CA2951664A1 - Identification of location of source of gamma ray radiation - Google Patents

Abstract

A method and a system for the measurement of gamma-ray radiation from a gamma ray Source based on using one or more sensors positioned at differing ranges from the Source. The sensors conduct a series of radiation measurements with the sensors in a series of different spatial positions relative to the radiation sources. Analysis of the radiation measurement data through use of non-linear equations provides an indication for the location of the radiation Source. The method and system allows the optional use of a real-time automatic control of an optimized search strategy.

Description

Title: IDENTIFICATION OF LOCATION OF SOURCE OF GAMMA RAY RADIATION
FIELD OF THE INVENTION
The present invention relates generally to determining an estimate for the location of a source of anomalous gamma-ray radiation when the radiation sensor or sensors and the radioactive radiation source or sources are located at different ranges with respect to each other. In particular, it relates to the use of gamma-ray radiation sensors deployed on aerial vehicles and single or multiple stationary gamma ray sensors positioned to detect emissions from moving or stationary sources.
BACKGROUND TO THE INVENTION
It is known to estimate the location of sources of radiation using a distributed array of sensors. It is also known to do so using sensors mounted on aerial vehicles, particularly on unmanned aerial vehicles - UAVs, also known as "drones".
Examples of references of this character include:
US 8,355,818 US 8,820,672 US 7,465,924 This invention addresses a new procedure for carrying-out this process and an apparatus and system by which such procedures are implemented.
There is a need for a system which can locate sources of gamma-ray radiation that may be used as Radiological Threat Agents for malicious purposes. Additionally, there is a need for a system to effect the identification and localization of illicit gamma-ray radiation sources being transported by vehicles, particularly within ground transport, within ships and by UAVs or drones, before they can effect damage. This is in addition to the determination of the source strength and other parameters such as type of source.
This invention addresses those needs amongst other objectives.
The use of "sensor" and "sensors" herein is intended to cover the use of single or multiple sensors as the context requires or permits. Multiple sensors may be employed both to detect different parameters and for redundancy. For example, one sensor could be highly sensitive and suitable for detecting signals long distances but because it is sensitive will saturate at closer ranges, requiring a 2nd sensor for closer range operations.
The invention in its general form will first be described, and then its implementation in terms of specific embodiments will be detailed with reference to the drawings following hereafter. These embodiments are intended to demonstrate the principle of the invention, and the manner of its implementation. The invention in its broadest and more specific forms will then be further described, and defined, in each of the individual claims which conclude this Specification.
SUMMARY OF THE INVENTION
According to one aspect of the invention an indication of the location of a source of gamma-ray radiation is obtained by detecting such radiation at differing ranges between the source of the gamma-ray radiation and the detecting radiation sensor(s). The primary sensed data includes the intensity of the gamma rays incident upon a gamma ray sensor sensitive volume e.g. scintillation counts per second. Preferably it also includes the energy of such detected gamma-rays, e.g.
the wavelength or energy content of the individual detected gamma ray photons based upon the brightness of scintillations. Analysis of this acquired data assumes that the source and sensor are separated by an intervening space that is occupied by air.
The location of the source is determined in whole or in part by taking into account, inter alia, the relative geometry of the disposition of the sensor and source;
the response function of the sensor; the intensity and energy of the gamma-ray radiation; the level of background radiation and the physical processes involved in the interaction of gamma rays with the intervening air. Optionally the type of source may be initially estimated to provide an energy value or the spectrum of the gamma

