=Paper=
{{Paper
|id=Vol-3719/137
|storemode=property
|title=A Graph-Based Model for Leveraging Spatial and Fingerprint Similarity in RF-based Indoor Positioning
|pdfUrl=https://ceur-ws.org/Vol-3719/paper7.pdf
|volume=Vol-3719
|authors=Liam Mark Self,Ian James Wassell
|dblpUrl=https://dblp.org/rec/conf/wiphal/SelfW24
}}
==A Graph-Based Model for Leveraging Spatial and Fingerprint Similarity in RF-based Indoor Positioning==
https://ceur-ws.org/Vol-3719/paper7.pdf
A Graph-Based Model for Leveraging Spatial and
Fingerprint Similarity in RF-based Indoor Positioning
Liam Mark Self1,* , Ian James Wassell1
1
Department of Computer Science and Technology, University of Cambridge, United Kingdom
Abstract
A limitation on conventional deep learning methods for fingerprint-based indoor positioning is the difficulty in
leveraging the underlying geometry of the environment. Solutions to this involving Graph Neural Networks
have been proposed, however these place a dominant focus on the geometric relationships between reference
points (RPs), which are often sparse in number, and ignore the relationships between the training data.
In this work, we present a proof-of-concept model for RF-based indoor positioning based on Graph Neural
Networks that captures both the spatial relationships between RPs and the similarity between fingerprints of
the training database. We use a Graph Attention Network to train a graph composed of 31 000 power readings
gathered from a large office simulation of a environment produced using a commercial ray-tracer, and a Graph
Convolutional Network to model the spatial relationships between RPs.
Preliminary evaluation shows a positioning accuracy of 0.78 m, a 29% improvement over benchmark models
using kNN, MLP and Random Forest, and suggests that combining both graph models outperforms the use of
either model independently.
Keywords
Indoor positioning, Fingerprinting, Graph Neural Networks, Data augmentation
1. Introduction and background
The rise of applications that require reliable, robust location information has increased rapidly in recent
times, and location and context-aware technology transcends numerous fields and areas, from au-
tonomous robotics[1], inventory management[2], interactive multimedia [3], through to the monitoring
of the health of vulnerable adults[4, 5].
While GNSS technologies such as GPS are considering the ‘gold standard’ of modern positioning
systems, their reliance on line-of-sight communication with satellites limits their practicality in indoor
environments. RF-based indoor positioning systems, then, often turn to terrestrial technologies to
provide reference points with which to locate devices, such as Bluetooth, Wi-Fi and Ultra Wide-Band
(UWB). The use of Wi-Fi, for example, is nowadays ubiquitous for network and Internet communications,
and while, for example, utilising channel state information (CSI) of wideband technologies like UWB
can result in very high precision position estimation (in ideal conditions), Wi-Fi base stations remain
a popular reference source due to the ability to leverage existing infrastructure. Information such as
CSI, carrier phase or received power with respect to an array of static reference devices can be used to
construct a unique fingerprint which can be mapped to a specific location or region. A database can
be constructed of such fingerprints collected across a wide area, and used to construct an estimated
channel model of that area.
Up until the last few years, the development of fingerprinting models for indoor positioning has
largely treated fingerprints as simple vectors, utilising techniques such as artificial neural networks[6, 7],
decision trees[8] and k-Nearest Neighbour[9]. While this format is common in machine learning, posi-
tioning is an inherently geometric problem; any such model will ultimately infer the spatial relationship
that maps fingerprints to coordinates, but ‘flattening out’ each fingerprint creates difficulty in incorpo-
rating information already known about the geometric structure of the environment or the relationship
WIPHAL 2024: Work-in-Progress in Hardware and Software for Location Computation, June 25-27, 2024, Antwerp, Belgium
*
Corresponding author.
$ liam.self@cl.cam.ac.uk (L. M. Self); ijw24@cam.ac.uk (I. J. Wassell)
0000-0002-7076-6613 (L. M. Self); 0000-0001-7927-5565 (I. J. Wassell)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
between individually collected fingerprints.
