Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise
Abstract
:1. Introduction
2. Materials and Methods
2.1. Stochastic Models for Plume and Background
2.1.1. Stochastic Model for Chemical Concentration Measurements
2.1.2. Stochastic Background Model
2.2. Estimation of the Models From the Concentration Readings
2.2.1. Bayesian Estimation of the Likelihood Map for Chemical Source Presence
2.2.2. Background Estimation
2.3. Description of the Synthetic Test Cases
2.3.1. Synthetic Scenario Description and Simulation
2.3.2. Synthetic Test Case 1: Behavior of the Binary Detector Algorithm Depending on the Background Level and Detector Threshold
2.3.3. Synthetic Test Case 2: Accuracy in the Estimation of the Background Level and the Expected Position of the Chemical Source
2.3.4. Synthetic Case 3: Influence of the Source Strength on the Concentration Based Algorithm
2.4. Scenario, Chemical Source Emission and Autonomous Vehicle Description for Real Experiments
3. Results and Discussion
3.1. Results of Algorithms Evaluation for Synthetic Experiments
3.1.1. Synthetic Case 1
3.1.2. Synthetic Case 2
3.1.3. Synthetic Case 3
3.2. Results for the Real Experiments
3.3. Computatitonal Cost
4. Conclusions
Supplementary Materials
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Supplementary Tables
Nc | Number of Cells in the Grid Area |
Lx | Length of each cell along the x-axis |
Ly | Length of each cell along the y-axis |
c | Instantaneously measured concentration |
cb | Concentration contribution due to the background |
cp | Concentration contribution due to the chemical plume |
Mean concentration at a fixed location | |
q | Source strength or release rate |
Ua | Mean wind speed in the downwind direction |
σy | Diffusion coefficient in the crosswind direction |
σz | Diffusion coefficient in the vertical direction |
Array of all possible instantaneous concentrations c | |
γ | Intermittency factor related to the chemical plume |
M | Mean concentration of a series of readings at a fixed location |
Standard deviation of a series of readings at a fixed location | |
Nb | Number of readings stored in the concentration buffer per each sensor |
cj | Measured concentration within cell j |
Ai | Event “there is a chemical source within cell i” |
B(tk) | Sequence of measured concentrations along the trajectory of the robots until time tk |
Prior probability of the presence of a chemical source within cell i | |
Probability that the measurement within cell j is due to the addition of the background at cell j and a chemical plume due to a source within cell i | |
Probability that the measurement of chemical at cell j is not due to a source emitting at cell i, thus cj is due to the current background at cell j | |
Probability of having a source in cell i given that a certain amount of chemical was measured at cell j at time tk | |
Normalized probability (over all cells) of having a chemical source within cell i based on a single measured concentration within cell j at time tk | |
Normalized probability (over all cells) of having a chemical source within cell i based on the sequence of measured concentrations along the trajectory of the robots (index j) until time tk |
For the Plume |
---|
Gaussian distribution for the time-averaged concentration |
concentration fluctuations governed by turbulences |
continuous release, source strength known q = 2.90 g/s |
one uniquely source at the position (400 m, 400 m) |
height, z = 2 m |
For the Background |
background is always present |
background relatively constant for the exploration time |
mean background level can change from one cell to another |
no intermittency |
Other Assumptions |
uniform wind field over the exploration time, speed Ua = 2.5 m/s, and 45° direction |
neutral atmospheric stability |
no deposition of the substance on surfaces |
cells are equally likely to contain the source at time t0 |
height of sensors is 2 m |
response-time of sensors faster than the typical 10min time-average of GPM |
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Pomareda, V.; Magrans, R.; Jiménez-Soto, J.M.; Martínez, D.; Tresánchez, M.; Burgués, J.; Palacín, J.; Marco, S. Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise . Sensors 2017, 17, 904. https://doi.org/10.3390/s17040904
Pomareda V, Magrans R, Jiménez-Soto JM, Martínez D, Tresánchez M, Burgués J, Palacín J, Marco S. Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise . Sensors. 2017; 17(4):904. https://doi.org/10.3390/s17040904
Chicago/Turabian StylePomareda, Víctor, Rudys Magrans, Juan M. Jiménez-Soto, Dani Martínez, Marcel Tresánchez, Javier Burgués, Jordi Palacín, and Santiago Marco. 2017. "Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise " Sensors 17, no. 4: 904. https://doi.org/10.3390/s17040904
APA StylePomareda, V., Magrans, R., Jiménez-Soto, J. M., Martínez, D., Tresánchez, M., Burgués, J., Palacín, J., & Marco, S. (2017). Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise . Sensors, 17(4), 904. https://doi.org/10.3390/s17040904