Proportional Integral Estimator

The standard Kalman filter requires that the statistical characteristics of system signal and noise are completely known. In practice, this is almost impossible to achieve. Numerous adaptive techniques have been developed to compensate for inexact system modeling. While some are not good enough, others are ad hoc approaches requiring substantial computer resources. A novel adaptive technique is proposed by adding to the standard Kalman estimator, an integral term which provides additional smoothing effect and design flexibility. Optimal structures are derived by using the innovation method for continuous and discrete data Gaussian process models with linear dynamics. The proportional integral estimator (PIE) is simple to implement, but by adjusting contributions from the proportional linear term and the integral term of filter residual, it provides flexible adaptive features to suit design requirements, such as robustness to parameter variation and maneuvering target tracking. An application to a tracking system is presented and the behavior of error covariance matrix is examined. The example included for comparison of the standard Kalman filter and the PIE, indicates that while the results obtained by using the two filters are comparatively close, significant improvement is observed in response time and noise smoothing capability.