Jacques Georgy

Modeling the Stochastic Drift of a MEMS-Based Gyroscope in Gyro/Odometer/GPS Integrated Navigation

To have a continuous navigation solution that does not suffer from interruption, GPS is integrated with relative positioning techniques such as odometry and inertial navigation. Targeting a low-cost navigation solution for land vehicles, this paper uses a reduced multisensor system consisting of one microelectromechanical-system (MEMS)-based single-axis gyroscope used together with the vehicles odometer, and the whole system is integrated with GPS. This system provides a 2-D navigation solution, which is adequate for land vehicles. The traditional technique for this multisensor integration problem is Kalman filtering (KF). Due to the inherent errors of MEMS inertial sensors and their stochastic nature, which is difficult to model, the KF with its linearized models has limited capabilities in providing accurate positioning. Particle filtering (PF) has recently been suggested as a nonlinear filtering technique to accommodate arbitrary inertial sensor characteristics, motion dynamics, and noise distributions. An enhanced version of PF is utilized in this paper and is called the Mixture PF. Since PF can accommodate nonlinear models, this paper uses total-state nonlinear system and measurement models. In addition, sophisticated models are used to model the stochastic drift of the MEMS-based gyroscope. A nonlinear system identification technique based on parallel cascade identification (PCI) is used to model this stochastic gyroscope drift. In this paper, the performance of the PCI model is compared with that of higher order autoregressive (AR) stochastic models. Such higher order models are difficult to use with KF since the size of the dynamic matrix and the error-covariance matrix becomes very large and complicates the KF operation. The performance of the proposed 2-D navigation solution using Mixture PF with both PCI and higher order AR models is examined by road-test trajectories in a land vehicle. The two proposed combinations are compared with four other 2-D solutions: a Mixture PF with the Gauss-Markov (GM) model for the gyro drift, a Mixture PF with only white Gaussian noise (WGN) for stochastic gyro errors, and two different KF solutions with GM model for the gyro drift. The experimental results show that the two proposed solutions outperform all the compared counterparts.

Low-Cost Three-Dimensional Navigation Solution for RISS/GPS Integration Using Mixture Particle Filter

Recent technological advances in both GPS and low-cost microelectromechanical-system (MEMS)-based inertial sensors have enabled the monitoring of the location of moving platforms for numerous positioning and navigation (POS/NAV) applications. GPS is presently widely used in land vehicles. However, in some environments, the GPS signal may suffer from signal blockage and multipath effects that deteriorate the positioning accuracy. When miniaturized inside any moving platforms, the MEMS-based inertial navigation system (INS) can be integrated with GPS and enhance the performance in denied GPS environments (like in urban canyons). Targeting a low-cost navigation solution for land vehicles, this paper uses a reduced inertial sensor system (RISS) with MEMS-based inertial sensors. In this paper, the RISS consists of one single-axis gyroscope and a two-axis accelerometer used together with the vehicles odometer, and the whole system is integrated with GPS to obtain a 3-D navigation solution. The traditional technique for this integration problem is Kalman filtering (KF). Due to the inherent errors of MEMS inertial sensors and the relatively high noise levels associated with their measurements, KF has limited capabilities in providing accurate positioning. Particle filtering (PF) was recently suggested as a nonlinear filtering technique to accommodate arbitrary inertial sensor characteristics, motion dynamics, and noise distributions. An enhanced version of PF is utilized in this paper and is called Mixture PF. The performance of the proposed 3-D navigation solution using Mixture PF for RISS/GPS integration is examined by road-test trajectories in a land vehicle. The proposed method is compared with four other solutions: 1) 3-D solution using KF for full INS/GPS integration; 2) 2-D solution using KF for RISS/GPS integration; 3) 2-D solution using Mixture PF for RISS/GPS integration; and 4) 3-D solution using sampling/importance resampling (SIR) PF for RISS/GPS integration. The experimental results show that the proposed solution outperforms all the compared counterparts.

