This paper presents our study on the precise non-linear mechanical stiffness Km(x)estimation used for improving the nonlinear behavior of a moving-coil loudspeaker suspension system.The exact stiffness curve of Km(x)was measured by using laser vibrometer,while the estimated Km(x)was obtained through an inverse method.The inverse method accounts for the direct problem,adjoint problem,and sensitivity problem in collaboration with the nonlinear conjugate gradient method.For solving the nonlinear ordinary differential equations for these three problems,the hybrid spline difference method is used for simple and precise numerical calculation.Experiments and numerical verifications have demonstrated that the presented method requires less iteration but is highly accurate with suitable input voltage for displacement driven space.The high accuracy of the proposed method in non-linear mechanical stiffness estimation is also verified even with the inclusion of inevitable measurement errors.