A. Background
We have been developing a pointing technique that is applicable to link initiation in FSO networking. At link initiation, each node measures its position by stand-alone GPS or DGPS. Then, it broadcasts this position information through a wireless RF data transceiver. In a centralized network (such as a ring network), a central node collects all position information from all nodes within the RF coverage region. Next, a central control node decides on the best ring topology from the available information, and sends out pointing commands to each node for the establishment of links. In a decentralized or distributed network, however, each node can make its own link decision based on the GPS location information from its neighbor nodes. Since the proposed pointing technique aims a point-to-point interconnection between any two nodes, it can be applied to centralized or decentralized networking.
Our pointing technique is based on measuring i) three dimensional attitude angles (roll, pitch, yaw) of an FSO transceiver mounted on a two-axis gimbal and ii) pointing vector of the transceiver (i.e., where the FSO transceiver is directing its laser beam). The attitude angles and pointing vector are measured on the local tangent plane or navigation frame, such as East-North-Up (ENU) coordinates. For example, as illustrated in Figure 1, the pointing procedure works as follows:
Pointing Procedures
-
The precise position of two FSO transceivers at
A
and
B
is measured referenced to a local origin in ENU coordinates.
-
The displaced angles,
\theta_{1}
and
\theta_{2}
, to the baseline
\overline{AB}
are determined; they become a control input to the gimbal.
-
The FSO transceivers at
A
and
B
are aligned to be on the baseline
\overline{AB}
; two transceivers point to each other (and become interconnected).
Once the baseline vector
\overline{AB}
or
\overline{BA}
is known in Step 1, each pointing system at
A
and
B
continues to Step 2, independently. The only necessary information for the two pointing systems at
A
and
B
is each other's location; then the two systems operate independently to align their FSO transceivers on the baseline. By this scheme, we can interoperate with another pointing system placed at
B
(whose system components may be different from those used at
A
) only if we know the coordinates of
B
.
C. Method of Pointing Vector Measurement
A vector is defined by two points in a coordinate frame; if the coordinates of the two points are
P_{1}
and
P_{2}
, respectively, then the vector is computed by the difference of the two coordinates,
P_{2}-P_{1}
, which is the vector from
P_{1}
to
P_{2}
. Likewise, knowing the pointing vector of an FSO transceiver requires measurement of two points on the path through which the laser beam of the transceiver passes. Figure 2 illustrates our method for pointing vector measurement. Figure 2a shows a GPS antenna mounted on FSO transceiver placed on a mobile platform which is stationary at a location
C_{1}
; then, the mobile platform moves forward in a straight line to another location
C_{2}.C_{1}
and
C_{2}
are RTK GPS coordinates for a GPS antenna mounted on the FSO transceiver, whose coordinates are
C_{1}=[E_{1},N_{1},U_{1}]^{T}
and
C_{2}=[E_{2},N_{2},U_{2}]^{T}
. Therefore, the pointing vector between
C_{1}
and
C_{2}
is calculated as:
u={[E_{2}-E_{1},N_{2}-N_{1},U_{2}-U_{1}]^{T}\over D},
\eqno{\hbox{(1)}}
View Source
u={[E_{2}-E_{1},N_{2}-N_{1},U_{2}-U_{1}]^{T}\over D},
\eqno{\hbox{(1)}}
where
D=\mid\mid[E_{2}-E_{1}, N_{2}-N_{1},U_{2}-U_{1}]^{ T}\mid\mid
and
\mid\mid\bullet\mid\mid
is the Euclidean vector norm. Figure 2b shows a second way of measuring the pointing vector: align FSO transceiver located at
C_{1}
to a pre-determined target at
C_{2}
(with previously determined position coordinates).
From the pointing vector
(u)
in Equation (1) and position coordinates of
C_{2}
,we can obtain the pointing vector centered at
C_{2}
as shown in Figure 2a (or
C_{1}
in Figure 2b), which is the current location of the FSO transceiver.
The RTK GPS position coordinates
C_{1}
and
C_{2}
contain measurement errors at the centimeter level. If we denote
{\varepsilon}_{1}
and
\varepsilon_{2}
as the three-dimensional measurement errors in
C_{1}
and
C_{2}
, respectively, then the unit vector
u
is expressed as:
u={[E_{2}-E_{1},N_{2}-N_{1},U_{2}-U_{1}]^{T}+(\varepsilon_{2}-\varepsilon_{1})\over D_{\varepsilon}},
\eqno{\hbox{(2)}}
View Source
u={[E_{2}-E_{1},N_{2}-N_{1},U_{2}-U_{1}]^{T}+(\varepsilon_{2}-\varepsilon_{1})\over D_{\varepsilon}},
\eqno{\hbox{(2)}}
where
D_{\varepsilon}=\mid\mid[E_{2}-E_{1}, N_{2}-N_{1}, U_{2}-U_{1}]^{ T}+(\varepsilon_{2}-\varepsilon_{1})\mid\mid
and
D_{\varepsilon}\leq D+\mid\mid\varepsilon_{2}-\varepsilon_{1}\mid\mid
by the Triangle Inequality [12].
