Is It Possible to Follow Position Commands Using Velocity Measurements? [Lecture Notes]

In a simplistic sense, position can be determined from measurements of velocity by integration, and velocity can be determined from measurements of position by differentiation. In the former case, integration requires an initial condition and thus requires at least one position measurement. However, even in the case where the initial position is known, constant-but-unknown velocity-measurement noise, that is, bias, produces a spurious ramp in the computed position. On the other side of the coin, the accuracy of differentiation is limited by sensor noise, and thus approximate differentiation must be used in practice. Hence, low-frequency noise is the bane of integration, whereas high-frequency noise is the nemesis of differentiation.