2 ray radiation as detected may be measured directly by a sensor to determine the type of source. Air density at the location of the sensor may be estimated or may be measured by detecting air pressure and temperature. Air density may also be established by measurements based upon multiple data acquisitions extracted by a sensor at different ranges between the relative locations of the source and sensor.
Such ranges may be changing with time. This latter condition may occur, for example, when the sensor is carried by a drone and the source is stationary or moving. Or it may occur where the radiation source is being carried by a seaborne vessel, a moving ground vehicle or an aerial vehicle and the sensor(s) is/are stationary. In such cases uncertainties will be introduced into the location information provided by the invention, but when the differential motion is small the determined location will still be meaningful.
Multiple data samples of gamma ray intensity and energy obtained while the sensor and the anomalous source of radiation are at different ranges from each other are then used to solve the following equations for the location of the source, e.g., solving for the x, y, z co-ordinates.
Equation 1 r n = [ xgr xnrs )2 + ygr ynrs )2 4_ ( 4.1Ir zli.s )2 }-2 Equation 2 T n = rn/k A1 S G R exp (¨(1+ al ) T n ) Equation 3 D n =
"2 n wherein D is the gamma-ray sensor intensity response in units of counts per second (cps) S is the gamma-ray radiation source strength in units of Curies (Ci) G is the gamma-ray constant for the type of radioisotope emitting gamma-rays in units of pSv / hr per Curie at 1 meter (pSv / hr / Ci @ 1m) R is the response function of the gamma-ray sensor in units of counts per second per pSv per hour (cps / pSv / hr)

3 k is the linear attenuation coefficient for the gamma-ray radiation of a specific energy in the intervening attenuating medium, i.e. air, in units of inverse meters m--1) r is the range or Euclidian distance between the source of gamma-ray radiation and the gamma-ray radiation sensor in units of meters (m) A1 source multiplication factor associated with Build-up (dimensionless) (1+a,) collision multiplication factor associated with Build-up (dimensionless) number of mean free paths of the estimated type of gamma-rays in air (dimensionless) and wherein the subscript n labels the time series of spatially separated radiation measurements; the superscript dr labels the coordinates of the location of the radiation sensor; the superscript rs labels the coordinates of the location of the anomalous source of radiation; and x, y, and z label latitude, longitude and altitude respectively (m).
Equation 3 is a condensed version of more elaborate equations wherein the terms A1, (1+al ) and T are taken from a Taylor expansion in order to simplify the equations.
In place of Equation 3 more terms may be employed from the Taylor expansion.
Finding the location (x, y and z) from a solution of the above n equations for D n will require at least as many data samples as there are unknowns. As progressively more sets of data samples are acquired more exact values for these parameters can be obtained once the equation set becomes over determined.
The equations assume that the Euclidian distance separation between source and sensor is effectively unchanging during the data sampling interval. This condition will be essentially met when the relative velocity between source and sensor is small.
Preferably the sampling interval at each data acquisition point should be as short as is consistent with obtaining meaningful data. And the delay between acquiring data at distinct data acquisition points should be similarly minimized. The motion of the

4 Source relative to the Sensor will show up as a progressively changing solution for the location of the Source every time the set of equations are solved.
Some of the parameters may be estimated or predetermined. For example, the technique of the invention can be applied where the source type and strength of the radiation are known, as where the source has been lost or stolen. Standard values for air density may be initially employed as an estimate. The values for these parameters may be iteratively adjusted as data acquisition allows improved estimates to be applied.
As a preferred feature of the invention, an estimate for the co-ordinates for a Source of gamma radiation of a specific type located on the surface of the Earth may be determined using an aerial vehicle by a method comprising the following steps:
a) introducing a gamma ray sensor carried by an aerial vehicle into a detectable range within the region of the Source;
b) causing the aerial vehicle to follow a preferably curvilinear flight path within such range;
c) establishing values corresponding to the intensity and preferably energy of gamma ray background signals within the region of the Source;
d) detecting and recording values for the intensity and preferably energy of gamma rays originating from the Source as provided by the sensor, correlated with the spatial coordinates of the sensor at corresponding multiple data acquisition points along the flight path;
e) providing a value for the density of air in the region around the aerial vehicle;
f) inputting a determinate number of values established by c), d), and e) above into a programmable computer configured to solve the above equations and provide the co-ordinate values for the location of the Source:
and lastly

