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On the Scheduling of Ranging and Distributed
Positioning Updates in Cooperative IR-UWB
Networks
B. Denis, Member,IEEE, M. Maman, L. Ouvry
CEA-Leti Minatec
17 rue des Martyrs, 38054 Grenoble Cedex 09, France
E-mails: [benoit.denis, mickael.maman, laurent.ouvry]@cea.fr
Abstract—The recent demonstration of precise ranging mea-
surements through low power Low Data Rate (LDR) Impulse
Radio - Ultra Wideband (IR-UWB) communications has disclosed
new perspectives for cooperative location-enabled wireless net-
works. With this respect, joint ranging and distributed posi-
tioning mechanisms supported by specific protocol transactions
have already been proposed within user-centric infrastructureless
applications. However, in spite of advanced medium access tech-
niques, those approaches still suffer from resource inefficiency.
In this paper, we describe and compare new scheduling strate-
gies regarding the joint update of ranging measurements and
positional information. One goal is to accelerate the convergence
of positioning errors and hence to reduce network latency and
overhead accordingly. As an example, one scheduling option
considers discarding so-called useless pair-wise links based on
the prior analysis of the conditional Cramer Rao Lower Bound
(CRLB) of positioning errors at each mobile node.
Index Terms—Cooperative Networks, Convergence, Dis-
tributed Positioning, Latency, Medium Access Control, Overhead,
Ranging, Scheduling, Time of Arrival, Ultra Wideband
I. INTRODUCTION
New integrated ranging solutions offered in short-range
wireless networks (e.g. [1] - [3]) make the advent of coop-
erative positioning more and more probable in a reasonably
near future. The benefits from mobile-to-mobile cooperation
with respect to location might be manifold, e.g. for the
sake of solving out local geometrical ambiguities, enhancing
final positioning accuracy through information redundancy and
spatial diversity, or simply improving coverage and continuity
of service (e.g. [4] - [7]).
However, recent experimental results in the field of Ultra
Wideband (UWB) cooperative positioning pointed out difficul-
ties in selecting pair-wise measurements that are worth taking
part into positional calculi (e.g. [7]). Indeed, depending on
the quality of local pair-wise measurements or on network
topology, it might happen that some radio links are almost use-
less and even harmful to final positioning results, for instance
by providing poor Geometric Dilution Of Precision (GDOP).
Another crucial aspect of the problem concerns specific user-
centric positioning implementations. Unlike centralized co-
operative approaches, distributed solutions imply that mobile
nodes locally compute their own locations. One motivation
is the necessity to operate within opportunist and perennial
networks in the lack of fixed infrastructure or if some nodes
are withdrawn from the sketch (intentionally or not). Then,
the idea consists in sharing computational load onto the entire
network, while preserving reasonable computational complex-
ity and low power consumption in each node, for instance
by applying distributed iterative techniques. Such approaches
usually claim to enjoy fine scalability in large-scale or densely
crowded networks as they tend to avoid the multi-hop relay
of location-dependent information to a collecting point, as
well as the centralized computation of unknown locations.
However, it is admitted that iterative distributed methods are
still too consuming in terms of time and resources, exhibiting
relatively slow convergence. This point is all the more critical
since stringent Low Duty Cycle (LDC) requirements might be
adversely imposed by regulatory bodies on the transmitting
activity per node (e.g. [8]). Consequently, new cooperative
cross-layer mechanisms have to be figured out to enhance
the convergence speed of positioning errors within iterative
distributed approaches.
In this context, in parallel of completed standardization
works focusing on peer-to-peer ranging through UWB Low
Data Rate (LDR) communications (e.g. [1]), previous attempts
already aimed at designing synergetic Medium Access Control
(MAC) and higher layers, adapting the LDR IEEE 802.15.4
MAC specifications into a beacon-enabled Time Division Mul-
tiple Access (TDMA) solution including Guaranteed Time
Slots (GTS) and slotted ALOHA, while providing adequate
support to jointly cooperative ranging and distributed posi-
tioning with optional data aggregation and broadcast, as well
as dynamic resource management for temporary applications
(including location-oriented needs) (e.g. [8] - [10]).
