Where am I? Sensors and Methods for Mobile Robot Positioning

112 Part I Sensors for Mobile Robot Positioning
4.2 Phase-Shift Measurement
The phase-shift measurement (or phase-detection) ranging technique involves continuous wave
transmission as opposed to the short pulsed outputs used in TOF systems. A beam of amplitudemodulated
laser, RF, or acoustical energy is directed towards the target. A small portion of this wave
(potentially up to six orders of magnitude less in amplitude) is reflected by the object's surface back
to the detector along a direct path [Chen et al., 1993]. The returned energy is compared to a
simultaneously generated reference that has been split off from the original signal, and the relative
phase shift between the two is measured as illustrated in Figure 4.21 to ascertain the round-trip
distance the wave has traveled. For high-frequency RF- or laser-based systems, detection is usually
preceded by heterodyning the reference and received signals with an intermediate frequency (while
preserving the relative phase shift) to allow the phase detector to operate at a more convenient lower
frequency [Vuylsteke, 1990].
n=8
n=7
n=6
n=5
Tx
x
n=1 n=2
n=3 n=4
Liquid
Surface
Rx
d
Figure 4.21: Relationship between outgoing and reflected waveforms, where x is the
distance corresponding to the differential phase. (Adapted from [Woodbury et al.,
1993].)
The relative phase shift expressed as a function of distance to the reflecting target surface is
[Woodbury et al., 1993]:
1 4%d
where
1 = phase shift
d = distance to target
= modulation wavelength.
(4.1)