More recently, a field has emerged which extends conventional deep learning architectures to accom-
modate spatial and structural relationships, by operating directly on data structured as graphs[10, 11].
Several models have been proposed since on graph-based positioning, but in general each proposition
focuses on a single structuring of the fingerprint database [12]. In this paper, we present a current
work-in-progress study which fuses two graph representations of a RF-based fingerprint database to
increase the expressiveness of the training data.
The remainder of this paper is organized as follows: In Section 2, we briefly present Graph Neural
Networks and the specific architectures used in this study. Section 3 describes the generation of a
simulated indoor positioning dataset and the multi-graph model we evaluate. The current results of our
work are given in Section 4, and in Section 5 we summarize our work so far and discuss the next stages
of our study.
2. Background on Graph Neural Networks
Graph Neural Networks[13] differ fundamentally from conventional neural networks in that the latter
can only operate on data ordered in vector or matrix form. GNNs, by comparison, can operate directly
on graph-structured data, allowing them to better leverage the relationship between data. We define a
graph as a pair 𝐺 = (𝑉, 𝐸) comprising a set of nodes — or vertices — 𝑉 and a set of edges 𝐸 ⊆ 𝑉 × 𝑉
defining relations between nodes. A node typically consists of a feature vector of fixed and consistent
size (heterogeneous graphs that contain nodes of varying feature size do exist but are not considered
for the purpose of this paper). GNNs are able to operate on graphs of arbitrary size, and are typically
invariant to the ordering of nodes.
2.1. Graph Convolutional Networks
In a conventional feedforward neural network, each layer 𝑙 applies a transformation
(︁ )︁
ℎ(𝑙+1) = 𝜎 𝑊 ℎ(𝑙) + 𝑏 (1)
where 𝑊 is a trainable weight matrix and 𝑏 is a trainable additive bias. 𝜎 is a non-linear activation
function such as ReLU. We let ℎ(0) be the original input feature vector. This forms the basis for the
transformation of node features in a Graph Convolutional Network (GCN). However, instead of a node
applying a transformation of its own representation from the previous layer, a GCN aggregates the
features of the node’s neighbours, a process known as message passing:
⎛ ⎞
(𝑙+1)
∑︁ 1
ℎ𝑖 = 𝜎⎝ 𝑊 ℎ(𝑙)
𝑣 +𝑏 (2)
deg(𝑖)
⎠
𝑣∈𝒩𝑖
(𝑙)
Here, 𝒩𝑖 is the neighbourhood of the 𝑖th node, and ℎ𝑣 the node embedding of neighbour 𝑣 at the 𝑙th
layer. deg(𝑖)
1
is a normalization constant which applies a weighting by the size of the node’s neighbour-
hood. One can observe an analogy between the aggregation of neighbouring nodes in a GCN and the
convolution of a filter with, say, an image within a layer of a Convolutional Neural Network.
By applying Equation 2 over a number of layers, a given node’s representation incorporates infor-
mation from deeper into the network. A three-layer GCN, then, will incorporate the features from
nodes three ‘hops’ from that node. Reaching a balance in the number of layers to use is an important
consideration; in a feedforward neural network, too many layers can result in vanishing gradients or
overfitting. In a GCN, there is an additional risk of every node embedding essentially converging to the
same value, as more nodes are being shared in the aggregations of each node.
Kipf et al.[14] further extended the update function to account for the observation that nodes with a
larger neighbourhood will naturally disseminate information wider than one with fewer neighbours.
They update the normalization constant of Equation 2 to redress this by increasing the weighting of
nodes with smaller neighbourhoods:
⎛ ⎞
(𝑙+1)
∑︁ 1
ℎ𝑖 = 𝜎⎝ 𝑊 ℎ(𝑙)
𝑣 +𝑏
⎠ (3)
deg(𝑖) deg(𝑣)
√︀ √︀
𝑣∈𝒩 𝑖
In some implementations, edges can be optionally assigned a numerical weight, to increase the influence
of certain nodes over others. For example, in a geometric scenario, one could weight edges by similarity
or distance between nodes. After a set number of message passing layers, the resulting node embeddings
can be returned as-is, further transformed, for example via a feedforward neural network, or aggregated
with other nodes to give a single graph-level representation.