In this paper, we propose and compare new scheduling
strategies that enable more efficient updates of positional
information and ranging measurements at various levels of
network coordination. The final aim is to reduce traffic,
overhead and network latency. One first proposal consists in
relying on the knowledge of the immediate neighborhood of
each mobile node. Another proposal mostly adapted to peer-
to-peer schemes is based on a prior analysis of the conditional
Cramer Rao Lower Bound (CRLB) of positioning errors,
enabling to determine the pair-wise range measurements that
can be discarded without degrading too significantly average
positioning accuracy. Accordingly, protocol transactions can
be alleviated before reaching convergence. For the sake of
illustration, we systematically consider the protocol described
in [8] as a basis here, whatever the evaluated scheduling
approach, keeping in mind underlying concepts could be
extended to other protocol schemes.
The paper is structured as follows. In Sections II and
III, we firstly recall examples of IR-UWB network topology
and protocol implementation supporting the required location
functionalities. In Section IV, we describe the new proposed
scheduling strategies, which are subsequently evaluated in
Section V through simulations. Finally, Section VI concludes
the paper.
II. CONSIDERED NE TWORK TOPOLOGY
We consider a mesh IR-UWB network under partial connec-
tivity, like in [12]. Each mobile node can perform precise peer-
to-peer range measurements, e.g. based on TOA estimation
(e.g. at the tight resolution of a few ns, or even below)
and multiple-way cooperative ranging transactions (i.e. with
further estimation and compensation of potential clock drift
effects) (e.g. [3]), not only with respect to a few anchors set
at known locations but also to other mobile nodes, as shown
on Figure 1. A typical network topology hence comprises N
nodes, including Naanchors (i= 1..Na) and Nmmobiles
(i=Na+ 1..N). The neighborhood of node i, namely
H(i) = {j/dij < dm}, is defined as the set of node indexes
enabling radio communications with respect to node iat
practical distances dij compliant with the maximal observable
transmission range dm. The entries Ii,j of the associated
adjacency matrix directly account for possible pair-wise radio
links (See Figure 1).
III. CONSIDERED LOC ATIO N-ENABLED PR OTO CO L
A. General Description
As seen on Figure 2, the considered protocol is TDMA-
oriented and beacon-enabled (e.g. [8]).
A typical Superframe (SF) of interest is split into distinct pe-
riods, as follows. The Beacon Period (BP) is used to transport
beacons, including the creation by the PicoNet Coordinator
(PNC) and the relaying by routers. The Guaranteed Time
Slot (GTS) Request Period is used to transport only the GTS
requests from the devices to the PNC. An optional Topology
Management Period (TMP) can also be used to transport
the HELLO frames for network discovery and Scheduling
Tree Update frames. The Contention Access Period (CAP)
is used to transport command frames, association frames and
specific frames for further distributed functionalities. Finally,
the Contention Free Period (CFP) is used to transport data
and ranging frames for guaranteed functionalities. Note the
payload of the beacon transmitted by the PNC at the beginning
of each SF entirely specifies the latter, from containing the size
of each period, the number of subslots per slot and the IDs of
the nodes communicating in guaranteed slots.
This structure offers a certain number of advantages, such
as fine flexibility via adjustable SF and period sizes and en-
ergy saving through beaconing (beacon payload information),
enabling efficient awake/asleep scheduling. Further details on
this protocol implementation can be found in [8].
B. Supported Location Functionalities
The supported location functionalities can be roughly split
into two main phases, namely coarse connectivity-based po-
sitioning during network initialization and further TOA-based
ranging for refined positioning.
1) Coarse Positioning: As a first step, connectivity-based
coarse positioning (e.g. through DV-Hop, [13]) can be per-
formed almost for free during network initialization. It is
advantageously coupled with association and neighborhood
discovery procedures (e.g. [8]). Nodes share information to
collectively determine the number of hops from each mobile
to anchors, the average distance per hop along paths to anchors
(flooded back to mobiles as a correction factor), and finally
coarse distances to anchors that locally enable positioning (e.g.
through centralized Least Squares). Usually, this technique
provides positioning errors with a standard deviation on the
order of a few meters, which can vary depending on the
anchors density and spatial network anisotropy. Each node
can use afterwards its own coarse estimate as an initial guess
feeding a refined positioning procedure.
