This study is devoted to design of the fault estimation adaptive observer. Initial observer is modified with correction filter in order to improve robustness against external disturbance with known spectral structure. Computation of correctors parameters is based on special spectral algorithm of SISO (Single Input and Single Output) H2 optimisation in frequency domain. Novel algorithm is proposed for practical implementation. Its effectiveness is demonstrated with example of successive additive fault estimation during marine ship yaw motion process.