A Proposed General Method for Parameter Estimation of Noise Corrupted Oscillator Systems

This paper provides a proposed means to estimate parameters of noise corrupted oscillator systems. An application for a submarine combat control systems (CCS) rack is described as exemplary of the method. Damped Oscillation The differential equation modeling damped harmonic oscillators in terms of time t is given as the linear second order homogeneous system, derived from Hooke’s Law and Newton’s Second Law m d2x dt2 + c dx dt + kx = 0 If the mass m is retarded by a frictional force, c dx dt , proportional to velocity with constant c, then dividing by m, provides x ′′ + 2bx ′ + ω2x = 0, ( b ≥ 0, ω > 0) where, 2b = c m for mass m and arbitrary constant c, ω = � k m . The characteristic equation is: r2 + 2br + ω2 = 0 and the roots are: −b ± �b2 − ω2