Conditional Random Field-Based Offline Map Matching for Indoor Environments
Abstract
:1. Introduction
2. Overview of the System
- The primary localization system that produces the first estimated trajectory. This can be any localization system that produces, as its output, a walking trajectory in the form of a time sequence of estimated location coordinates. This trajectory will be the input of the map matching algorithm.
- The semantic map generation system, a unit that models the floor plan obtained from CAD files in a semantic format that can be used by the map matching algorithm. In our case, a grid-based map model was employed in which the floor plan map is divided into square uniform-grid cells. Each cell is associated with a semantic representation of its contents, for example if it contains a wall or a free space.
- The map matching algorithm that refines the estimated trajectory (path) using the CRF technique and the semantic floor plan information.
2.1. The Semantic Map Generation System
2.2. The Map Matching Algorithm
Algorithm 1. CRF Algorithm for the Map Matching Problem | |
1 | Input : Observation = a vector of coordinates of the input estimated trajectory |
2 | Output: CorrectedPath = a vector of coordinates of the output corrected trajectory |
3 | Forward Phase: |
4 | For each observation (Observationj) %Observation j = coordinates of the input at time step j |
5 | For all cells (i) |
6 | For all neighbor cells of i (k) |
7 | fdis = T(i,k)/Distance (k,Observationj)%T(i,k): transition possibility from cell i to cell k {0,1} |
8 | Potential(k,Observationj) = exp(fdis); |
9 | Z = sum(Potential(:,j)) % normalization factor |
10 | ConditionalProbabilty (k,Observationj) = Potential(k,Observationj)/Z |
11 | If (ConditionalProbabilty (i,Observationj-1) > ConditionalProbabilty (bestParent (k)) |
12 | then CorrectedParent(k) = i |
13 | End |
14 | End |
15 | End |
16 | End |
17 | Backward Phase |
18 | #CandidatePaths = #Cells |
19 | For p = 1➜ #CandidatePaths % p is the last cell in the CandidatePaths |
20 | k = p % k is the current cell in the CandidatePath |
21 | Construct each CandidatePath: |
22 | For all observations (j ➜1) |
23 | CandidatePath(j) = k; %add cell K to the path at time step j |
24 | sum(CandidatePath) = sum(CandidatePath) + ConditionalProbabilty(k,j) |
25 | k = BestParent(k,j) % choose the best parent of k to be the next cell in the path |
26 | End |
27 | End |
28 | CorrectedPath = CandidatePath with highest sum of ConditionalProbabilities |
3. Results and Discussion
3.1. Simulations
3.2. Real Measurements
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
GNSS | Global Navigation Satellite System |
CRF | Conditional Random Fields |
HMM | Hidden Marcov Models |
PDR | Pedestrian Dead-Reckoning |
DXF | Drawing Interchange file format |
CDF | Cumulative Distribution Function |
iHDE | improved Heuristic Drift Elimination |
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Noise Level | Mean (m) | Standard Deviation (m) |
---|---|---|
1 | 1.3 | 1 |
2 | 1.6 | 1.1 |
3 | 2.0 | 1.3 |
4 | 2.5 | 1.8 |
Cell Size (m) | Noise Level | Number of Crossed Obstacles | Cumulative Error (m) | |
---|---|---|---|---|
50% | 90% | |||
0.8 | 1 | 0 | 0.9867 | 2.6699 |
2 | 0 | 2.682 | 19.7820 | |
3 | 0 | 5.7945 | 32.464 | |
4 | 0 | 6.5158 | 32.3861 | |
1 | 1 | 0 | 1.1574 | 3.078 |
2 | 0 | 1.2463 | 3.8172 | |
3 | 0 | 1.4853 | 5.1879 | |
4 | 0 | 2.1409 | 11.1061 | |
1.5 | 1 | 0 | 19.4403 | 70.7003 |
2 | 0 | 16.6941 | 61.6751 | |
3 | 0 | 17.7461 | 68.5491 | |
4 | 0 | 20.0473 | 71.8129 |
Estimation Frequency | Buffer Size | Cumulative Error (Meters) | |
---|---|---|---|
50% | 90% | ||
1 Hz | 1 cell | 12.4931 | 33.1054 |
2 Hz | 1 cell | 1.1348 | 2.4989 |
1 Hz | 2 cells | 1.1574 | 3.078 |
2 Hz | 2 cells | 1.3639 | 3.0044 |
Algorithm | Number of Crossed Obstacles | Cumulative Error (m) | |
---|---|---|---|
50% | 90% | ||
iHDE | 15 | 1.2861 | 2.6858 |
iHDE + CRF | 0 | 1.0634 | 2.2316 |
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Bataineh, S.; Bahillo, A.; Díez, L.E.; Onieva, E.; Bataineh, I. Conditional Random Field-Based Offline Map Matching for Indoor Environments. Sensors 2016, 16, 1302. https://doi.org/10.3390/s16081302
Bataineh S, Bahillo A, Díez LE, Onieva E, Bataineh I. Conditional Random Field-Based Offline Map Matching for Indoor Environments. Sensors. 2016; 16(8):1302. https://doi.org/10.3390/s16081302
Chicago/Turabian StyleBataineh, Safaa, Alfonso Bahillo, Luis Enrique Díez, Enrique Onieva, and Ikram Bataineh. 2016. "Conditional Random Field-Based Offline Map Matching for Indoor Environments" Sensors 16, no. 8: 1302. https://doi.org/10.3390/s16081302
APA StyleBataineh, S., Bahillo, A., Díez, L. E., Onieva, E., & Bataineh, I. (2016). Conditional Random Field-Based Offline Map Matching for Indoor Environments. Sensors, 16(8), 1302. https://doi.org/10.3390/s16081302