New V-A square root filter

Two new square root Kalman filtering algorithms are presented. Both algorithms are based on the spectral factors V-?? of the covariance matrix where V is the matrix whose columns are the eigenvectors of the covariance and ?? is the diagonal matrix of its eigenvalues. The algorithms use the covariance mode in the time propagation stage and the information mode in the measurement update stage. This switch between modes, which is trivial in the V-?? representation, increases the efficiency of the algorithms. In the first algorithm, which is a continuous/discrete one, the V and ??1/2 matrices are propagated in time in a continuous manner, while the measurement update is a discrete-time procedure. In the second algorithm, which is a discrete/discrete one, the time propagation of the V-??1/2 factors is performed in discrete time too, using a procedure which is similar to the one used for the discrete measurement update. The discrete propagation and the measurement update are based on singular value decomposition algorithms. The square root nature of the algorithms is demonstrated numerically through a typical example. While promising all the virtues of square root routines the V-?? filters are also characterized by their ability to exhibit singularities as they occur.