2.2. Graph Attention Networks
Graph Attention Networks [15] (GATs) are an adaptation of GCN which differ in the way in which
they aggregate each node’s neighbourhood. From Equation 3 one can note that the update functions
is an isotropic aggregation in which each node equally contributes towards the new representation
of a node, while other implementations that allow for edge weighting require these weights to be
known and specified in advance. GATs assign a different weighting to each edge via learnable ‘attention
coefficients’:
(𝑙) (𝑙)
𝑧𝑖 = 𝑊 ℎ𝑖 (4)
(𝑙) 𝑇 (𝑙) (𝑙)
𝑒𝑖𝑘 = LeakyReLU(𝑎(𝑙) (𝑧𝑖 ⊕ 𝑧𝑗 )) (5)
(𝑙)
(𝑙) exp(𝑒𝑖𝑘 )
𝛼𝑖𝑗 = ∑︀ (𝑙)
(6)
𝑘∈𝑁 (𝑖) exp(𝑒𝑖𝑘 )
⎛ ⎞
(𝑙+1) (𝑙) (𝑙)
∑︁
ℎ𝑖 = 𝜎⎝ 𝛼𝑖𝑗 𝑊 (𝑙) ℎ𝑖 ⎠ (7)
𝑗∈𝒩 (𝑖)
(𝑙) (𝑙)
where ⊕ is the concatenation operator. 𝑎𝑖𝑗 applies a softmax to the so-called ‘attention score’ 𝑒𝑖𝑗 , the
purpose of which is to calculate the relative importance of a particular neighbour.
3. Methodology
3.1. Proposed model
We propose a graph-based model that models both the relationship between individual fingerprints in a
pre-collected database, and the underlying geometric structure of the environment. To achieve this, we
consider a fingerprint database comprising the received power, phase and delay spread between a given
location and a set of static reference points (RPs) within an indoor environment. This database is then
transformed into two graph representations; one based primarily on the sampled locations, and the
other on the reference points.
In the former case, which we will denote as the fingerprint graph, we define a graph 𝐺fp (𝑉fp , 𝐸fp )
with each node 𝑣𝑖 ∈ 𝑉fp being a point in the fingerprint database sampled at a given location with
(0)
initial node feature ℎ𝑣 set to the concatenated fingerprint (comprising the received power, phase and
delay spread) from each RP at 𝑣. In our study we use an environment with eight RPs, and therefore
have an initial feature vector of length 24. For each node 𝑣 ∈ 𝑉fp , for some value 𝑘 ∈ N, 𝑘 ≥ 1 an
incoming edge is created between the 𝑘 most similar fingerprints (by euclidean distance) and 𝑣. In our
experiments we find that 𝑘 = 3 yields optimum performance. This graph is static throughout training,
Figure 1: Summary schematic of our proposed model
meaning its edge set and initial nodes states are unchanged. When evaluating an unseen location, the
new fingerprint is incorporated into the graph, and the 𝑘 incoming edges for the new node computed,
but the remainder of the graph remains unchanged.
For the RP graph, 𝐺RP , we instead define a fully connected graph (every node has a bidirectional edge
to all other nodes, without, in this case, self-loops) in which the nodes are defined as the individual
RPs. The node features for this graph are unique to each individual location sampled in the fingerprint
database; for each location we get the initial node state of the 3-feature fingerprint for each RP.