2) Cooperative Ranging: In a first simple Peer-to-Peer
(P2P) 3-Way Ranging scheme, 3 adjacent slots are guaranteed
by the PNC to a pair of devices. If node iintends to perform
a P2P procedure with respect to one neighbor j, it can send
to the PNC one specific packet in the GTS request period,
asking for 3 more GTS in the CFP dedicated to peer-to-peer
communications with j. Another option is that the PNC itself
schedules the allocation of 3 GTS, without any GTS request
emanating from the devices. Then, once the coordinator ac-
cepts or schedules this P2P ranging transaction, it indicates
in the next beacon when node iis expected to start its P2P
Ranging procedure with respect to node j. Subsequently, node
isends a request packet to node jin a first specified GTS and
receives a response (resp. drift) packet in a second (resp. third)
slot from node j. In the example, the overhead over 3 slots
represents at least 538 bits (i.e. including packet headers and
data used for location purposes), as shown on Figure 2. Note
that further data (not necessarily related to location) could also
be included in the payloads of transmitted packets.
As for Aggregate and Broadcast 3-Way Ranging (A&B),
which was initially described in [9], resources and traffic are
optimized for a better support of location-oriented function-
alities. It uses the same SF structure but GTS are allocated
for ranging communications with respect to several neighbors
simultaneously. Each ranging packet broadcasted to neighbors
contains the latest request/response/drift timing information
and estimated position available at each transmitting node. Just
like the P2P scheme, either requests from the devices or PNC
scheduling can be considered. However, if the network needs
to frequently update its knowledge about mobile positions, it
is preferable that the PNC is in charge of ranging scheduling
so as to save communication resources.
For both ranging schemes, based on unitary TOA estima-
tions (i.e. collecting the arrival times of exchanged packets),
one range measurement is issued at the initiator of the trans-
action. Note the residual errors affecting range measurements
after clock drift correction can be statistically characterized (in
terms of their standard deviation σT) as a function of involved
protocol durations and TOA noise standard deviation (e.g. [9],
[11]).
3) Cooperative Positioning: Assuming independent mea-
surements, the Log-Likelihood of joint pair-wise ranges in
[12] is maximized with respect to mobile coordinates set as
optimization variables. Then, adopting an iterative and asyn-
chronous gradient-descent approach, distributed positioning
requiring local pair-wise exchanges of positional information
can be advantageously coupled with the ranging transactions
described above. At the kth step, the update of i’s estimated
coordinate bxi,k−1(and similarly for the yand zcoordinates)
is realized each time ireceives bxj,k−1and byj,k−1from its
available neighbor j, as follows:
bxi,k =bxi,k−1+δij,k (1a)
δij,k =αij,k∂Λij
∂dij e
dij =e
d∗
ij,k
dij =b
dij,k−1
∂dij
∂xixi=bxi,k−1
xj=bxj,k−1
dij =b
dij,k−1
(1b)
where Λij =ln(p[e
dij /dij ]),∂dij /∂xi= (xi−xj)/dij ,
b
dij,k ,p(bxi,k −bxj,k)2+ (byi,k −byj,k)2is the estimated
distance between nodes iand j, based on the estimated coordi-
nates bxi,k,byi,k ,bxj,k and byj,k,αij,k is a dynamic optimization
step used to mitigate or inflect the ascent direction, and e
d∗
ij,k
is a function of all the available range measurements between
iand jup to step k. For instance, it can be equal to e
dij,k
if only the instantaneous ranging measurement is used or to
the average of k0< k range measurements available up to the
kth update step in low-mobility applications (optionally, with
a given memory factor).
Finally, if no refined prior ranging error model is avail-
able (e.g. assuming no bias statistics but uniquely Gaussian
centered noise affecting range measurements with a standard
deviation σT,ij,k in first approximation), the algorithm is
equivalent to Distributed Least-Squares (DLS) (e.g. [8], [12]).
For instance, under the simplified assumption that σT,ij =
σT=cst and invariant in time (i.e. over k), one can use
directly Λij = ( e
dij −dij )in the expression of the coordinate
update (1b).
IV. PROPOSED SCHEDULING STRATEGIES
As already pointed out, ranging measurements and posi-
tioning updates within cooperative distributed and iterative ap-
proaches can be crucial with respect to final positioning accu-
racy (in terms of achievable error floor and convergence time),
but also to prevent from divergence problems in case of limited
connectivity (and hence poor graph rigidity/realizability) or
wrong initialization. In this section, we define and compare
new scheduling policies as regards to such measurements and
estimation updates.
