# Radiation Mapping in Post-Disaster Environments Using an Autonomous Helicopter

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction and System Overview

## 2. Autonomous Radiation Mapping

#### 2.1. Radiation Detection System

#### 2.2. Radiation Detection Background

^{−}), X-rays, and gamma rays. Unfortunately for detection purposes, alpha particles, beta particles, and X-rays suffer from self-absorption within the source, resulting in different emission characteristics for different source shapes. Therefore, radiation detection instruments rely on impingement of gamma rays [1].

_{k}, y

_{k}, z

_{k}) is the position of detector k, (x

_{0}, y

_{0}, z

_{0}) is the position of the source, and λ

_{b}is the background intensity at the measurement point. All measurements in this paper assume a constant altitude difference, so z

_{k}− z

_{0}= C.

^{2}= λ) on which many recursive Bayesian estimators (RBEs) rely.

#### 2.3. Prior Work in Radiation Source Localization

## 3. Recursive Bayesian Estimation Method

#### 3.1. Localization Algorithm

repeat | |

observedCounts ← current observation | |

if observedCounts > background then {the source is detected} | |

for all cell ∈ grid do | |

5: | expectedCounts ← getSourceCounts (sensor, cell) |

cellLikelihood ← poisspdf (x = observedCounts, λ = expectedCounts) | |

end for | |

else {the source is not detected} | |

for all cell ∈ grid do | |

10: | expectedCounts ← getSourceCounts (sensor, cell) |

probabilityOfDetection ← 1 − poisscdf(x = background, λ = expectedCounts) | |

cellLikelihood ← 1 − probabilityOfDetection | |

end for | |

end if | |

15: | prior ← prior · gridLikelihood {update prior} |

$\mathit{prior}\leftarrow \frac{\mathit{prior}}{\text{SUM}(\mathit{prior})}\{\text{normalize}\hspace{0.17em}\text{prior}\hspace{0.17em}\text{to}\hspace{0.17em}\text{PDF}\}$ {normalize prior to PDF | |

confidence ← max (prior) | |

sensor ← moveSensor (sensor, target) | |

until confidence ≥ 90% |

#### 3.2. Grid-Based Localization Results

^{75}Se at 1.7 Ci,

^{60}Co at 0.3 Ci (about half as strong as the selenium source), and

^{192}Ir at 6.7 Ci (about twice as strong as the selenium source). The background radiation detected by the sensor was set at a constant 1,000 counts, a reasonable average value for an open field in southwest Virginia. For all trials, the field was a 160,000-square-meter area with a resolution of 1 m for a total of 160,801 grid cells. The source was randomly placed exactly on a grid cell within a 100 m radius of the center to ensure detection during the localization flight and the sensor was initially located randomly without restriction within the search area. The sensor velocity was limited to 4 m/s, which is the maximum horizontal velocity of the Aeroscout B1-100 in an assisted stability flight mode. The helicopter can move at 10 m/s straight forward, but in these simulations, it was allowed to move in any direction, necessitating the constraint. The sensor altitude was maintained at 60 m for all simulations.

_{i,j}p

_{i,j}= 1), but raising that confidence to p = 0.9 may take many more iterations. As a result, the two events may occur simultaneously, but it is guaranteed that because of this relationship, once the algorithm declares itself finished, the error is zero. The results of these simulations demonstrate that the algorithm is both very fast and very accurate.

## 4. Radiation Contour Mapping

#### 4.1. Algorithm Overview

#### 4.2. Contour Detection

#### 4.3. Contour Following

_{d}is the desired contour count level. The adjustment is necessary to ensure the algorithm begins on the inside of the contour and it serves as a safeguard against receiving an anomalously-high count and beginning the contour mapping prematurely.

_{d}, the helicopter turns to the right; if a measured count is less than λ

_{d}, the helicopter turns to the left. The result is that the helicopter follows the contour in a counterclockwise direction. The forward speed of the helicopter is set at the beginning of the test, and should be adjusted by the operator for the size of the search area, the desired speed of the search, and the desired accuracy and completeness of the finished contour. A faster search will result in less accuracy in the analysis step, but some loss of accuracy may be acceptable for the time saved. A large search area or physically large contours (a low λ

_{d}for a strong source, for example) allow much higher forward speeds, while tight contours (relatively high λ

_{d}) require a slower scan to follow the contour properly. The limiting factor from the helicopter for these considerations is the maximum turn rate. The Aeroscout B1-100 has a maximum yaw rate of 30°/s in its assisted stability flight mode, but such a high yaw rate coupled with high forward speeds may result in sideslip, which would draw the vehicle off the contour and result in a lower turn rate than the commanded yaw rate. For this reason, yaw rates in this chapter are limited to 15°/s, which simulations have shown can be translated directly into turn rates.