We divide our fingerprint database into a train and test set, and construct a single fingerprint graph
for the training set. When considering a given location, we identify that node in the fingerprint graph,
and distribute its feature vector across the nodes in our RP graph. We pass the fingerpring graph
through a GAT network, and the RP graph through a number of GCN layers. ReLU is used as the
non-linearity for both models. The final node embedding of the targeted node is then extracted from the
GAT network, and concatenated with a Global Mean Pool1 readout of the final RP graph. The resulting
vector is then passed through a feedforward neural network, finally outputting a length-2 vector which
we take as the coordinate prediction. A schematic of our model is shown in Figure 1.
3.2. Data generation
To initially evaluate the potential of our positioning model, we constructed an approximately 368 m2
simulated environment indicative of a medium-sized office floor, comprising a number of rooms varying
from 4.1 m2 to 50 m2 connected by corridors. The environment was constructed using the Blender® 3D
modelling software[16], and imported into the Remcom Wireless InSite® EM propagation software[17].
The environment was divided into a grid of 3.68 million 1 cm2 squares, into which a receiver antenna
was positioned. Eight transmitters were placed throughout the environment, along the main corridor
and in each of the large atriums. Figure 2a shows the positions of the transmitters, indicated in green.
The receivers and transmitters were configured according to the parameters given in Table 1 and the
EM environment configured as in Table 2, and pairwise propagation simulations performed between
every Tx and Rx, from which received power, phase and delay spread were obtained. An example of a
received power plot is shown in Figure 2c.
While such a high resolution dataset would be impractical to gather in reality, we are able to sample
from the dataset to emulate measurement campaigns of varying degrees of coverage and uniformity
1
Global Mean Pool aggregates the information in a graph by taking a mean average of each feature across all nodes in the
graph.
Table 1
Antenna Parameters
Antenna type Omnidirectional
Maximum Gain 2.5 dBi
Receiver Threshold −142 dBm
Carrier Frequency 2.4 GHz
Table 2
Simulation Parameters
Reflections 6
Transmissions 8
Outer wall material Brick
Inner wall material Layered drywall
Floor/Ceiling material Concrete
InSite Propagation Model X3D Ray
Ceiling Height 3m
Table 3
Multi-graph model hyperparameters
Hyperparameter Search space Value in optimum model
Fingerprint GAT final embedding size 24, 48, 96 48
Fingerprint GAT layers 1, 2, 3, 4 2
Fingerprint GAT hidden embedding size 8, 16, 32, 64 32
RP GNN final embedding size 10, 20, 40 20
RP GNN layers 1, 2, 3, 4 2
FC Layers [64, 32, 16], [32, 16], [16,8] [32,16]
without the need to perform multiple time-consuming simulations. In this instance, to replicate the
performing of a realistic fingerprint measurement campaign as closely as possible, as well as to allow
for the future extension of this environment towards training with sequential path data (for which the
availability of robust public datasets is limited), random walking paths through the environment were
generated using MATLAB’s Navigation Toolbox. Positions were sampled every 10 cm, and the power,
phase and delay spread estimated by means of linear interpolation. A total of 137 paths, shown in Figure
2b, were generated for the purpose of this study, comprising 30 496 individual locations. Gaussian noise
was then applied to the data to add additional uncertainty to the simulated data.
3.3. Pre-processing
All data in the fingerprint database, including the ground truth labels, was standardized prior to use
using so-called robust standardization, a variant of Z-score standardization more robust against outliers
which uses the median and inter-quartile range of each feature in place of mean and standard deviation,
respectively.
4. Results
The graph models were implemented using PyTorch Geometric[18], an extension to PyTorch for graph-
based learning, and trained using the Adam optimizer, and MSE loss functions. Batch size was set to 32,
and the learning rate 1 × 10−4 . The hyperparameters tuned for our model are given in Table 3.
We compared the accuracy of our model against several reference models; kNN, for values of k from
1 to 30 and using cosine, euclidean and Manhattan distance metrics; Random Forest[19] with 8, 16, 32,
64, 128, 256, 512 and 1024 trees; and a multilayer perceptron (MLP), with tuned hyperparameters for
(a)
(b) (c)
Figure 2: Simulated office environment used for study.