A. Scheduling Schemes Based on Node Neighborhood
We firstly define connectivity-based scheduling strategies, in
the sense they mostly rely on the knowledge of the immediate
neighborhood of each mobile node. These schemes can be
applied either with P2P or A&B exchanges indifferently.
1) Optimal & Ordered: During network initialization, a
list is drawn containing the anchor indexes first, and then
the indexes of mobile nodes sorted as a decreasing function
of their number of neighbors (i.e. the first nodes mentioned
having the highest numbers of direct neighbors). Ranging slots
(in P2P or A&B) are assigned so that mobile nodes speak and
update their position according to the global ordered list, but
only with respect to all their neighboring anchors first. Once
the previous update round is performed (i.e. with the update of
all the mobiles at least once with respect to all their available
anchors), mobile nodes update their positions following the
same ordered list as previously, but this time with respect to
their neighboring mobiles sequentially. The complete update
list is used at least once, ensuring all the nodes are updated
once with respect to each one of their neighbors.
2) Sequential & Ordered: The same list as previously is
drawn. Mobile nodes update their position with respect to
the ordered list sequentially (including anchors and mobiles)
within one single round. The complete update list is used at
least once.
3) Half-Random: A list is drawn with anchor indexes first,
and then random mobile indexes. Mobiles are unsorted but
cited at least once per list. The updates follow exactly the
same procedure as previously, but with the new list. The
complete update list is used at least once. Note a couple of
more P2P slots could be added on top of a steady state A&B
structure, so as to favor the updates of specific nodes in case
of measurement outliers (or mobility) detected locally.
4) Purely Random: No prior list is required. In A&B, in
each active ranging slot, only one possible node is randomly
chosen to send a ranging packet, whereas in P2P, at each set
of 3 slots, a pair of nodes is randomly chosen to complete one
single ranging transaction.
5) Purely Random & Slot Reuse: Idem as previously. In
A&B, at each active ranging slot index, 3 competing nodes are
randomly chosen to send one ranging packet simultaneously,
whereas in P2P, at each set of 3 slots, 3 pairs of nodes are
randomly chosen to complete 3 distinct ranging transactions
6) Uncoordinated SxM:Each node locally determines
when it sends its last ranging packet, choosing randomly one
SF over the next SSF (since its last ranging transmission) and
one slot among the Mranging slots available per SF.
The previous strategies are sorted in terms of their coordi-
nation needs. For instance, the most demanding ”Optimal &
Ordered” scheme practically implies a coordinator preliminar-
ily collects information related to nodes connectivity, builds up
the scheduling list, and finally assigns the corresponding slots
to mobiles nodes in successive beacons. On the contrary, the
”Uncoordinated” scheme requires that mobile nodes locally
take the initiative to broadcast regularly their ranging packets,
without paying attention to potential collisions. Note that if
we are to consider beacon-enabled PicoNet synchronization
and preserve a global TDMA-oriented structure of the SF, this
”Uncoordinated” scheme means ranging transactions would
occur in an extended CAP, with nodes competing for common
time resources.
B. Scheduling Schemes Based on Deliberate Link Discarding
Ignoring deliberately links and ranges for the computation
of mobile locations, one can expect to save time resources as
a lower number of packet exchanges and ranging slots would
be required. Then one question is about the election of so-
called useless links that can be discarded to save resources
without degrading too significantly the overall positioning
accuracy. With this respect, we propose a new scheduling
strategy adapted to P2P transactions, based on the evaluation
of the conditional CRLB of unbiased position estimators after
removing artificially radio links.
We assume that the pair-wise range measurements resulting
from TOA estimation and cooperative protocol transactions
between nodes iand jare affected by Gaussian centered noise
with a standard deviation equal to σT,ij . Under the previous
assumptions, adapting the results from [6], one can compute
the minimal spatial deviation, or equivalently the theoretical
Root Mean Square Error (RM SEm), of any unbiased position
estimator for each node i, as a function of all the actual node
locations {(xi, yi)},i= 1..N (i.e. including mobiles and
anchors) and the pair-wise noise standard deviations {σT,ij }
associated with active i−jradio links, as follows:
[RMSEm]i= ([Fxx −Fxy F−1
yy FT
xy]−1
i,i +[Fyy −FyxF−1
xx FT
yx]−1
i,i )1/2
(2)
where
[Fxx]k,l =
Pi∈H(k)1
σ2
T,ik
(xk−xi)2
d2
ik
if k=l
−IH(k)(l)
σ2
T,kl
(xk−xl)2
d2
kl
otherwise (3)
and
[Fxy]k ,l =
Pi∈H(k)1
σ2
T,ik
(xk−xi)(yk−yi)
d2
ik
if k=l
−IH(k)(l)
σ2
T,kl
(xk−xl)(yk−yl)
d2
kl
otherwise
(4)
with H(i)the 1-Hop neighborhood of node i, and IH(i)(j) =
Ii,j = 1 if j∈H(i).
