Interpretable Physics Informed WiFi Indoor Localization: Learning an Effective Access Point Geometry and Using It to Prune
Authors: Arshia Eftekhari zadeh, Rezvan Nasiri, Hadi Moradi
Organizations: School of Electrical and Computer Engineering University of Tehran Tehran, Iran · Advanced Robotics and Intelligent Systems Laboratory School of Electrical and Computer Engineering University of Tehran Tehran, Iran
Deep learning models can achieve high accuracy for indoor localization, but their black-box nature limits interpretability and the reuse of learned information. We propose a hierarchical deep learning framework for WiFi fingerprint-based indoor localization that jointly predicts user location and learns an effective geometry of the surrounding access points (APs). Physics-informed decoders infer this geometry directly from RSSI measurements and labelled user positions, without requiring the true AP coordinates during training. The learned geometry is then used to rank and prune APs. On the UJIIndoorLoc dataset, the proposed chained model achieves a mean 3D localization error of 7.07 m, reducing error by 26% to 36% compared with baseline models. Previously published methods evaluated on the same official split report errors 10.6% to 31.0% higher. Pruning 35% or 50% of the APs causes only a small loss in localization accuracy. The inferred geometry also enables Fisher-information-based AP ranking even when fingerprint databases do not contain surveyed AP coordinates. Experiments on the Tampere/TUT and UTSIndoorLoc datasets show that geometry-guided AP selection performs comparably to selectors built directly from labelled data. These results show that physics-informed interpretability can improve indoor localization while also supporting effective feature selection.
Figures & tables
Fig. 1: PhysicsChainedNet . The two channel input (normalized RSSI and detection mask, aligned by index) passes through the residual MLP encoder to the latent vector z , then through the chained building → floor → position heads. Two decoders reconstruct RSSI from different representations: the physics decoder from the predicted position p^ and the building/floor distributions, and the latent decoder from z . Only the physics decoder carries interpretable radio parameters, and its learned AP coordinates cj are the effective geometry of panel 5. Training time paths beyond teacher forcing are omitted; see Section III-C .
Fig. 2: The residual block used throughout the encoder stack. The skip path carries the input around the two linear layers and rejoins before the final activation.
Fig. 3: Left: campus map, the transmitter (Tx) buildings colored (map from [ 23 ] ). Right: learned effective AP coordinate (red × ) versus the centroid based initial guess (grey dot), from a model given no real building shape or AP location (quantitative faithfulness check in Section V-C ).
Fig. 4: The training procedure. Left of the vertical rule, the physics prefit fits the decoder’s own parameters against true training positions, before the encoder is trained at all. The three frames to its right are the curriculum rounds, each drawing the same model schematic: a dashed grey decoder outline marks an objective that is not yet engaged, a solid outline one that is active. Access point anchor state follows the legend, and in the final round the anchors become trainable and are drawn drifting from their prefit positions. The vertical rule marks the boundary between the second and third rounds, where the teacher forcing ratio reaches zero. Table I gives the corresponding weights.
Round 1
Round 2
Round 3
Share of epoch budget
0–25%
25–50%
50–100%
Position wpos
5
8
25
Floor wfloor
20
15
20
Building wbuild
15
10
8
Physics recon. wphy
0.83
8.27
9.93
Latent recon. wrec
1.0
0.8
0.5
TABLE I: Settings that change from round to round. Loss weights are those of the tuned configuration (Section III-E ); a dash marks a term inactive in that round. The physics prefit preceding round 1 runs 17 epochs at learning rate 0.0313.
Model
Mean 3D (m)
P90 (m)
Floor Acc.
Ours (full, physics)
7.07 ± 0.06
15.97
93.38%
WKNN ( k =7)
9.61
19.45
88.57%
KNN ( k =1)
10.19
21.17
88.57%
Simple MLP
10.89
21.58
91.54%
TABLE II: Full model vs. classic baselines. Our model: mean ± std over 5 seeds.
Method
Mean 3D (m)
Floor Acc.
Build. Acc.
vs. Ours
Ours (full, physics)
7.07
93.38%
99.93%
-
ISDL [ 4 ]
7.82
95.05%
100%
+10.6%
MG-HGNN [ 5 ]
7.83
94.24%
100%
+10.7%
Liu et al. [ 7 ]
7.96
94.70%
100%
+12.6%
Li et al. [ 6 ]
8.19
93.34%
100%
+15.8%
Etiabi et al. [ 9 ]
8.80
94.87%
99.90%
+24.5%
TABLE III: Comparison with published results on the official UJIIndoorLoc split. The numbers are from the referenced papers.
Fig. 5: Mean 3D error, our full model versus both the classic baselines (Table II ) and published results on the official UJIIndoorLoc split (Table III ), ours highlighted in red, sorted ascending.
Condition
Mean 3D (m)
Floor Acc.
Full model
7.07 ± 0.06
93.38%
Fixed AP geometry
7.21 ± 0.10
92.31%
No censored likelihood
7.22 ± 0.10
91.90%
No physics loss
7.27 ± 0.14
91.76%
Randomized AP geometry
7.29 ± 0.16
92.53%
TABLE IV: Physics ablation, mean 3D error (m), mean ± std over 5 seeds.
Method
0%
20%
35%
50%
65%
Fisher
7.07 ± .06
7.22 ± .11
7.21 ± .10
7.27 ± .16
8.12 ± .25
MSCP
7.16 ± .07
7.31 ± .10
7.34 ± .04
7.57 ± .15
Detect. count
7.33 ± .17
7.36 ± .06
7.44 ± .09
8.08 ± .12
Mutual info
7.36 ± .05
7.32 ± .18
7.34 ± .11
7.71 ± .15
Random
7.62 ± .15
8.26 ± .06
9.62 ± .28
12.45 ± 1.16
TABLE V: UJIIndoorLoc: mean 3D error (m), mean ± std over 5 seeds, by method and pruned input features (%). Fisher (in bold) is the geometry only selector, computed from the learned effective geometry and nothing else.
Fig. 6: (a) Mean 3D error and (b) P90 3D error versus pruned input features (%), per selection method. The geometry only Fisher score tracks the selectors built from labels through moderate pruning.