_{k}and the contour level λ

_{d}and returns the desired helicopter yaw rate ψ

_{d}:

_{p}, k

_{d}, and k

_{i}are PID controller constants, derived below. Proportional error differs from the simple error from λ

_{d}to adjust for the 1/R

^{2}relationship of radiation emission intensity to distance. For extremely high contour levels, an error of as little as 1 m may result in hundreds or thousands of counts of error; an extreme turn will take the vehicle off the contour. Conversely, for very low contour levels, a displacement of several meters may result in tens of counts of error, so the helicopter must react quickly.

_{p}, k

_{d}, and k

_{i}are modified by σ

_{λ}so that the same constants may be used for any desired contour level. An unconstrained nonlinear optimization method was used to generate error-optimal PID constants using the 2,000-count contour of Figure 2(d) with an update rate of 1 Hz at 1 m/s. The resulting values are presented in Table 3.

_{d}undergoes several checks before it is applied to the helicopter. It is first limited to the maximum yaw rate ψ

_{max}:

#### 4.4. Contour Following Results

#### 4.5. Source Localization

cImage ← getImage(contourPoints) | |

cImage ← downsample(cImage) | |

$\mathit{maxRadius}\hspace{0.17em}\leftarrow \hspace{0.17em}\frac{\text{MIN}(\text{DIM}(\mathit{cImage}))}{2}$ | |

$\mathit{minRadius}\hspace{0.17em}\leftarrow \hspace{0.17em}\frac{\mathit{maxRadius}}{8}$ | |

5: | cand ← houghCircles(cImage; minRadius; maxRadius) |

cand ← deleteInvalidCandidates(cand; cImage) | |

cand ← upsample(cand) | |

while length(cand) > 0 do | |

bestCand ← cand(cand.c = = max(cand.c)) | |

10: | for all cand s.t. cand:center is within bestCand:radius of bestCand:center do |

delete from cand | |

end for | |

end while | |

repeat | |

15: | for all est ∈ estimates do |

est.intensity ← estimateIntensity(est) | |

estimates ← adjustCounts(estimates) | |

end for | |

maxChange ← max(estimates:adjustment) | |

20: | until maxChange = = 0 |

_{source}if r

_{source}is redefined as the radius associated with a source estimate:

_{contour}. Once an intensity estimate is derived for a source, its effect on each of the other sources is calculated; the corrected estimate replaces I

_{contour}and the loop repeats until each estimate converges.

#### 4.6. Contour-Based Localization Results

^{2}to just over 5000 m

^{2}, a reduction of 99.5%. The result is even more useful when determining safety perimeters for rescue personnel: slightly larger inaccuracies do not affect perimeter assignment nearly as much as search efforts. The safety zone will certainly include a buffer that will easily correct for this worst-case inaccuracy of less than 50 m.

## 5. Conclusions

## References

- Knoll, G. Radiation Detection and Measurement; John Wiley and Sons: New York, NY, USA; p. 2000.
- Howse, J.; Ticknor, L.; Muske, K. Least squares estimation techniques for position tracking of radioactive sources. Automatica
**2001**, 37, 1727–1737. [Google Scholar] - Brennan, S.; Mielke, A.; Torney, D. Radioactive source detection by sensor networks. IEEE Trans. Nuclear Sci
**2005**, 52, 813–819. [Google Scholar] - Muske, K.; Howse, J. Comparison of Recursive Estimation Techniques for Position Tracking Radioactive Sources. Proceedings of the 2001 American Control Conference, Arlington, VA, USA, 25–27 June 2001; pp. 1656–1660.
- Morelande, M.; Ristic, B.; Gunatilaka, A. Detection and Parameter Estimation of Multiple Radioactive Sources. Proceedings of 10th International Conference on Information Fusion, Quebec, QC, Canada, 9–12 July 2007; pp. 1–7.
- Brewer, E. Autonomous Localization of 1/R
^{2}Sources Using an Aerial Platform. MA Thesis, Mechanical Engineerin, Virginia Tech, Blacksburg, VA, USA. 2009. [Google Scholar] - Thrun, S.; Burgard, W.; Fox, D. Probabilistic Robotics; The MIT Press: Cambridge, MA, USA, 2005. [Google Scholar]

**Figure 4.**Following 2000-count contours of various source combinations. Red ‘+’ marks indicate c

_{k}< ψ

_{d}and green ‘×’ marks indicate c

_{k}≥ ψ

_{d}.

**Figure 5.**Initial Hough transform results. The black line is the contour; green dots and circles represent source position estimates and associated radii; and red ‘×’ marks are the true target positions.

**Figure 6.**Best-choice source estimates for contours. The black line is the contour; blue dots and circles represent source position estimates and associated radii; and red circles are the true target positions.

