Gram-Schmidt algorithms for covariance propagationThis paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.
Document ID
19770029594
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
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)