This letter presents a new detectability criterion and a new observer design method for a class of linear time varying systems. The concept is based on the stabilization of the system's non-negative Lyapunov exponents. The proposed observer design guarantees exponential convergence of the estimation error. Compared to classical techniques, the computational complexity of the resulting observer is drastically reduced if the number of non-negative Lyapunov exponents is small compared to the system order. A numerical simulation example demonstrates the effectiveness of the proposed approach.