After completing network initialization, it is assumed that
the PNC can compute approximated versions of the previous
conditional CRLB, using the coarse position estimates deliv-
ered through DV-Hop as conditioning variables, namely {bxi}
and {byi},i=Na+ 1..N (i.e. instead of the true mobile
locations, which are obviously unknown). A first reference
CRLB is then computed under initial connectivity assuming
the true adjacency matrix I, i.e. assuming all the links that
are physically addressable after network discovery. Then the
conditional CRLB is evaluated again while discarding various
combinations of these feasible links, resulting into poorer
connectivity conditions characterized by the new matrix I0.
One can keep on discarding links till the corresponding
estimates of [RMSEm]i,i=Na+ 1..N , respect a positive
threshold reflecting the maximal tolerated degradation of the
average positioning accuracy after discarding pair-wise links
and measurements, as follows
T r(RM SEm|I0,{(x,y)}={(bxi,0,byi,0)})
< Nm+T r(RM SEm|I,{(x,y)}={(bxi,0,byi,0)})(5)
where T r[A]denotes the trace of matrix A.
The combination of discarded links that provides the best
theoretical positioning accuracy with the highest cardinal and
still respects the previous tolerance criterion, is finally chosen
for the final scheduling of both range measurements and
positioning updates. At this point, note that any of the basic
scheduling schemes described in IV-A can then be applied
with the connectivity matrix I0resulting from link discarding.
In the following, we make the distinction between exact or
genius-aided link discarding assuming perfect knowledge of
{eσT,ij }={σT ,ij }in (2) and an approximated version that
assumes all the pair-wise links experience worst case noise
conditions with {eσT,ij }={maxi,j [σT ,ij ]}(i.e. RM SEmem-
phasizing only topological effects on theoretical performance),
what is already one step beyond in comparison with simpler
connectivity-based approaches.
V. CONVERGENCE TIME, LATEN CY A ND OVERHEAD
In this section, we illustrate the impact of the different
scheduling strategies proposed in IV on the convergence
of average positioning errors, latency, traffic and overhead
through canonical simulation results.
For a first set of packet-oriented simulation results, we
consider two examples of sparse and dense networks. The
realizations associated with the dense (resp. sparse) case
comprise N= 40 (resp. N= 15) nodes randomly placed
on a 40m∗40mscene, including Na= 5 anchors, with
a maximum transmission range dm= 12m, which can be
lower depending on local Signal to Interference and Noise
Ratio (SINR) conditions. The corresponding average number
of neighbors per node is equal to 6 (resp. 4) in the provided
examples. The PNC, which is systematically located in the
center of the scene, also plays the role of an anchor. Four more
surrounding anchors are placed at the corners of the scene.
Each pair-wise range measurement is simulated under a real-
istic channel configuration Ch ={LO S, NLOS, NLOS2}
(e.g. [12]), drawn as a random variable conditioned upon
the actual range. The estimated TOA of each ranging packet
is also affected by a systematic bias following a mixture-
based distribution and Gaussian noise terms with a standard
deviation σT OA =√K.dβCh /c with K= 0.001,βLOS = 2,
βNLO S = 2.25,βNLO S2= 2.5(e.g. [8]). Positioning relies
on the iterative DLS algorithm previously described in III-B3,
with αij,k = 0.25 (resp. 1) for position updates with respect to
mobile neighbors (resp. anchors). The curves are obtained after
averaging over random configuration trials (including different
TOA noise occurrences, random pair-wise channel realizations
and distinct sequences of tested nodes during neighborhood
discovery).
