ION GNSS 2012
Session F1: Urban & Indoor Navigation: GNSS & Assisted-GNSS

Title: Non-Linear Modeling of Pseudorange Errors for Centralized Non-Linear Multi-Sensor System Integration
Author(s): U. Iqbal, Queen's University, Canada and Royal Military College of Canada; J. Georgy, W.F. Abdelfatah, Trusted Positioning Inc., Canada; M. Tamazin, M. Korenberg, Queen's University, Canada; A. Noureldin, Royal Military College of Canada/Queen's University, Canada
Date/Time: Wednesday, September 19, 2012, 11:26 a.m.
Room: Grand Ballroom Center (Renaissance)

The determination of accurate and reliable navigational states without interruptions is an important task for many applications. Global Navigation Satellite Systems (GNSS) has made the determination of position and velocity feasible for outdoor scenarios by making range measurements to GNSS satellites (at least four satellites) with good geometry. The most recognized operational GNSS is the Global Positioning System (GPS) and the number of users of GPS is growing exponentially due to its applications for land transportation and the fact that its basic navigational services are free-of-charge for civilians world-wide. Advanced technologies have empowered the manufacturing of compact, inexpensive, and low power consumption receivers providing incentive for innovative applications in numerous domains. However, the signals transmitted by the GPS satellites can suffer frequent interference and signal blockage in urban canyons and thick foliage where an uninterrupted clear view of the sky is not feasible for the receiver causing intermittent or erroneous determination of position and velocity.

To provide continuously accurate and reliable full navigational states (i.e. position, velocity and attitude), the GPS has to be combined with other complementary navigational sensors such as inertial sensors and an odometer. By integrating the GPS with these motion sensors, an always available solution can be obtained that is often more accurate than that of GPS alone. Different manufacturers provide solutions which fulfill the requirements of continuity, reliability and availability for an exclusive class of users as they are ready to spend a hefty amount of money. However, for the average consumer, only smaller, cheaper and lower power solutions can be feasible. Low cost Micro-Electro-Mechanical Systems (MEMS) based on inertial sensors fulfill the requirements of common users, but MEMS sensors have composite error characteristics that need to be accounted for before the data is made useful. Full inertial measurement units (IMUs), commonly used in integrated navigation solutions, are composed of three accelerometers and three gyroscopes. To decrease the reliance on MEMS sensors and decreasing their error contribution in the integrated navigation, reduced inertial sensor system (RISS) which is based on only one single axis gyroscope, two accelerometers together with the vehicle´s odometer and integrated with GPS, was proposed earlier, to provide a full 3D land vehicle navigation solution. To further enhance the aiding of the RISS based system, tightly-coupled integration was proposed which could provide GPS aiding for a navigation solution when the number of visible satellites is three or less, eliminating the foremost requirement of loosely-coupled integration which is the visibility of at least four satellites.

Particle filter (PF), a nonlinear filtering technique, is utilized in this paper to perform tightly coupled integration of a 3D RISS with GPS to avoid the linearization errors that result from Kalman Filter (KF), the conventional technique used for data fusion. An enhanced version of PF, called Mixture PF, is employed for tightly-coupled RISS/GPS integration utilizing pseudoranges and pseudorange rates measured by the GPS receiver. The accuracy of the position estimates is dependent on the accuracy of the range measurements. The tightly-coupled solutions presented in the literature assume that the pseudorange measurements, after correcting for ionospheric and tropospheric delays, satellite clock errors, and ephemeris errors, only have errors due to the receiver clock errors and white noise. Consequently, the latter two are the only errors modeled inside the measurement model in the tightly-coupled solutions presented in the literature.

This paper proposes a solution that exploits the fact that PF can accommodate any nonlinear models by incorporating Parallel Cascaded Identification (PCI) models for the correction of residual pseudorange correlated errors in the measurement model used inside the filter. PCI is a nonlinear system identification technique that is used to improve the overall navigation solution by modeling residual pseudorange correlated errors and thus correcting these measurements. In full GPS coverage when four or more satellites are available to the GPS receiver, the PF integrated solution provides adequate position benefiting from both GPS and RISS measurements, and the PCI works on building models for the pseudorange errors for each visible satellite. The measured pseudorange of each visible satellite is used as an input to the model; the target output is the error between the corrected pseudorange (i.e. calculated based on corrected receiver position from the integrated solution) and the measured pseudorange. This target output provides the reference output to build the PCI model of the pseudorange residual errors.

During partial GPS outages (i.e. characterized by the availability of less than four satellite signals), each PCI model, built during full GPS coverage, estimates the correction for the corresponding pseudorange error. The PCI-corrected GPS pseudoranges of the outlasting visible satellites during the partial outages will be used as measurements in the PF. This improvement in pseudorange measurements results in a more accurate aiding for RISS, and thus more accurate estimates of the navigational states.

The effectiveness of the proposed algorithm is verified by different real-life road tests during GPS signal degradation and blockage using low cost MEMS-based RISS. Results for scenarios with intentionally inserted GPS outages where the number of visible satellites varies between 3, 2, 1, and 0 are presented to demonstrate the usefulness and performance of the proposed technique. The results are examined and compared with PF tightly-coupled RISS/GPS integration without the pseudorange corrections using the PCI modules. The results are also compared with KF tightly-coupled RISS/GPS integration with and without pseudorange corrections using PCI modules. The comparison demonstrates the advantages of using PCI modules for correcting pseudoranges for tightly-coupled integration using PF.

The proposed navigation system, including the PCI modules used with PF, provides continuous determination of the navigational states with higher performance along with considerable reduction in the cost, size, and power consumption due to the use of fewer low-cost MEMS-based inertial sensors, vehicle odometer, and a low-cost GPS receiver. These features make the proposed system a viable product that can provide an accurate, always available positioning solution for the common consumer.

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