5 g) causing the computer to output the estimate for the co-ordinates of the Source as established by f), above, and thereby provide the estimate for the location of the Source of gamma radiation.
Monitoring shipping and ground vehicles As a further feature of the invention estimated spatial co-ordinates for a Source of gamma radiation of an estimated type moving on the surface of the Earth may be determined using a series of stationary sensors deployed as an array on the surface of the Earth by a method comprising the steps set-out above, the stationary sensors being located at the corresponding data acquisition points. For the purposes of this disclosure "surface of the Earth" is to be understood as including both surfaces on land and the surface of water, as in the case for example of rivers and harbours with shipping present on the water. This series of stationary sensors deployed as an array on the surface of the Earth may be augmented by sensors carried in aerial vehicles.
Dispersed Radioactive on Ground According to another aspect of the invention radiation from a dispersed anomalous radiation sources may be detected and analyzed. This variant is relevant where a radiation spill or intentional dispersal may have occurred. The location of the dispersed Source will be indicated by a spread of location values within the dispersal zone.
Determining Uncertainties in Location, Energy and Source Strength Another useful aspect of the present invention resides in its ability to provide data on the uncertainties in the identified location, energy and radioactive source strength of said anomalous radiation sources.
Graphical User Interface Optionally but preferably, the method and system of the invention may include a real-time graphical user interface providing system operators with information including map overlays, collateral video images, and computer-generated optimized search strategies. This permits meaningful and rapid human interpretations of and

6 interventions in radiation measurements being obtained from an aerial vehicle.
Such interventions could adjust the otherwise automated flight path of a UAV-carried sensor or otherwise allow adjustment of an automatic search strategy.
Collateral imaging of Sensor field of view In conjunction with obtaining radiation information from a region of interest, contemporary or archival still, video or Radar images of the region may be correlated with the radiation data. This will assist in distinguishing amongst multiple possible vehicles that may be carrying the Source. This can also assist on-site personnel in response and inspection of a Source. Once a visual identification is made of a Source carrier, it may be tracked visually as by a drone with image-following capability.
The foregoing summarizes the principal features of the invention and some of its optional aspects. The invention may be further understood by the description of the preferred embodiments, in conjunction with the drawings, which now follow.
Wherever ranges of values are referenced within this specification, sub-ranges therein are intended to be included within the scope of the invention unless otherwise indicated or are incompatible with such other variants. Where characteristics are attributed to one or another variant of the invention, unless otherwise indicated, such characteristics are intended to apply to all other variants of the invention where such characteristics are appropriate or compatible with such other variants.
BRIEF SUMMARY OF THE FIGURES
The present invention will now be described in more detail with reference to the accompanying Figures, as follows:
Figure 1 is a schematic depiction of a volume of space showing the geometry wherein a gamma-ray radiation sensor is located in space at a distance r from a single gamma-ray radiation point Source at rest at a specified location, e.g., on the surface of the

7 Earth. The precise location of the radiation Source is unknown but the co-ordinates for the sensor are known (as by GPS).
Figure 2 is a graph showing the loss of gamma ray signal strength as a function of the distance from the Source due to the 11r2 loss or inverse square law effect in a hypothetical vacuum where the Source is Cesiumi32.
Figure 3 is a graph showing the loss of gamma ray signal strength with increasing distance from a Source based upon the progressive absorption of gamma rays by air over the intervening distance from the Source where the Source is Cesium-137.
In this graph the curve of values appears as a straight line due to the use of a semi-log scale for the Y axis.
Figure 4 is a graph showing the combined effects of the effects depicted in Figures 2 and 3.
Figure 5 is a graph showing the enhancing effect of "Build-up" on the measured strength of gamma rays detected by a sensor as a function of the distance of the sensor from the Source where the Source is Cesiumi32.
Figure 6 is a graph showing the curve of Figure 4 and an additional curve showing the enhancing effect arising from including the "Build-up" factor depicted in Figure 5 in establishing the measured strength of the gamma ray signal strength as a function of the distance from the Source.
Figure 7 is a reproduction of Figure 1 wherein the vehicle carrying the gamma ray sensor is following a flight path and data based on detection of gamma ray signals is being acquired at multiple data acquisition points along the flight path.
DESCRIPTION OF EMBODIMENTS OF THE INVENTION
Premises In the following description, location and spatial location measurements are made in a system of coordinates which provide latitude, longitude and altitude with respect to the center of the Earth. It is understood that latitude, longitude and altitude may be stated and

