IEEE - Aerospace and Electronic Systems - August 2022 - 29

Schwung and Lunze
Table 1.
Parameters of the Simulation Analysis
Description
Transmission power level P0
Packet size M
Bandwidth B
Ricean factor K
Receiver sensitivity Srs
Mean packet loss probability pe;max
this packet is considered to be lost, because the information
is not useful any more. To reduce the freValue
2W
128
bytes
35 kbps
10
40dBm
0.03
channel with a bandwidth B. The data can be received
with the sensitivity Srs. The parameters of the channel are
summarized in Table 1. The transition probabilities of the
two-state Markov model are given by
pgg ¼ 0:995;pbb ¼ 0:5;pgb ¼ 0:005;pgb ¼ 0:5
to represent the correlation of the packet losses. The probabilities
are derived by a channel estimation method where
a sequence of packets is sent into the network and compared
with the received sequence of packets. The method
can be found in [2]. An analysis ofthe runtimes ofthe control
algorithms of the objects gives the bound tc;max ¼
33 ms of the computation times.
A data transmission under the condition that no packets
get lost causes large time delays, because the data rate
with which the information is transmitted may not exceed
the capacity of the channel. In order to reduce the conservatism
of the estimate, it is accepted that communication
takes place with the mean packet loss probability pe;max
according to Assumption 3. This fact results in smaller
values for the estimate ~tmaxðdð~tiÞÞ but might also cause
the unnecessary invocation of event eG2, because a
packet is not lost but just received after the time span
~tmaxðdð~tiÞÞ. Then, according to the " Literature " section
Table 2.
Results of the Simulation
dð~tiÞ=m ~tmax=ms peðdð~tiÞÞ¼ pe;max
10
50
100
1000
1250
1500
AUGUST 2022
218
241
253
311
319
325
0.03
0.03
0.03
0.03
0.03
0.03
~tmax=ms peðdð~tiÞÞ
227
251
264
0.01
0.01
0.01
325 0.012
333 0.012
340 0.012
quency of communication the event thresholds in the
" Prediction Unit " section are determined under the
assumption that at an event time instant tk the data are
received. If the information is received later, the standon
object could approach the give-way object unnoticed
and it is not ensured any more that a violation of
control aim (A1) can be prevented.
For the first part of the evaluation, the estimate of the
time delay ~tmaxðdð~tiÞÞ is determined with (9) and de ¼ 1
for six different distances dð~tiÞ between the objects. The
mean packet loss probability peðdð~tiÞÞ is derived from several
simulations with 10,000 communication time instants
each. The results of the simulation are given in Table 2,
where in the second column the estimated time delay
~tmaxðdð~tiÞÞ is given. It can be seen that the time delay
increases with an increasing distance between the objects.
The third column states the mean packet loss probability
for the estimates. As it was stated before, it can be seen
that the packet loss probability peðdð~tiÞÞ equals the bound
pe;max from Assumption 3.
In the second part of the analysis the adjustment factor
is chosen to be de ¼ 1:05 as a tradeoff to reduce the unnecessary
invocation of event eG2 but not to increase the
value of the estimate massively. Again, the estimate
~tmaxðdð~tiÞÞ is derived with (9), while the mean packet loss
probability peðdð~tiÞÞ results from several simulations with
10,000 communication time instants each. The adjustment
causes that the estimated time delay is increased by 5%.
The results of the adjusted estimate are given in the two
right-hand columns of Table 2. It can be seen that
peðdð~tiÞÞ is reduced significantly compared to the packet
loss probability stated in the third column, while the estimated
time delays ~tmaxðdð~tiÞÞ are only slightly increased.
Again ~tmaxðdð~tiÞÞ increases with an increasing distance
between the objects. Furthermore, now the packet loss
probability increases slightly as well.
As a result, a small adjustment of the transmission
delay tn;maxðdð~tiÞÞ by the factor de reduces the unnecessary
invocation of event eG2 significantly. Hence, the estimation
method is suitable to achieve the control aim.
COMMUNICATION FLOW OVER AN UNRELIABLE
NETWORK
The communication flow of the control method is shown in
the flow chart in Figure 6. The time instants when communication
is invoked are written at the top ofan execution step.
The time delays are indicated at the arrows. The communication
is split into an initialization phase and an execution
phase. Initially at t ¼ 0 the give-way object sends a request
RGð0Þ to the stand-on object to obtain its initial data
IEEE A&E SYSTEMS MAGAZINE
29
IEEE - Aerospace and Electronic Systems - August 2022

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