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Session C3: Multisensor Integrated Systems and Sensor Fusion Technologies

Tightly Coupled GNSS/INS Integration based on Robust M-Estimators
Omar Garcia Crespillo, Daniel Medina, German Aerospace Center (DLR), Germany; Jan Skaloud, Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland; Michael Meurer, DLR, Germany
Location: Windjammer
Alternate Number 4

Nowadays, there is an increase of applications requiring reliable navigation information, from civil aviation where the safety issue is clear, to other means of transport like trains or cars. For applications that are closer to the ground, like small Unmanned Aerial Vehicles (UAVs) or automotive, stand-alone Global Navigation Satellite Gystems GNSS cannot be considered as the unique navigation sensor due to satellite line-of-sight signal blockage, physical effects like multipath or other radio frequency threats. That is why the combination of (GNSS) and Inertial Navigation System (INS) has become the baseline for many applications. One good example is its widespread usage for commercial quadcopters, where low cost inertial sensors are not only useful in improving the navigation continuity but are also necessary to estimate the attitude that is needed for the control of the vehicle.
The integration of GNSS with INS is normally performed by an error-state Extended Kalman Filter (EKF) that estimates the error in the inertial system by including the information of GNSS. In particular, in a tightly coupled version of the filter, the pseudorange (and delta-range) measurements from GNSS are the observations for the update of the EKF. Due to the presence of faulty GNSS measurements, from system level to multipath or non-line-of-sight (NLOS), the navigation estimation can be highly corrupted. It may cause even the divergence of the filter. Therefore, in parallel with the EKF, there are normally implemented some type of fault detector and exclusion. Some approaches for fault detection mechanism includes the use of parallel sub-filters[1], the use of the innovation sequences [2,3] or even the KF residuals [4]. One problem associated with the fault detection approach is that the distribution of the test statistics and the thresholds to determine the presence of a fault are ultimately dependent on the assumed model of the measurements (e.g., the expected uncertainty sigma of the pseudoranges). However, in challenging GNSS environments for instance with time-varying multipath error, the measurement may not follow the expected model nor even the Gaussian assumption and the detectors may not perform as expected.
An alternative to classical fault detection mechanism can be found in the framework of robust statistics [5]. Here, the estimator tries internally to adjust at the same time the state of interest and the residual error of the measurements [5] by a certain de-weighting function. This approach handles in a more tightly way the estimation and fault detection and exclusion mechanism. These estimators are so called robust because they are more resilience already in the estimation step to faulty measurements or outliers.
In the GNSS domain, robust estimators have been already proposed and analyzed in the literature as an alternative to (A)RAIM [6]. They have been also studied in a loosely-coupled fashion with INS in [7]. The major drawback of these robust schemes is the need for a large number of measurements to accommodate efficiently the faulty ones. In GNSS however, we do not have many satellites in view (i.e. less than 12 if we consider stand-alone GPS), and this number decreases if we consider urban scenarios. Therefore, the use of robust estimator in this context brought only marginal improvement in the past even with current multi-constellation [8].
On the other hand, the inclusion of the inertial sensor within the robust estimation process and its short-term high accuracy may increase drastically the redundancy and therefore the performance of the robust estimator. The use of an accurate prediction measurement from the inertial sensor compared to the pseudoranges, can potentially substitute the need of a large number of GNSS measurements for the robust estimation to achieve a superior performance. Following this thought, in [9] we first proposed the use of a tightly coupled GNSS/INS with a modified robust update step based on an Huber estimator.
In this work, we follow up the work in [9]. We first revisit the design of the filter and the modified update step based on the reshape of the KF update equation to a batch formulation. Here, some modifications are needed to account for the numerical problems due to the rank deficient covariance matrix of the KF prediction. We perform a more profound analysis of the role of the inertial unit in the robust estimation and its dependency with the quality of inertial sensors. We show the improvements in fault resilience with respect to the level of integration, i.e., loosely or tightly coupled. We also show the difference in performance of the proposed robust KF with respect to the classical EKF with a fault detection/exclusion mechanism based on innovations.
[1] U. I. Bhatti and W. Y. Ochieng, “Detect Multiple Failures in GPS/INS Integrated System: A Novel Architecture for Integrity Monitoring," Journal of Global Positioning Systems, vol. 8, no. 1, pp. 26{42, 2009.
[2] R. K. Mehra and J. Peschon, “An Innovations Approach to Fault Detection and Diagnosis in Dynamic Systems," Automatica, vol. 7, no. 5, pp. 637{640, 1971.
[3] C. Tanil, S. Khanafseh, M. Joerger, and B. Pervan, \Kalman Filter-based INS Monitor to Detect GNSS Spoofers Capable of Tracking Aircraft Position," in IEEE/ION PLANS 2016, Savannah, GA, 2016.
[4] O. Garcia Crespillo, A. Grosch, J. Skaloud, and M. Meurer, “Innovation vs Residual KF Based GNSS/INS Autonomous Integrity Monitoring in Single Fault Scenario,” in The 30th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ ), At Portland, OR (USA).
[5] P. Huber, Robust Statistics. Wiley, N. Y., 1981.
[6] N. Knight and J. Wang, \A Comparison of Outlier Detection Procedures and Robust Estimation Methods in GPS Positioning," The Journal of Navigation, vol. 62, pp. 699{709, 2009.
[7] Arias Medina, Daniel and Romanovas, Michailas and Herrera Pinzón, Iván Darío and Ziebold, Ralf (2016) Robust Position and Velocity Estimation Methods in Integrated Navigation Systems for Inland Water Applications. ION PLANS 2016, 11-14 April 2016, Savannah, Georgia USA.
[8] Pozo Perez, Jose Antonio and Arias Medina, Daniel and Herrera Pinzón, Iván Darío and Heßelbarth, Anja and Ziebold, Ralf (2017) Robust Outlier Mitigation in Multi-Constellation GNSS Positioning for Waterborne Applications.
[9] Garcia Crespillo, Omar and Arias Medina, Daniel and Grosch, Anja and Skaloud, Jan and Meurer, Michael (2017) Robust Tightly Coupled GNSS/INS Estimation for Navigation in Challenging Scenarios. European Navigation Conference 2017, Lausanne, Switzerland



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