8 expressed in units of meters with respect to an origin different from the center of the earth or in any other appropriate frame of reference.
The physical quantities, equations and units of measurement employed herein are useful for the present purposes. It is well-known that other quantities and units of measurement can be used equivalently with the appropriate conversion factors.
Alternative equations can be used to describe the physical processes of the emission, transport and sensing of gamma-ray radiation.
Transport of gamma-ray radiation through air The wording "gamma-ray sensor" used herein refers to a sensor which provides a real-time response to gamma rays interacting with the sensor. This response of the sensor to gamma-ray radiation may provide data including:
1). the intensity of radiation incident on the sensor or equivalently the number of gamma-ray photons interacting with the sensor per unit time expressed in suitable units such as counts per second (cps) or micro-Sieverts per hour (pSv/hr) 2). the energy values of individual gamma ray photons included in the spectrum of the radiation incident on the sensor.
Well-known examples of such gamma-ray radiation sensors may include but are not limited to plastic scintillation sensors, Sodium Iodide scintillation sensors, Geiger tube sensors, etc. For brevity, "sensor" as used herein denotes any type of gamma-ray sensor that records the intensity and, optionally, the energy content of gamma-ray radiation.
Physical processes The physical processes determining the response of a gamma-ray sensor to a gamma-ray source in an infinite attenuating medium include:

9 1) The gamma-ray radiation Source strength expressed in units of Curies;
2) the Euclidian distance between the sensor and the Source of gamma-ray radiation in units of meters;
3) the reduction of initially uncollided gamma-rays by the intervening medium between the Source and the sensor as expressed through the mass attenuation coefficient in units of cm2/gm;
4) secondary radiation arising from gamma rays which collide with collaterally located air molecules en route, and are incident upon the sensor expressed through the dimensionless Buildup Factor, and 5) the gamma-ray sensor response function expressed in counts per second per microSievert.
The sensor response function may be determined by a calibration of the sensor.
The sensor response function may be omnidirectional or may have a dependence on the angle of incidence of the radiation on the sensor. In the absence of a significant collimating configuration, the Response function need not be strongly or significantly dependent on the angle of incidence. In such cases variations in the angle of incidence within the Sensor's field of view may be ignored. Further, the Sensor response function may be dependent on gamma-ray energy and therefore the type of source.
The invention does not require that the Sensor be collimated and have the capacity to be pointed at a radiation Source in order to detect the location of the Source.
However, shielding to reduce background noise may give the Sensor a preferred field of view in which it is more sensitive to the detection of gamma rays. Within the field of view the Sensor is multidirectional.

Calculations For a sensor at a distance r - 31 from a source of gamma-ray radiation as shown in Figure 1, the gamma rays incident on the sensor are proportional to the total number of gamma ray photons given off by the source. Further, for a sensor at a distance r from a source of gamma-ray radiation, the gamma rays incident on the sensor are proportional to the ratio of the intercepting area of the sensor divided by the area of the sphere with radius r. This the well-known 117-2 signal diminution parameter that depends on range. This effect is shown in Figure 2.
Still further, for a sensor at a distance r from a source of gamma-ray radiation, the uncollided gamma rays incident on the sensor are proportional to the fraction of gamma rays which do not collide with the medium and are not thereby absorbed or otherwise attenuated by interaction with the medium. This fraction may be expressed as e-kr wherein the constant k is the linear attenuation constant and is determined by the composition and density of the medium and the gamma ray energy. For air a typical value for k is 0.08 cm2/gm at 600 KeV and varies slowly over the gamma-ray energy region of interest. The value also varies slightly with air pressure and moisture content but such variations may be ignored when satisfactory accuracy is otherwise being achieved. The effect is shown in Figure 3.
Figure 4 then shows the net consequences of these two effects combined.
Yet further, for a sensor at a distance r from a source of gamma-ray radiation, the gamma rays incident on the sensor are proportional to the gamma rays which are scattered into the detector ¨ Figure 6. These can be rays that are initially directed collaterally from the direct path to the sensor but which scatter from the medium to be redirected towards and become incident on the sensor. This factor of proportionality, known as Build-up may be expressed as B and is determined by the composition and density of the medium and the gamma ray energy. An example of the dependency of Buildup on separation between the Source and the sensor in air is shown in in Figure 5.

