Comparison of Innovations-Based Analytical Redundancy Methods

Innovations-based analytical redundancy methods process the "innovations" ("residuals") of a normal-mode Kalman filter to detect and isolate failures and to correct state estimates. Failures are often manifested by sudden transitions in a bias vector in the process input or output. This paper discusses ad compares two methods for estimating these bias transitions and for correcting the state estimates: the first is the maximum likelihood method developed by Friedland and the second is the generalized likelihood ratio (GLR) method of Willsky and Jones. After a review of the underlying theory and algorithms a simulation study is reported in which the two algorithms are tested on a dynamic model of the pitch motion of an aircraft that was used in an earlier study by Friedland. Both algorithms are found to work very well when the failure amplitude is at a 10¿ level (where ¿ is the res noise present on the sensor). The GLR method, which is more complex and requires more computer memory to implement, however, performs substantially better than the simpler maximum likelihood method at a failure amplitude of 2¿. Severl possibilities for combining the best features of each algorithm are suggested.