This work investigates a functional estimation problem for single input single output linear and nonlinear systems. It finds application in enabling accelerationbased semi-active control. Solvability of a linear functional estimation problem is studied from a geometric approach, where the functional dynamics are derived, decomposed, and transformed to expose structural properties. This approach is extended to solve a challenging nonlinear functional observer problem, combining with the exact error linearization. Existence conditions of nonlinear functional observers are established. Simulation verifies existence conditions and demonstrates the effectiveness of the proposed functional observer designs.