In summary, Figure 6 depicts the effect of combining this Build-up effect with the attenuating factors of Figures 2 and 3. Further Figure 6 contrasts the inclusion of Buildup with the effects of only 1/r2 and attenuation.
A consequence of these considerations is that, at relatively further ranges from a Source, the rate of fall-off or diminution of a signal available to be detected is reduced, or colloquially, the curve is flattened. Accordingly, the refinements in the sensitivity and precision of identifying the location of a Source which have been disclosed can improve the range at which a Source may be reliably located. This is a valuable benefit of the invention.
Math ¨ assuming no Background radiation Figure 7 depicts a vehicle carrying the gamma ray sensor 20 along a flight path having 6 data acquisition points. The Source 7 is stationary. At each data acquisition point 1 ¨ 6 the intensity, and optionally, the energy of the gamma rays 18 is measured along with the location of the data point, e.g. acquired by a GPS receiver.
Time may also be recorded for use in cases where the Source is moving.
In instances wherein a radioactive source of gamma-ray radiation is lost or stolen, then, the radioactive isotope and thereby the gamma-ray energy is known and the radioactive source strength is known. These known factors then reduce the number of, or place restrictions on, the values of some of the unknown variables in the set of simultaneous equations. The knowledge of the gamma-ray energy relieves the requirement for a measured determination of that parameter and its attendant measurement uncertainties. The radioactive source strength can set an upper bound on that parameter, as determined by for example a least squares solution of the simultaneous equations. The possibility of unknown shielding of the lost or stolen Source results in an unknown apparent or effective radioactive Source strength outside the possible shielding; however, that apparent Source strength may not exceed the known lost or stolen Source strength.

This data is then applied to the equation 3, above, to generate a set of simultaneous nonlinear equations which may be solved for the location of the Source.
Methods for solution are well known. A determined set of equations will normally give one solution.
In some cases, as where, for example, the sensor 20 is moving along a straight line, dual or mirror solutions may be delivered. This can be addressed by having the sensor 20 depart from following a straight course to follow a curvilinear flight path.
Alternately the sensor 20 may be configured to distinguish between dual solutions, as by bifurcating the sensitive volume to create left and right fields of view.
Poisson statistics Gamma-ray radiation measurement data are the result of stochastic processes and are described by Poisson statistics. Specifically, the measurement uncertainty in each measurement of sensed gamma-ray radiation in the method of the present invention may be described by Poisson statistics. Additionally, there is measurement uncertainty in other measurements in the method of the present invention including sensor position and gamma ray photon energy. Finally, there is uncertainty inherent in the measurement data and analytic methods underlying tabulated parameters used in the method of the present invention and in their interpolation.
Over Determined equations Additionally, the number of measurement points along a flight path may exceed the number of unknown variables in the set of simultaneous non-linear equations. Thus, the set of simultaneous non-linear equations is overdetermined. Multiple values for the location of the Source may then be presented. As a consequence it may be appropriate to use a least squares procedure, or other applicable methodology, to provide a preferred solution for the over determined case Background radiation (real world) The above analysis assumed the absence of background radiation. In fact, the total sensed gamma-ray radiation measurement data at any location and at any time will consist of the sum of counts arising from measurement data from normally occurring background gamma-ray radiation and gamma-ray radiation measurement data from any anomalous Source or Sources of gamma-ray radiation.
The gamma ray natural background radiation intensity and energy spectrum may be measured or estimated from other measurements carried out in the absence of an anomalous Source or Sources of gamma-ray radiation. It is well-known that the background gamma-ray radiation intensity data must be subtracted from the total sensed radiation measurement intensity data in order to obtain measurements of the intensity of any anomalous gamma-ray radiation at any measurement location.
This represents the simplest method of addressing Background radiation.
Illustrative Case: Aerial Vehicle and known Source with Unknown Location Reference is made to Figure 7. A gamma-ray radiation 18 sensor 20 is carried by an aerial vehicle 11 such as, but not restricted to, an unmanned aerial vehicle, commonly known as a drone 21, along a flightpath 8. A series of measurements of gamma-ray radiation intensity are made by the sensor 20 at a series of spatially distinct points, numbered as 1 through 6, along the flightpath. All flightpath spatial location measurements can be made with respect to a system of coordinates which provide latitude 11, longitude 12 and altitude 13 with respect to the center of the Earth. The radiation intensity measurement data are the result of sensed natural background radiation together with sensed radiation 18 from the known anomalous gamma-ray radiation source 7.
The present invention provides a method for determining an estimate of the location and the source strength of the found source of gamma-ray radiation together with an estimate of the uncertainty in the location estimate 9 as shown in Figure 1.

