1. Small Humans Project Chad Waddington Mathematics PhD Student, RPI
Mentor: Dr. Analee Miranda
The difficulty with implementing these more accurate human models is that in order to make them meet the anthropometric data it is necessary to place the spheres and cylinders too close to one another to allow for Sarabandi/Polatin’s constraints. Put another way, in order to use the current mathematical model for the Electromagnetic scattering it is required that we make the distances between the individual objects above, especially the “neck length,” so great compared to the object’s relative size that the model no longer accurately represents the measurements of a human.
We Hope to overcome this difficulty by returning to Sarabandi/Polatin’s work and removing the assumption 𝜌> 2 𝑎 𝑐 2 𝜆 , 𝐿 2 𝜆 ≥𝜌> 2 𝑎 𝑐 2 𝜆 . This would allow for the construction of a more general model which may be able to account for the tighter distances we desire.
The Dielectric Challenge
The second difficulty which must be overcome is the dielectric challenge. Although Sarabandi/Polatin’s paper provides an excellent look at the scattering from two adjacent conducting objects this is not entirely appropriate when considering human targets. Humans are best treated as dielectric objects and have scattering properties quite different from purely conductive targets.
In order to take into account the scattering for multiple adjacent dielectric objects it will be necessary to modify the model further to account for the differences in target properties. Barber and Yeh have written an excellent paper on the Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies. Their derivation uses the Extended Boundary Condition Method along with the Schelkusnoff’s equivalence theorem determine the scattered field in terms of the incident field coefficients. Their method is most applicable to to objects in the resonance region.
Using the methods above they develop a set of simultaneous linear equations which can be solved for the expansion coefficients of the field:
𝐼= 𝑘 2 𝜋 𝑠 𝑛 ∙ 𝑀 𝑣 3 (𝑘 𝑟 ′ )× 𝑀 𝑢 1 ( 𝑘 ′ 𝑟 ′ )𝑑𝑆
𝐽= 𝑘 2 𝜋 𝑠 𝑛 ∙ 𝑀 𝑣 3 (𝑘 𝑟 ′ )× 𝑁 𝑢 1 ( 𝑘 ′ 𝑟 ′ )𝑑𝑆
𝐾= 𝑘 2 𝜋 𝑠 𝑛 ∙ 𝑁 𝑣 3 (𝑘 𝑟 ′ )× 𝑀 𝑢 1 ( 𝑘 ′ 𝑟 ′ )𝑑𝑆
𝐿= 𝑘 2 𝜋 𝑠 𝑛 ∙ 𝑁 𝑣 3 (𝑘 𝑟 ′ )× 𝑁 𝑢 1 ( 𝑘 ′ 𝑟 ′ )𝑑𝑆
These equations can then be solved numerically and applied to find the scattered field from the target objects.
Abstract:
Understanding that better the informed the warfighter is regarding the demographics of an area, the more effective he or she will be in carrying out his or her mission we seek to develop methods for distinguishing between children and adults in radar data. We consider the possible radar target models which can be implemented to this purpose and how they may be approved upon. This project will also collect data from humans along with anthropometric data to aid in the building of an SVM classifier for the two groups.
Electromagnetic Scattering from Two Adjacent Objects
With two objects illuminated by an electromagnetic wave and with the scattered wave observed at a point 𝑝 it is possible, using the Reaction Theorem 𝑠1 𝐸 1 × 𝐻 2 − 𝐸 2 × 𝐻 1 ∙𝑑𝑠= 𝑠2 ( 𝐸 2 × 𝐻 1 − 𝐸 1 × 𝐻 2 )∙𝑑𝑠 for two antennas, to describe the scattering from object two due to the secondary illumination from the scattered field due to object one. See figure 1.
Using this, Sarabandi and Polatin describe a model for the scattering from a forest canopy which is not radically different from the constraints posed by anthropometry on a human model. They stipulate that the interaction is between a conical sphere and cylinder pairing, where the cylinder is in the far field of the sphere and the sphere is in the near field of the cylinder with respect to the cylinder’s longitudinal dimension. Mathematically this translates to 𝜌> 2 𝑎 𝑐 2 𝜆 , 𝐿 2 𝜆 ≥𝜌> 2 𝑎 𝑐 2 𝜆 where 𝜌 is the distance between the cylinder axis and the sphere center. See figure 2.
Using these constraints they arrive at a scatter field model where
𝑬 𝑐 𝑠 = 1 sin(𝜃) 𝑚=−∞ ∞ [ 𝐴 𝑚 𝑖 − cos 𝜃𝜌 + sin 𝜃𝑧 + 𝐵 𝑚 𝑖 𝜙] 𝑒 𝑖𝑚( 𝜙 𝑠 − 𝜙 𝑖 )
This allows for the investigation of the scattering of arbitrarily shaped complex objects made up of spheres and cylinders obeying these rules.
The Human Model
The first difficulty which must be overcome is that of creating a realistic human model which both satisfies the constraints of Sarabandi/Polatin but remains reasonably close to the anthropometry data that we have examined. Currently we are looking at a two cylinder one sphere model which meets these criteria. (See figure 3) This model is clearly a higher degree of simplification than would be ideal. In time it is hoped that we may be able to advance to a more realistic human model which would resemble either Figure 4 or Figure 5.
Support Vector Machines
An SVM accepts a vectorized input and outputs a classification based on similarity to previous ‘support’ vectors with know classifications. For instance if 𝑋 is a set of HRR profiles from known targets classified into a subset of 𝑌 possible groupings, i.e. Child or Adult an SVM attempts to output a classification for a new observation 𝑥 of unknown grouping based on its similarity to known support vectors. The process is shown geometrically below.
Live Data
To date we have test collected data on about a dozen individuals and on two human analog dummies filled with a dielectric fluid to simulate muscle and fat tissues. The data clearly indicates a difference in type and form of scattering returned from each target beyond just an amplitude difference. See the plots below.
Conclusion and Future Work
In summary, much of the necessary ground work for this project has been laid. It remains, however, to bring this work together and expand upon it in order to achieve the final objective of creating a realistic model of a human radar target. We will need to consider the relaxing of the constraints posed by the Sarabandi/Polatin paper and continue researching methods for combining their work on conducting objects with that of Barber and Yeh’s work on dielectric bodies. Once this is done we will be able to consider seriously the question of how to make an intelligent distinction between the types of human targets detected by the radar. This will be done by considering the wealth of anthropometric data we have access to and by conducting live empirical tests of the system on both children and adults. As we move forward and gain a greater understanding of the differences between the two we will become better able to tailor our model to each groups distinctive characteristics.
Fig. 3
Fig. 4
Fig. 5
Fig. 1
Fig. 2