On Figure 3, we compare the convergence of the average
positioning error (computed over all the mobile nodes and
network realizations) in A&B (resp. P2P) transactions with 6
(resp. 6/30) ranging slots per SF for different connectivity-
based scheduling strategies (See IV-A). At each trial, these
strategies have been tested under similar conditions as regards
to network topology, range measurements, and initial guess
(i.e. from DV-Hop results). Note that initialization, which does
not fall in the scope of our comparison here, can last for
a few tens/hundreds of consecutive SFs prior to the shown
refinement phase (e.g. 200 SFs from scratch in the provided
examples). On Figure 4, we report the corresponding number
NGT S/SF of ranging slots consumed per SF, the number
NSF |e<1mof SFs before achieving an average positioning
error e < 1m(resp. 0.5m), the elapsed time Te<1massum-
ing a SF duration of 200ms like in [8], the average data
rate DRdedicated to location, the average overhead O(i.e.
the data consumed over communication means), the number
NRNG|e<1mof successful ranging transactions vs. the number
of tempted ranging transactions (along with their ratio in %),
and finally the data cost CRNG of one single ranging update.
Figures 3 and 4 show the benefits from ”Exhaustive” (in
the sense all the links are updated at least once according to
a list) and ”Ordered” (in the sense all the links are updated
according to a sorted list) scheduling, in comparison with
blind strategies. Exhaustive scheduling within A&B enables
the update of each node with respect to all its neighbors
after 2Nranging slots and proves to be the most efficient
scheme in dense networks. The cost of one ranging update
with exhaustive scheduling represents 125 bits in A&B and
538 bits in P2P. The comparison between A&B ”Sequential
& Ordered” and ”Purely Random” shows the relevance of
exhaustive approaches in terms of ranging efficiency (100% vs.
49.3%). The ”Sequential & Ordered” strategy in A&B makes
the mobiles with numerous neighbors in their neighborhood
converge well and faster in a first step (in priority with respect
to other nodes with numerous neighbors), hence providing
afterwards other mobiles suffering from less favorable connec-
tivity conditions with reliable neighbors (almost as reliable as
new anchors). From an interference mitigation perspective, the
A&B ”Purely Random” strategy still relies on a coordinated
mode and hence can also regulate collisions through slot reuse,
whereas such regulation is impossible within ”Uncoordinated”
modes. In the back-off strategy of A&B ”Uncoordinated”
schemes with 2x6(resp. with 10x6), the average number of
transmitting nodes per ranging slots is 4.3in dense networks
(resp. 1.2) and 1.66 for sparser networks (resp. 0.45). For
comparison purposes, this figure is equal to 1(resp. 3) with
A&B ”Purely Random” (resp. in the A&B ”Purely Random
& Slot Reuse”). The equivalent contention back-off window
of ”Uncoordinated” schemes is not appropriately dimensioned
with sparse networks and thus convergence is slower. The
reuse of ranging slots degrades performance because ranging
collisions can hardly be avoided in smaller networks. As
for P2P, increasing the number of ranging slots per SF can
help to enhance convergence at the price of worse energy
consumption. Actually, with 6 ranging slots per SF (resp. 30),
the SF is composed of 100ms of active part (resp. 180ms) and
100ms of inactive part reserved for sleep mode and energy
efficiency (resp. 20ms). Hence, P2P is more suitable to sparser
networks, what results from the fact that convergence does not
directly depend on the number of nodes in the network (unlike
A&B) but mostly on the number of links. As an example,
in a sparse network realization with N= 15 and 38 links
overall, an exhaustive A&B strategy requires 2∗15 = 30
ranging slots vs. 3∗38∗2 = 228 with P2P (assuming bilateral
measurements). Finally, one can also notice the benefits from
more frequent updates in the ”Uncoordinated” scheme with
2x6in comparison with the equivalent scheme for 10x6.
Note that in the most favorable A&B case, positioning
refinement (e.g. down to an average error better than 1m)
takes approximately 8 more seconds (i.e. 40 consecutive SF
of 200ms each) after initialization if the network starts from
scratch. However, once convergence is achieved in reasonably
low-mobility scenarios, only timely updates and measurements
can be performed in the steady-state regime. In other words,
position estimates are continuously available at mobile nodes
with no information relaying, and only local updates might
be performed on demand. Furthermore, note A&B positioning
could also be enhanced with a spatial reuse of ranging slots
(i.e. allocating slots to nodes that are geographically far from
each other to minimize interference).