If we assume that
\mid\mid\varepsilon_{1}\mid\mid
and
\mid\mid\varepsilon_{2}\mid\mid
are less than 3 cm, then
\mid\mid\varepsilon_{2}-\varepsilon_{2}\mid\mid\leq\mid\mid\varepsilon_{2}\mid\mid+\mid\mid\varepsilon_{1}\mid\mid\leq
<6cm. Therefore, if
D
is much larger than both
\mid\mid\varepsilon_{1}\mid\mid
and
\mid\mid\varepsilon_{2}\mid\mid({\rm e.g}., D=6m)
, then the following relations are hold:
\eqalignno{&{(\varepsilon_{2}-\varepsilon_{1})\over D_{\varepsilon}}\leq{\mid\mid\varepsilon_{2}-\varepsilon_{1}\mid\mid\over D_{\varepsilon}}\leq{\mid\mid\varepsilon_{2}\mid\mid +\mid\mid\varepsilon_{1}\mid\mid\over D_{\varepsilon}}\simeq{\mid\mid\varepsilon_{2}\mid\mid+\mid\mid\varepsilon_{1}\mid\mid\over D}\simeq 0&{\hbox{(3)}}\cr
&u\simeq{[E_{2}-E_{1},N_{2}-N_{1},U_{2}-U_{1}]^{T}\over D} &{\hbox{(4)}}}
View Source
\eqalignno{&{(\varepsilon_{2}-\varepsilon_{1})\over D_{\varepsilon}}\leq{\mid\mid\varepsilon_{2}-\varepsilon_{1}\mid\mid\over D_{\varepsilon}}\leq{\mid\mid\varepsilon_{2}\mid\mid +\mid\mid\varepsilon_{1}\mid\mid\over D_{\varepsilon}}\simeq{\mid\mid\varepsilon_{2}\mid\mid+\mid\mid\varepsilon_{1}\mid\mid\over D}\simeq 0&{\hbox{(3)}}\cr
&u\simeq{[E_{2}-E_{1},N_{2}-N_{1},U_{2}-U_{1}]^{T}\over D} &{\hbox{(4)}}}
Hence, as
D
increases, the pointing vector becomes closer to the true one without measurement errors.
The East and North components of the pointing vector determine yaw
(\psi)
. With roll and pitch from local angular sensors and yaw from RTK GPS, we have complete attitude angle information of the FSO transceiver which is necessary to convert the pointing vector in the navigation frame (ENU coordinates) to the one in the body frame by the following equations:
P_{B}=C_{ENU}^{B}P_{ENU}=C(\phi)C(\theta)C(\psi)P_{ENU},
\eqno{\hbox{(5)}}
View Source
P_{B}=C_{ENU}^{B}P_{ENU}=C(\phi)C(\theta)C(\psi)P_{ENU},
\eqno{\hbox{(5)}}
where
-
(\phi,\theta,\psi)
: Attitude angles
-
C(\phi),C(\theta),C(\psi)
: Rotation matrices
-
C_{ENU}^{B}=C(\phi)C(\theta)C(\psi)
: Transformation matrix from the ENU coordinates to the body frame.
-
F_{ENU}
: Position in the ENU coordinates
-
F_{B}
: Position in a body frame.
With the baseline vector
{AB}
or
{BA}
transformed to the body frame by Equation (5), the control input to the gimbal (i.e., heading and elevation angles in Figure 1) is computed from the pointing vector and the baseline vector transformed to the body frame (we skip the details here).
The advantages of this pointing method are summarized as:
-
Conceptually simple and easy to implement.
-
A complete attitude angle can be measured only by RTK TK GPS, if the the surface is flat or as long as we can keep the surface level using a stabilizer.
-
RTK GPS consists of a GPS unit and a wireless RF data transceiver; the precise position data will be sufficient to track mobile nodes. Its high accuracy will improve the performance of position position and velocity estimation ofa mobile node.
-
The precise heading information from RTK GPS can be combined with the roll and pitch outputs from INS mounted on an aircraft [13]
[14]; thus enabling us to use the pointing technique in a dynamic environment.
Since RTK TK GPS requires the observation of at least five GPS satellites to yield such high accurate position coordinates, our basic assumption in this pointing method is that there is no significant GPS signal blockage on the site where the pointing system is being operated.