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This paper deals with the problem of state estimation for a class of lineartime-invariant systems with quadratic output measurements. An immersion-typeapproach is presented that transforms the system into a state-affine system byadding a finite number of states to the original system. Under suitablepersistence of excitation conditions on the input and its higher derivatives,global state estimation is exhibited by means of a Kalman-type observer. Anumerical example is provided to illustrate the applicability of the proposedobserver design for the problem of position and velocity estimation for avehicle navigating in the $n-$dimensional Euclidean space using a singleposition range measurement.

State Estimation for a Class of Linear Systems with Quadratic Output