Kalman Filter Implementation With Improved Numerical Properties

This paper presents a new form of Kalman filter-the sigmaRho filter-useful for operational implementation in applications where stability and throughput requirements stress traditional implementations. The new mechanization has the benefits of square root filters in both promoting stability and reducing dynamic range of propagated terms. State standard deviations and correlation coefficients are propagated rather than covariance square root elements and these physically meaningful statistics are used to adapt the filtering for further ensuring reliable performance. Finally, all propagated variables can be scaled to predictable dynamic range so that fixed point procedures can be implemented for embedded applications. A sample problem from communications signal processing is presented that includes nonlinear state dynamics, extreme time-variation, and extreme range of system eigenvalues. The sigmaRho implementation is successfully applied at sample rates approaching 100 MHz to decode binary digital data from a 1.5-GHz carrier.