Derivation of iterative estimation algorithm based on colored noise

In this paper, we present a new iterative estimation algorithm, which is based on colored noise and correlated noise. The detailed derivation procedure of this algorithm is given in this paper using two different methods, It has two advantages over traditional algorithms, one is that it has less computation burden than traditional Kalman filter under the same colored and related noise, another is that it needs no augmenting the original systems to much more higher dimensions. Finally, the simulation scheme was proposed.