For joint estimation of state variables and unknown parameters, adaptive observers usually assume some persistent excitation (PE) condition. In practice, the PE condition may not be satised, because the underlying recursive estimation problem is ill-posed. To remedy the lack of PE condition, inspired by the ridge regression, this paper proposes a regularized adaptive observer with enhanced parameter adaptation gain. Like in typical ill-posed inverse problems, regularization implies an estimation bias, which can be reduced by using prior knowledge about the unknown parameters.