Finally, we show on Figure 5 the convergence times required
to reach e < 1mfor basic ”Purely Random” and ”Optimal &
Ordered” scheduling strategies with P2P transactions in a net-
work comprising Nm= 15 mobile nodes and Na= 5 anchors.
In this new example, range measurements are only noised
with Gaussian centered error terms with a standard deviation
σT,ij uniformly distributed over [0,0.5]m, what is still in line
with recent IR-UWB experiments [3]. Convergence times are
averaged over hundreds of network and noise realizations, and
then normalized with respect to the time elapsed with another
”Optimal & Ordered” scheduling strategy that discards radio
links based on a prior CRLB analysis, as proposed in IV-B.
In other words, one of the two curves associated with basic
scheduling exceeding 1 (e.g. at 1.x) practically means the
strategy discarding links provides better convergence (i.e. the
other strategy takes approximately x% more time to converge).
It is worth noting here that there seems to exist an optimal
value of the maximal tolerated positioning accuracy degra-
dation in (5), depending on network density. When the
tolerance threshold is too strict (e.g. at = 10−3), only a few
radio links are discarded and almost no resource can be saved
accordingly, so that convergence speed is hardly enhanced.
On the contrary, if the tolerance threshold is too relaxed (e.g.
at = 10−1), numerous links are discarded but positioning
accuracy (i.e. the error floor) globally degrades and further
convergence problems might appear.
Another remark is that the gain is less evident as node
density gets smaller and smaller. When the number of available
neighbors per node is low, redundancy is significantly miti-
gated and each link is useful. Consequently, there is no more
practical interest in removing pair-wise range measurement.
Similar effects are observed on Figure 6 for Nm= 10
and different average RMSE targets. One can also note
the link discarding strategy based on CRLB approximation
enjoys approximately the same performance as that of the
genius-aided scheme, and globally better performance than the
basic ”Optimal & Ordered” scheme, especially at demanding
average RMSE targets.
Finally, note link discarding looks less evident for A&B.
In the latter, each node indeed broadcasts its own packets
to available neighbors, so that no protocol resource can be
directly saved by discarding specific range measurements.
Further investigations have to be carried out to figure out how
link discarding could be adapted to A&B schemes as well.
VI. CONCLUSION
In this paper, we have described and evaluated new schedul-
ing strategies for jointly cooperative ranging and iterative
distributed positioning in user-oriented IR-UWB networks.
One of the proposed options discards useless links to save
time resources and reach faster convergence under imposed
peer-to-peer transactions, while a second family of ordered and
exhaustive updates giving priority to nodes with high connec-
tivity seems more adapted to Aggregate and Broadcast pro-
tocol schemes (e.g. ”A&B Sequential and Ordered”). Future
works should address a)the adaptation of prioritized distributed
protocols, which already showed relevance for scalable and
dense tracking-enabled IR-UWB networks (e.g. [11]), b)the
evaluation of scheduling robustness under realistic mobility for
a more precise assessment of instantaneous network latency
in the steady-state regime, and possibly, c)the introduction
of TOA bias statistics in the computation of CRLB for
link discarding purposes, d)the evaluation of adaptive link
discarding based on estimated locations while converging.
ACKNOWLEDGMENT
This work has been performed in the framework of the ICT
project ICT-217033 WHERE, which is partly funded by the
European Union.
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Fig. 1. Example of mesh network topology (left) and connectivity matrix
I(right), with Nm= 18 mobiles, Na= 4 anchors and a maximum
transmission range dm= 20m
Fig. 2. Ranging slots and example of data amount consumed in Peer-to-Peer
(P2P) ranging transactions
Fig. 3. Average positioning errors with Na= 5 anchors and Nm= 35
(top) or Nm= 10 (bottom) mobiles on a 40m∗40mscene as a function of
the number of SF for different scheduling strategies
Fig. 4. Latency and overhead for different scheduling strategies (including
network initialization lasting for 200 SFs of 200ms each, i.e. 40s)
Fig. 5. Normalized convergence times before achieving an average
RMSE = 1m, for different scheduling strategies (including exact CRLB-
aided link discarding) and 2 distinct network densities
Fig. 6. Empirical CDF of convergence times at RM SE = 1mand 0.5m,
for different scheduling strategies (including approximated and exact CRLB-
aided link discarding with = 5cm) at 2 distinct network densities, with
Nm= 10 mobiles and Na= 5 anchors
