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Tire normal forces are difficult to measure, but information on the vehicle normal force can be used in many automotive engineering applications, e.g., rollover detection and vehicle and wheel stability. Previous papers use algebraic equations to estimate the tire normal force. In this article, the estimation of tire normal force is formulated as an input estimation problem. Two observers are proposed to solve this problem by using a quarter-car suspension model. First, the Youla Controller Output Observer framework is presented. It converts the estimation problem into a control problem and produces a Youla parameterized controller as observer. Second, a Kalman filter approach is taken and the input estimation problem is addressed with an Unbiased Minimum Variance Filter. Both methods use accelerometer and suspension deflection sensors to determine the vehicle normal force. The design of the observers is validated in simulation and a sensitivity analysis is performed to evaluate their robustness.