Enhanced mobile robot outdoor localization using INS/GPS integration

An unprecedented surge of developments in mobile robot outdoor navigation was witnessed after the US government removed selective availability of the global positioning system (GPS). However, in certain situations GPS becomes unreliable or unavailable due to obstructions such as buildings and trees. During GPS outages, a positioning solution with a minimum cost is preferred for small wheeled robots. A low-cost inertial measurement unit (IMU) is a good choice to provide such a solution; however, low-cost MEMS-based inertial sensors suffer from several errors that are stochastic in nature. These errors accumulate and cause a rapid deterioration in the quality of position estimate. The purpose of this paper is to describe an enhanced low-cost 3-D navigation system using a Kalman filter (KF) that integrates odometry from wheel encoders, low cost MEMS-based inertial sensors, and GPS. The proposed technique uses reduced inertial sensor system (RISS). The RISS used here includes three accelerometers and one gyroscope aligned with the vertical axis of the body frame of the robot. The benefits of eliminating the two other gyroscopes normally used are decreasing the cost further, and improving the performance by having less inertial sensors and thus less contribution of these sensors errors towards positional errors. These two eliminated gyroscopes were used to calculate pitch and roll which are now calculated using the two horizontal accelerometers. The experimental results show that, during GPS outages, this KF with velocity update derived from the forward speed from wheel encoders is a good technique for greatly reducing localization errors. Real localization data from one trajectory is presented. This data is post-processed and some simulated GPS outages are introduced to assess the effectiveness of the proposed technique.

FPGA-Based Real-Time Embedded System for RISS/GPS Integrated Navigation

Navigation algorithms integrating measurements from multi-sensor systems overcome the problems that arise from using GPS navigation systems in standalone mode. Algorithms which integrate the data from 2D low-cost reduced inertial sensor system (RISS), consisting of a gyroscope and an odometer or wheel encoders, along with a GPS receiver via a Kalman filter has proved to be worthy in providing a consistent and more reliable navigation solution compared to standalone GPS receivers. It has been also shown to be beneficial, especially in GPS-denied environments such as urban canyons and tunnels. The main objective of this paper is to narrow the idea-to-implementation gap that follows the algorithm development by realizing a low-cost real-time embedded navigation system capable of computing the data-fused positioning solution. The role of the developed system is to synchronize the measurements from the three sensors, relative to the pulse per second signal generated from the GPS, after which the navigation algorithm is applied to the synchronized measurements to compute the navigation solution in real-time. Employing a customizable soft-core processor on an FPGA in the kernel of the navigation system, provided the flexibility for communicating with the various sensors and the computation capability required by the Kalman filter integration algorithm.

Improved Inertial/Odometry/GPS Positioning of Wheeled Robots Even in GPS-Denied Environments

Eric North1, Jacques Georgy2, Umar Iqbal3, Mohammed Tarbochi4 and Aboelmagd Noureldin5 1Canadian Forces Aerospace and Telecommunications Engineering Support Squadron 2Trusted Positioning Inc. 3Electrical and Computer Engineering Department, Queen’s University 4Electrical and Computer Engineering Department, Royal Military College 5Electrical and Computer Engineering Department, Royal Military College/Queen’s University Canada

Mixture Particle Filter for Low Cost INS/Odometer/GPS Integration in Land Vehicles

Global Positioning System (GPS) is currently the common solution for land vehicle positioning. However, GPS signals may suffer from blockage in urban canyons and tunnels, and the positioning information provided is interrupted. One solution to have continuous vehicle positioning is to integrate GPS with an inertial measurement unit (IMU) and the navigation solution is achieved using an estimation technique which is traditionally based on Kalman filter (KF). In order to have a low cost navigation solution for land vehicles, MEMS-based inertial sensors are used. To achieve a better performance during GPS outages, the speed derived from the vehicle odometer is used as a measurement update. To improve the positioning accuracy of the MEMS-based INS/Odometer/GPS integration, particle filtering (PF) is used as a nonlinear filtering technique, which does not need to linearize the models as in Extended KF (EKF). Because of PF ability to deal with nonlinear models, it can accommodate arbitrary sensor characteristics and motion dynamics. An enhanced version of PF is used which is called Mixture PF. While the Sampling/Importance Resampling (SIR) PF samples from the prior importance density and the Likelihood PF samples from the observation likelihood, the Mixture PF samples from both densities, then appropriate weighting is achieved followed by resampling. This mixture of importance densities leads to a better performance. The performance of this method is examined by road test trajectories in a land vehicle and compared to KF.

