Analytical solution for continuous-time Kalman tracking filterswith colored measurement noise in frequency domain

New expressions are given for analytical solutions to the steady-state Kalman gains of the two-state exponentially correlated velocity (ECV) and the three-state exponentially correlated acceleration (ECA) tracking filters with position measurements by using spectral factorization method. The measurement colored noise model is characterized by a correlation time 1/λ. The vehicle oscillations such as wind-induced-bending is also considered in the modeling of the system which leads to the most generalized state transition matrix     

Complexity analysis of wavelet signal decomposition andreconstruction

We give certain sequential and parallel algorithms and their computational analysis for signal decomposition and reconstruction based on wavelets. The signal decomposition (respectively, reconstruction) process is separated into two stages: the first is the preprocessing stage where certain constants are computed for implementation to prepare for the second stage in which signal decomposition (respectively, reconstruction) is performed. In the decomposition (respectively, reconstruction) stage, the input signal is transformed via different methods to compute the output signal without changing the setup initialized in the preprocessing stage. We describe certain sequential algorithms for both the preprocessing and the decomposition (respectively, reconstruction) stages, and parallel algorithms for the latter. The algorithms are finally illustrated for compactly supported spline-wavelets and are analyzed in detail in terms of the required arithmetic operations