(a) 3D model of the environment showing positions of transmitters (green points);
(b) ‘Walking paths’ used to generate fingerprint database;
(c) Indicative received power plot at Transmitter 1
the number of layers and hidden channel size. In addition, the multi-graph method was compared with
the performance of each respective graph model alone.
The performance of the optimum models and benchmarks are summarized in Figure 3. We can see
from the results that our model appears to improve upon these benchmark models by a significant
degree, with a 29% reduction in average error than using just an MLP, the best performing non-graph
model. It is also interesting to observe that the combination of both the fingerprint and RP graphs
results in a greater accuracy than either graph model used individually. This suggests that both
graph representations capture and utilise information not present in the other, and further supports
the argument that graph-based models are a promising and effective way of incorporating relevant
structural information that would otherwise have been lost in a simple vector-based fingerprinting
model.
We observe that our model results in significantly fewer outliers, which contributes strongly to the
improvement in mean accuracy, though median error is currently higher than our benchmark models
(Figure 4. The maximum error encountered using Random Forest, for example, was over 30 metres,
compared to 5.43 m using our own model. The coverage of our dataset is not uniformly distributed
throughout the environment; the corners of rooms in particular are sparsely sampled in comparison
Figure 3: Comparison of our model with reference benchmarks
Figure 4: Hair-and-whisker plots for kNN, Random Forest, and our model.
to high-traffic areas such as the main corridors. Distributed and crown sourced walking surveys is a
common means of data collection for positioning systems [20], though more so in models that locate a
user to within a discrete region as opposed to specific coordinates, and achieving uniformly distributed
training data can be time consuming. Accordingly, the kNN model struggled to correctly position
locations at the boundaries of the sampled area. By comparison, our model was able to position outlying
test locations to within 2 m, even in these sparse regions.
With respect to data collection, we note that the 10cm resolution at which locations were sampled
for the purpose of training the models may present challenges when transferring this method to the
real world. While this resolution may be possible at an acceptable sampling frequency using bespoke
hardware, smartphones are typically constrained in their maximum sample rate. In recent versions of
the Android operating system, for example, the time to complete a scan of broadcasting WiFi devices
and their signal strengths is around 3-5 s depending on handset model[21]. A data collection campaign
of the scale described in our paper could take many hours to complete, even accounting for a division
of labour using multiple devices. A possible solution to this is currently ongoing, which is investigating
the feasibility of transfer learning, which has previously been applied to RF data[22, 23], to augment a
smaller amount of manually sampled locations with a higher resolution synthetic dataset, to allow for a
shorter data collection campaign while maintaining acceptable localisation performance.
5. Conclusion and future work
We have presented a new RF-based positioning model which combines two different graph repre-
sentations of a simulated indoor environment. Current results have indicated a 32 cm improvement
over all benchmarks, and stronger performance compared to the use of only one or the other graph
representation. Considering future work, with respect to the fingerprint graph, at present we only
consider each location independently, and incorporating new ones into the graph does not affect the
rest of the graph (new incoming edges can added to allow information to propagate to unseen nodes,
but this does not allow information flow in the other direction). One might consider the case where
multiple users are present in the same environment. In this case, it may be advantageous to consider
the relationship between users, turning this problem into one of collaborative positioning. Future work
is, at the time of writing, underway to investigate the potential for this model to be extended into a
collaborative one, to explore the use of temporal data (the dataset having been constructed as a set of
walking paths) to further improve model performance, and to further evaluate performance against
industry standard datasets such as UJIIndoorLoc[24]. Noting the improvement in accuracy in outlying
regions of our environment, we also wish to explore the extent to which our model is able to mitigate
against inconsistent and non-uniform measurement campaigns.
Acknowledgments
Liam M. Self was supported by the UK Engineering and Physical Sciences Research Council (EPSRC)
grant EP/S023046/1 for the EPSRC Centre for Doctoral Training in Sensor Technologies for a Healthy
and Sustainable Future.
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