Aerial vehicle measurement data as system of simultaneous nonlinear equations Further reference is made to Figure 7 in which the radiation measurement data locations are shown as a series of six points, labeled 1 through 6. Each data acquisition point is at a differing range 31 from the Source 7. The number of points at which gamma-ray radiation measurements are made, shown in Figure 7 as six points, is one example. Data can be acquired continuously and used to solve sets of determined or over determined equations as is most preferred.
At each of the data acquisition points the intensity of the sensed gamma-ray radiation 18 is measured. From the known energy of the Source of gamma-ray radiation 18, if known, the energy-dependent multiplicative factors A1 and al may be obtained by interpolation of data contained in well-known tables of these factors. Further, the gamma-ray constant G for the radioisotope is contained in well-known tables of these factors. Still further, from the known value for the maximum gamma-ray energy, the energy dependent mean free path factor T
may be interpolated from published tables of the linear attenuation coefficient k.
Alternately, this data may be acquired by solving the set of equations using the necessary larger number of data acquisition samples.
The intensity of background gamma-ray radiation from previously recorded data made by others or estimated from background measurements made prior to the search is subtracted from the total sensed gamma-ray radiation data to obtain the gamma-ray radiation data from the unknown anomalous Source 7 at the measurement points on the flightpath 1 ¨
6. From this data sufficient information is obtained to specify the D i, values at each data point which are due to the signal of interest from the anomalous Source of gamma-ray radiation by subtracting the Background level from the apparent value of D.
Reference is made to Equations 1, 2 and 3. A substitution is made of the factors obtained from the measurements of gamma-ray radiation intensity and the energy, as above, and further, substitution is made of the position measurements of location of the sensor 20 for each of the corresponding radiation measurements. This results in a set of equations with each equation of the set in a one to one correspondence to a sensor 20 measurement location.

Solve for source strength and location Once sufficient measurements have been made at multiple data acquisition points 1 ¨6 this data may be used to create a set of equations based on equations 1 ¨ 3. This provides a set of simultaneous non-linear equations which may be solved by well-known analytic or numeric methods for the remaining unknown four quantities which are:
the gamma-ray radiation source strength outside of any shielding in units of Curies (Ci) xrs, yrs, zrs the latitude, longitude and altitude of the anomalous radiation source Figure 7 depicts a stationary Source 7 and a moving sensor 20 carried by a drone 21. It can equally depict buoys in a harbour, each carrying a sensor 20 and a stationary vessel carrying the Source 7. The buoys would be positioned at each of the data acquisition points 1 ¨ 6. Even when the Source 7 is moving, data acquired simultaneously at each buoy location can be applied to equations 1 ¨ 3 to produce the necessary set of simultaneous equations. Thus, the case of a moving Source and multiple stationary sensors 20 has also been addressed.
Conclusion The foregoing has constituted a description of specific embodiments showing how the invention may be applied and put into use. These embodiments are only exemplary.
The invention in its broadest, and more specific aspects, is further described and defined in the claims which now follow.
These claims, and the language used therein, are to be understood in terms of the variants of the invention which have been described. They are not to be restricted to such variants, but are to be read as covering the full scope of the invention as is implicit within the invention and the disclosure that has been provided herein.

