odometer. The idea is to invest the ground reflection and derive the forward speed of the onboard vehicle as the ACC keep a safe distance between the cars. A novel method based on extracting the ground reflection features is introduced to obtain the onboard vehicle's speed. The obtained speed is utilized with two accelerometers and one vertical gyroscope to produce the Radar-based RISS system. The proposed system has been integrated with the GPS producing a Radar-based RISS/GPS integrated navigation system. The system has been tested on a real road trajectory in a downtown area and involved several GPS signal outages. The results show the significant capabilities of the proposed system in keeping the navigation solution drift to a minimum especially when the GPS signal is in outage compared with the traditional RISS/GPS system.