Fast triangular formulation of the square root filter.

A new, triangular formulation of the square root Kalman filter is presented. An efficient analytic algorithm is derived for maintaining the covariance square root matrix in triangular form during the incorporation of measurements. The triangular form provides significant computational savings in the square root time update calculations. This savings tends to offset the computational disadvantage of square root methods in general, due to the greater complexity of incorporating process noise. The new square root method is shown to be typically 50% faster than the Potter square root method, 100% faster than the Joseph conventional method, and comparable in speed to the standard Kalman method. Numerical precision of the new method is greater, and storage requirements equal to or less than those of other methods.