  This paper deals with the problem of state estimation for a class of linear
time-invariant systems with quadratic output measurements. An immersion-type
approach is presented that transforms the system into a state-affine system by
adding a finite number of states to the original system. Under suitable
persistence of excitation conditions on the input and its higher derivatives,
global state estimation is exhibited by means of a Kalman-type observer. A
numerical example is provided to illustrate the applicability of the proposed
observer design for the problem of position and velocity estimation for a
vehicle navigating in the $n-$dimensional Euclidean space using a single
position range measurement.