Claims (2)

1. A method of providing an indication of the location of a source of gamma-ray radiation comprising the steps:
1) detecting with a gamma ray sensor the intensity of gamma rays incident upon the sensor at a series of data acquisition points, each point being at differing ranges between the source and the sensor with the intervening space being occupied by air;
2) establishing the intensity level of background radiation in the intervening space;
3) establishing a value for the Air density in the intervening space;
4) subtracting the value for the intensity of background radiation from the measured value of the gamma ray intensity established at each data acquisition point to provide a detected intensity of the Source radiation;
5) inputting a determinate number of values established by 1), 2), 3) and 4) above into a programmable computer configured to solve an equation that states a value for the detected intensity of the Source radiation as a function of:
a) the coordinates of the source b) the coordinates of the sensor at each data acquisition point;
c) the air density d) the energy of the Source radiation e) the Euclidian distance between the sensor and the Source of gamma-ray radiation;
f) the mass attenuation coefficient for the reduction of initially uncollided gamma-rays by the intervening medium between the Source and the sensor;
g) the source multiplication Buildup factor for secondary radiation arising from gamma rays which collide with collaterally located air molecules en route, and are incident upon the sensor;
h) the collision multiplication factor associated with Build-up i) the sensor response function;
j) the gamma-ray radiation source strength;
k) the gamma-ray constant for the type of radioisotope emitting the gamma-rays, and l) T the number of mean free paths of the estimated type of gamma-rays in air to provide the co-ordinate values for the location of the Source, and 6) cause the computer to output the estimate for the location of the Source as established, thereby providing the estimate for the location of the Source of gamma radiation.

2. A method of estimating the location of a source of gamma radiation of an estimated type located on the surface of the Earth comprising the following steps:
a) introducing a gamma ray sensor carried by an aerial vehicle into a detectable range within the region of the Source;
b) causing the aerial vehicle to follow a path within such range;
c) establishing values corresponding to the strength of gamma ray background signals within the region of the Source;
d) recording sensor outputs corresponding to the strength of gamma ray signals detected once the sensor is within detectable range of the Source at multiple locations along the flight path sufficient to solve the equations following below;
e) recording values corresponding to the spatial coordinates of the sensor at which the sensor outputs are recorded f) providing a value for the density of air in the region around the aerial vehicle;
g) inputting a determinate number of values established by c), d), e) and f) above into a programmable computer configured to solve the following equations for the x,y, and z co-ordinate values for the location of the Source:
Equation 1 r n = [ + + ] -2 Equation 2 .tau. n = r n/k Equation 3 D n = wherein D the gamma-ray sensor response in units of counts per second (cps) S the estimated gamma-ray radiation source strength in units of Curies (Ci) G the gamma-ray constant for the estimated radioisotope emitting gamma-rays in units of pSv / hr per Curie at 1 meter (µSv / hr / Ci @ 1m) R the response function of the gamma-ray sensor in units of counts per second per µSv per hour (cps / µSv / hr) k linear attenuation coefficient for the estimated gamma-ray radiation of a specified energy in the intervening attenuating medium in units of inverse meters ( m -1) r the Euclidian distance between the source of gamma-ray radiation and the gamma-ray radiation sensor in units of meters (m) A1 source multiplication factor (dimensionless) (1+.alpha.1 ) collision multiplication factor (dimensionless) .tau. number of mean free paths of gamma-rays in air (dimensionless) wherein the subscript n labels the time series of spatially separated radiation measurements; the superscript dr labels the coordinates of the location of the radiation sensor; the superscript rs labels the coordinates of the location of the anomalous source of radiation; and x, y, and z label latitude, longitude and altitude respectively (m), and h) causing the computer to output the co-ordinates of the Source as established by f), above, and thereby providing an estimate the location of the Source of gamma radiation.