Tightly Coupled Low Cost 3D RISS/GPS Integration Using a Mixture Particle Filter for Vehicular Navigation

Satellite navigation systems such as the global positioning system (GPS) are currently the most common technique used for land vehicle positioning. However, in GPS-denied environments, there is an interruption in the positioning information. Low-cost micro-electro mechanical system (MEMS)-based inertial sensors can be integrated with GPS and enhance the performance in denied GPS environments. The traditional technique for this integration problem is Kalman filtering (KF). Due to the inherent errors of low-cost MEMS inertial sensors and their large stochastic drifts, KF, with its linearized models, has limited capabilities in providing accurate positioning. Particle filtering (PF) was recently suggested as a nonlinear filtering technique to accommodate for arbitrary inertial sensor characteristics, motion dynamics and noise distributions. An enhanced version of PF called the Mixture PF is utilized in this study to perform tightly coupled integration of a three dimensional (3D) reduced inertial sensors system (RISS) with GPS. In this work, the RISS consists of one single-axis gyroscope and a two-axis accelerometer used together with the vehicle’s odometer to obtain 3D navigation states. These sensors are then integrated with GPS in a tightly coupled scheme. In loosely-coupled integration, at least four satellites are needed to provide acceptable GPS position and velocity updates for the integration filter. The advantage of the tightly-coupled integration is that it can provide GPS measurement update(s) even when the number of visible satellites is three or lower, thereby improving the operation of the navigation system in environments with partial blockages by providing continuous aiding to the inertial sensors even during limited GPS satellite availability. To effectively exploit the capabilities of PF, advanced modeling for the stochastic drift of the vertically aligned gyroscope is used. In order to benefit from measurement updates for such drift, which are loosely-coupled updates, a hybrid loosely/tightly coupled solution is proposed. This solution is suitable for downtown environments because of the long natural outages or degradation of GPS. The performance of the proposed 3D Navigation solution using Mixture PF for 3D RISS/GPS integration is examined by road test trajectories in a land vehicle and compared to the KF counterpart.

Quantitative comparison between Kalman filter and Particle filter for low cost INS/GPS integration

Recent technological advances in both GPS and low cost micro-electro mechanical system (MEMS)-based inertial sensors enabled monitoring the location of moving platforms for numerous positioning and navigation (POS/NAV) applications. When miniaturized inside any moving platforms, MEMS-based inertial navigation system (INS) can be integrated with GPS and enhance the performance in denied GPS environments (like in urban canyons). The combination of the two systems, traditionally performed by Kalman filtering (KF), exploits their complementary characteristics. Due to the inherent errors of MEMS inertial sensors and the relatively high noise levels associated with their measurements, KF has limited capabilities in providing accurate positioning. Particle filtering (PF) was recently suggested to accommodate for arbitrary inertial sensor characteristics, motion dynamics and noise distributions. This article gives detailed comparison between KF and PF as applied to MEMS-based INS/GPS integration and examines the performance of both methods during a road test experiment.

Nonlinear Modeling of Azimuth Error for 2D Car Navigation Using Parallel Cascade Identification Augmented with Kalman Filtering

Present land vehicle navigation relies mostly on the Global Positioning System (GPS) that may be interrupted or deteriorated in urban areas. In order to obtain continuous positioning services in all environments, GPS can be integrated with inertial sensors and vehicle odometer using Kalman filtering (KF). For car navigation, low-cost positioning solutions based on MEMS-based inertial sensors are utilized. To further reduce the cost, a reduced inertial sensor system (RISS) consisting of only one gyroscope and speed measurement (obtained from the car odometer) is integrated with GPS. The MEMS-based gyroscope measurement deteriorates over time due to different errors like the bias drift. These errors may lead to large azimuth errors and mitigating the azimuth errors requires robust modeling of both linear and nonlinear effects. Therefore, this paper presents a solution based on Parallel Cascade Identification (PCI) module that models the azimuth errors and is augmented to KF. The proposed augmented KF-PCI method can handle both linear and nonlinear system errors as the linear parts of the errors are modeled inside the KF and the nonlinear and residual parts of the azimuth errors are modeled by PCI. The performance of this method is examined using road test experiments in a land vehicle.

Basic Navigational Mathematics, Reference Frames and the Earth’s Geometry

Navigation algorithms involve various coordinate frames and the transformation of coordinates between them. For example, inertial sensors measure motion with respect to an inertial frame which is resolved in the host platform’s body frame. This information is further transformed to a navigation frame. A GPS receiver initially estimates the position and velocity of the satellite in an inertial orbital frame. Since the user wants the navigational information with respect to the Earth, the satellite’s position and velocity are transformed to an appropriate Earth-fixed frame. Since measured quantities are required to be transformed between various reference frames during the solution of navigation equations, it is important to know about the reference frames and the transformation of coordinates between them. But first we will review some of the basic mathematical techniques.