**Figure 7.**Visual comparison of source position estimate errors between ideal and stochastic (Poisson) contours.

90% Confidence | Zero Error | |
---|---|---|

n | 1,195 | 1,195 |

Mean | 25.07 | 4.74 |

Std. Dev. | 4.90 | 3.93 |

Median | 26 | 4 |

Mode | 26 | 1 |

Min. | 16 | 0 |

Max. | 38 | 22 |

Combination | Intensity (Counts) | Separation (m) | Figure |
---|---|---|---|

One Weak Source | 5000 | — | Not Shown |

One Strong Source | 50,000 | — | 2(a) |

Two Equal Sources | (20,000, 20,000) | 500 | 2(b) |

Two Unequal Sources | (50,000, 5,000) | 500 | 2(c) |

Three Unequal Sources | (5,000, 10,000, 5,000) | (250, 250) | 2(d) |

Constant | Value |
---|---|

k_{p} | −23.6648 |

k_{d} | −11.9835 |

k_{i} | −0.0037 |

DR | Position (m)
| Conf. | Raw Intensities
| Adj. Intensities
| |||||
---|---|---|---|---|---|---|---|---|---|

Est. | Err. | I | Err. | Rel. Err. | I | Err. | Rel. Err. | ||

Ideal | (245, 0) | 5.00 | 1.00 | 22,694 | 2,694 | 0.1347 | 20,963 | 963 | 0.0481 |

(−245, 0) | 5.00 | 0.95 | 22,694 | 2,694 | 0.1347 | 20,872 | 872 | 0.0436 | |

Stochastic | (231, 0) | 19.00 | 1.00 | 26,036 | 6,036 | 0.3018 | 24,297 | 4,297 | 0.2148 |

(−250, 0) | 0.00 | 0.84 | 23,125 | 3,125 | 0.1562 | 20,900 | 900 | 0.0450 | |

(−31,–69) | 229.61 | 0.31 | 2,845 | −17,155 | −0.8578 | 414 | −19,586 | −0.9793 |

Position (m)
| Conf. | Raw Intensities
| Adj. Intensities
| ||||||
---|---|---|---|---|---|---|---|---|---|

Est. | Err. | I | Err. | Rel. Err. | I | Err. | Rel. Err. | ||

Ideal | (242, 0) | 8.00 | 1.00 | 6,909 | 1,909 | 0.3818 | 6,035 | 1,035 | 0.2071 |

(−243, 0) | 7.00 | 0.98 | 6,805 | 1,805 | 0.3610 | 5,920 | 920 | 0.1840 | |

(−2, 0) | 2.00 | 0.57 | 12,734 | 2,734 | 0.2734 | 10,915 | 915 | 0.0915 | |

Stochastic | (−35, 0) | 35.00 | 1.00 | 12,580 | 2,580 | 0.2580 | 10,546 | 546 | 0.0546 |

(211, 9) | 40.02 | 0.95 | 9,347 | 4,347 | 0.8694 | 7,757 | 2,757 | 0.5514 | |

(−227, 2) | 23.09 | 0.80 | 7,336 | 2,336 | 0.4671 | 5,334 | 334 | 0.0667 | |

(47, 111) | 120.54 | 0.33 | 2,642 | −7,358 | −0.7358 | 303 | −9,697 | −0.9697 | |

(−320, −38) | 79.65 | 0.30 | 2,180 | −2,820 | −0.5640 | 720 | −4,280 | −0.8559 | |

(58, −119) | 132.38 | 0.28 | 2,245 | −7,755 | −0.7755 | 225 | −9,775 | −0.9775 |

Source Combination | Raw Rel. Err.
| Adj. Rel. Err.
| Δ Rel. Err.
| |||
---|---|---|---|---|---|---|

Ideal | Stochastic | Ideal | Stochastic | Ideal | Stochastic | |

Two Equal Sources | 0.3563 | 0.5121 | 0.1693 | 0.2120 | 0.1868 | 0.3001 |

Two Unequal Sources | 0.1347 | 0.2184 | 0.0459 | 0.1298 | 0.0888 | 0.0886 |

Three Unequal Sources | 0.2667 | 0.3716 | 0.0268 | 0.1104 | 0.2399 | 0.2613 |

Overall Means | 0.2525 | 0.3674 | 0.0807 | 0.1507 | 0.1718 | 0.2167 |

## Share and Cite

**MDPI and ACS Style**

Towler, J.; Krawiec, B.; Kochersberger, K.
Radiation Mapping in Post-Disaster Environments Using an Autonomous Helicopter. *Remote Sens.* **2012**, *4*, 1995-2015.
https://doi.org/10.3390/rs4071995

**AMA Style**

Towler J, Krawiec B, Kochersberger K.
Radiation Mapping in Post-Disaster Environments Using an Autonomous Helicopter. *Remote Sensing*. 2012; 4(7):1995-2015.
https://doi.org/10.3390/rs4071995

**Chicago/Turabian Style**

Towler, Jerry, Bryan Krawiec, and Kevin Kochersberger.
2012. "Radiation Mapping in Post-Disaster Environments Using an Autonomous Helicopter" *Remote Sensing* 4, no. 7: 1995-2015.
https://doi.org/10.3390/rs4071995