Adaptive Kalman Filter Tuning In Integration of Low-Cost MEMS-INS/GPS

Navigation grade Inertial Navigation System (INS) use precise accelerometers and gyros. But due to their high cost, they are generally unable to penetrate beyond the realm of defense and aerospace sectors. Advances in Micro-machine technology have produced low cost MEMS inertial sensors. The MEMS are integrated micro devices or systems combining electrical and mechanical components whose sizes range from micrometers to millimeters. Given their low precision they are not directly usable as sole navigation systems. But by integrating with GPS, they can achieve the navigation grade accuracy. The cost and space constraints are currently driving the INS manufacturers to investigate and develop low cost and small size but reasonably accurate navigation systems to meet the fast growing civilian market demands. The MEMS inertial sensors exhibit large random errors, but the complimentary characteristics of GPS and MEMS-INS allow on line estimation and compensation of MEMS-INS errors using a Kalman filter and thereby acquire navigation grade accuracy. However in order to obtain the best possible results from such recursive Kalman filter approaches it is necessary to properly tune the filter parameters off line before implementing the filter on line. This paper deals with the application of such an adaptive Kalman filter tuning of the parameters. Using Myers and Tapley algorithm with some modifications the filter parameters have been derived and utilized to minimize the cost function J that is dependent on the innovations which is the difference between the model output and the measurement. Integration of MEMS-INS/GPS is carried out in loosely coupled mode in which GPS measured position and velocity aids the MEMS-INS, which also provides position and velocity based on sensed acceleration. The implementation is done in error state space formulation with feedback mechanization in closed loop operation in a decentralized filter with time varying Kalman gains provided by the adaptive tuning of the filter parameters namely initial state, process and measurement noise covariance. The present work shows the importance of properly tuning the filter parameters which help the filter to learn better from the measurements as can be seen from the larger gains of the adaptive filter when compared to lower gains of the Nonadaptive filter. Also one can note the behavior of these adaptively estimated Kalman gains, which tend to steady state values. These constant gains can be used for on line applications thus avoiding the covariance propagation, which is highly time consuming. Further these adaptively estimated gains provide robustness to the filter than dealing with the highly sensitive statistics of the filter parameters whose choice can lead to wide variations in the results. It turns out that in real time operations any further unmodelled or unmodellable effects do not lead to much loss of accuracy of the filter results when based on the adaptive gains.