UDU/T/ covariance factorization for Kalman filteringThere has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
Document ID
19810030952
Acquisition Source
Legacy CDMS
Document Type
Other - Collected Works
Authors
Thornton, C. L. (Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Bierman, G. J. (California Institute of Technology, Jet Propulsion Laboratory, Pasadena Calif., United States)