On-line Tuning of an Extended Kalman Filter for INS/GPS Navigation Applications

Chris Goodall, Naser El-Sheimy, Zainab Syed

Abstract:	The demand for civil navigation systems in harsh environments has been growing over the last several years. The Global Positioning System (GPS) has been the backbone of most current navigation systems, but its usefulness in downtown urban environments or heavily treed terrain is limited due to signal blockages. To help bridge these signal gaps inertial navigation systems (INS) have been used. An integrated INS/GPS system can provide a continuous navigation solution regardless of the environment. For consumer applications the use of MEMS sensors are needed due to cost, size and regulatory restrictions of higher grade inertial systems. The Kalman filter has traditionally been used to optimally weight the GPS and INS measurements, but when using MEMS grade sensors the optimal a priori error statistics needed to run the filter can be difficult to determine. Large turn on biases combined with high sensor noise characteristics make filter estimation a dangerous task if using poor statistical estimates of these errors. For low-cost MEMS INS/GPS navigation systems, determination of these errors (also referred to as tuning) is a time consuming and expensive process that is rarely performed in practice. Typical Kalman filter values are often used, but there are several factors which can lead to suboptimal estimation; statistical parameters can be different among similar inertial units, they can change over time, and they are subject to environmental fluctuations. Initial statistical parameters are often obtained in a laboratory setting using Allan variance analysis. From these, tuning of the Kalman filter is performed using collected field test data. This lab and field test procedure can easily exceed the cost of the sensor assembly itself. . Reinforcement learning techniques have been used to tune the filter parameters. The emphasis is to slowly converge to the correct parameters with time as the unit is used. As the user navigates, data can be collected to test past statistical hypotheses and adapt them as needed. Simulated GPS signal outages are used on-line to test the accumulation of inertial errors during Kalman filter prediction mode. This creates a divergence of the filter estimates which can be used as an indicator of filter performance. The tuning parameters dictate the initial prediction error from the innovation sequence, so the task of the intelligent algorithm is the minimization of this error using optimal parameters. The RL approach is similar to a Multiple Model Adaptive Estimation technique, except the multiple models are tested over time and learning is used to remember the tuning procedure for future tuning or tuning of other similar sensors. Results largely depend on the starting parameters and starting knowledge. If the initial tuning parameters for the Q and R matrices are very close to optimal and do not change over time then minimal improvement is obtained. But for most MEMS sensors coming off the assembly line there can be large variances, leaving plenty of room for improvement. Three separate tests were performed. Simulated data was used to control the stochastic errors. The convergence to the true solution could then be analyzed. Real MEMS data was also tested, but only relative improvements could be analyzed. Finally, an extension from one MEMS sensor to another was performed to analyze the convergence properties of model extension between two similar sensors.
Published in:	Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008) September 16 - 19, 2008 Savannah International Convention Center Savannah, GA
Pages:	38 - 47
Cite this article:	Goodall, Chris, El-Sheimy, Naser, Syed, Zainab, "On-line Tuning of an Extended Kalman Filter for INS/GPS Navigation Applications," Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September 2008, pp. 38-47.
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