International Journal of Control, Automation, and Systems Vol. 1, No. 4, December 2003 444
Centralized Kalman Filter with Adaptive Measurement Fusion: its Application to a GPS/SDINS Integration System with an Additional Sensor
Abstract: An integration system with multi-measurement sets can be realized via combined
application of a centralized and federated Kalman filter. It is difficult for the centralized
Kalman filter to remove a failed sensor in comparison with the federated Kalman filter. All
varieties of Kalman filters monitor innovation sequence (residual) for detection and isolation of
a failed sensor. The innovation sequence, which is selected as an indicator of real time
estimation error plays an important role in adaptive mechanism design. In this study, the
centralized Kalman filter with adaptive measurement fusion is introduced by means of
innovation sequence. The objectives of adaptive measurement fusion are automatic isolation
and recovery of some sensor failures as well as inherent monitoring capability. The proposed
adaptive filter is applied to the GPS/SDINS integration system with an additional sensor.
Simulation studies attest that the proposed adaptive scheme is effective for isolation and
recovery of immediate sensor failures.
Keywords: Centralized Kalman filter, federated Kalman filter, innovation sequence, adaptive
measurement fusion, GPS/SDINS integration system with an additional sensor.
The CKF (Centralized Kalman Filter) can be applied to a system with multi-measurement sets to determine an optimal estimation of global system states. Although the CKF provides an optimal solution to the estimation problem, the large number of states often requires processing data rates that cannot be maintained in practical real time applications. Moreover, the estimate contains the measurement history of all previous updates. If a sensor failure is detected, it is difficult to remove the failed sensor data from the estimate. For these reasons, parallel structures can often provide improved failure detection and correction, enhanced redundancy management, and decreased costs for system integration. As such, there has recently been considerable interest shown in decentralized Kalman filter architectures.
One architecture that has received considerable attention as a practical means of decentralization is the FKF (Federated Kalman Filter). FKF differs from the conventional Kalman filter because each measurement is processed in local filters, and the results are combined in a master filter. The local filters run completely independent of each other, providing isolation between filters in the instance of sensor failure. The primary disadvantage is that the FKF does not give performance equal to that of the CKF, even when local filters are based on true models of the system. Furthermore, the FKF with the existing system requires additional processor burden to implement the local filters [1, 2].
The accuracy of Kalman filters depends on a priori knowledge of system models and noise statistics. In practical applications, priori knowledge is somewhat inaccurate. The estimation accuracy will be degraded from the theoretical prediction. The purpose of an adaptive filter is to reduce or bound the gaps by modifying or adapting the Kalman filter. A number of approaches can be taken to adaptive filtering. Since the basic source of uncertainty is due to unknown priori statistics of noise, one can estimate them on-line from the observed data. Another approach is to estimate the optimal Kalman gain directly without estimating the covariance of the process and measurement noise [3-5].
In the navigation system, a number of researches are to integrate the GPS (global positioning system) into the INS (inertial navigation system) [6-10]. In addition, the GPS/INS integration system employing other navigation systems is designed to provide a high level of accuracy and fault detection/isolation. That can be realized via the application of a CKF, a FKF and an adaptive filter [1, 2, 7].
In this study, first, the CKF and the FKF are summarized. Secondly, the adaptive measurement
M anuscript received November 15, 2002; revised April 30, 2003; accepted July 24, 2003. Recommended by Editorial Board member Taek Lyul Sang under the direction of Editor Chung Choo Chung.
Tae-Gyoo Lee is with the Inertial Navigation Laboratory, Agency for Defense Development, Yuseong P. O. BOX 35-5, Daejeon, Korea (e-mail: firstname.lastname@example.org).