Resonance Based Feature Extraction of 3D Objects from RCS Data

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ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)

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ISSN (PRINT) : 2320 – 8945, Volume -2, Issue -5,6 2014 19

Resonance Based Feature Extraction of 3D Objects from RCS Data

1S Anuradha, ²Jyothi Balakrishnan

1,2Department of Electronic Science, Bangalore University, Bengaluru, India Email: ¹[email protected], ²[email protected]

Abstract –Classification of objects based on Radar Cross Section (RCS) has several military and civilian applications. Feature extraction is an important step in the classification process. The resonances (features) of an object are unique and are independent of the look angles (aspect). A database created with the resonances of known radar targets help in the classification of targets. A method to extract the Natural Resonant Frequencies (NRFs) of 3- dimensional (3D) canonical shaped objectsusing the Vector Fitting (VF) algorithm is formulated and the results are presented in this paper.

Keywords – classification; feature extraction; RCS;

resonances.

I. INTRODUCTION

Feature extraction forms an important part of classification. In non-cooperative target recognition, the feature set of unknown targets is compared with that of known targets in the database for classification. The correctness of the feature extraction of known objects influences the accuracy of identification. The features extracted for an object should be such that it best represents the object with minimum number of elements in the feature set.

The feature set of a radar target, should be aspect independent in nature. Some of the parameters that are chosen as features in target recognition are polarizability, modulation capability, resonances etc [1].

Among these, the resonances obtained from RCS data are known to be aspect independent by nature. The singularity expansion method suggests that the back scattered electromagnetic returns of a target contains sinusoids (resonances) that are representative of target’s shape size and material composition[2].Based on this proposition, the resonances of an object stands out as the best choice as a feature to characterize any object.

The NRFs of a canonical object such as wires and spheres can be determined analytically [3]. However, for a complex shaped object such as an aircraft, it is formidable. Therefore resonances of such objects have to be extracted from experimentally obtained back scattered data. The resonances from time or frequency data are determined using Prony’s algorithm [4] and Matrix pencil of function [5].

In this paper, the Vector Fitting algorithm [6] is used.

This is an algorithm that represents the frequency response data by a transfer function containing a series of simple poles.This method is used to identify the NRFs of a cone and a cylinder.

II. STATEMENT OF THE PROBLEM

Two Perfectly Electrically Conducting (PEC) 3D objects – cone and cylinder have been considered in this study.

The objectsare modeled using commercial, computational electromagnetic field software [7].

A linear plane wave of unit amplitude is incident at(ϕ = 0°,θ= 0°) aspect. The scattered responses are observed at θ=0ô, θ=30ô and θ=60ô. The simulation is done for frequencies ranging from 0.01GHz to 5GHz.

The scattered electric field response for acone of height 0.1m and diameter of the base equal to 0.1m is shown in Fig.1.

Fig.1. (a) PEC cone model of d=h=0.1m

Fig.1. (b) Scattered E-field response of PEC cone A similar simulation study was done on a PEC cylinder of height 0.1m and diameter 0.1m. The results are shown in Fig.2.

Fig.2. (a) PEC cylinder model of d=h=0.1m

0 1 2 3 4 5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Frequency (GHz)

E-field magnitude (v)

0 degree 30 degree 60 degree

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Fig.2. (b) Scattered E-field response of PEC cylinder of d=h=0.1m.

III. DETERMINATION OF NRFS

The vector fitting algorithm is used to extract the true NRFs of the objects from its frequency response. The number of starting poles N is decided by computing the Root Mean Square Error (RMSE) for different number of starting poles N. The RMSE converges to a very low value as the order N is increased. An optimum value for N is chosen such that further increase in N does not appreciably improve the accuracy of the fit. The true NRFs for the models are decided by applying the criteria proposed in [8].

IV. RESULTS AND CONCLUSIONS

The NRFs of a cone and a cylinder are determined at different aspect angles using the criteria for selection of true NRFs from VF poles. Further, the common dominant resonances (nearly same) among the NRFs at each aspect (observation angle) is identified, by choosing the poles with small real parts, to create a database for the object.

Table 1 presents the results for the cone and Table 2 for the cylinder.

Table 1: Extracted true NRFs of cone

Observation angle

VF poles NRFs of cone Database NRFs for cone

0 degree

-1.0743±0.3142i -0.5285±0.9743i -0.8698±1.9603i -1.3381±3.0863i -1.1720±4.1551i -0.9134±5.0284i -84.8960±0.00i 123.9054±0.00i

-1.0743±0.3142i -0.5285±0.9743i -0.8698±1.9603i -1.3381±3.0863i -1.1720±4.1551i

-0.8454±0.3010i -0.5285±0.9743i -0.8193±2.0189i -1.1092±2.9389i -1.0540±3.7096i -0.5955±4.8492i

30 degree

-0.8454±0.3010i -0.5323±0.9728i -0.8193±2.0189i -1.0540±3.7096i -0.9287±4.7465i 1.6302±6.5297i 7.3332±3.2740i

-0.8454±0.3010i -0.5323±0.9728i -0.8193±2.0189i -1.0540±3.7096i -0.9287±4.7465i

60 degree

-1.0721±0.00i 5.7190±0.00i -0.5299±0.9751i -0.8610±2.0066i -1.1092±2.9389i -1.1658±3.7789i -0.5955±4.8492i 4.9583±4.2625i

-0.5299±0.9751i -0.8610±2.0066i -1.1092±2.9389i -1.1658±3.7789i -0.5955±4.8492i

Table 2: Extracted true NRFs of cylinder

Observation angle

VF poles NRFs of cone Database NRFs for cone

0 degree

-0.4719±0.7140i -0.3757±1.3708i -0.0003±2.3176i -0.7744±2.1877i 2.702 ± 1.0846i -0.0005±3.4767i -0.0002±3.6904i 2.553 ± 3.1546i -1.2845±3.9152i -1.1792±4.6161i -0.0013±4.8229i 1.9959± 5.0996i

-0.4719±0.7140i -0.3757±1.3708i -0.7744±2.1877i -0.0003±2.3176i -0.0005±3.4767i -0.0002±3.6904i -1.2845±3.9152i -1.1792±4.6161i -0.0013±4.8229i

-0.4315±0.7308i -0.3757±1.3708i -0.0003±2.3176i -0.0002±3.6904i -0.0036±4.1864i -0.7926±4.4204i -0.0013±4.8229i

30 degree

-0.5643±0.0000i 2.4944 ±0.0000i -0.4513±0.7054i -0.3866±1.3799i -0.0015±2.3185i 2.4498± 2.0200i -0.9683±3.3804i -0.0004±3.6905i -0.0036±4.1864i 2.1596± 3.9542i -0.8108±4.5577i

0.0003 ±4.8236i 0.9345± 5.9653i

-0.4513±0.7054i -0.3866±1.3799i -0.0015±2.3185i -0.9683±3.3804i -0.0004±3.6905i -0.0036±4.1864i -0.8108±4.5577i

60 degree

-1.2048±0.0000i 2.8513±0.0000i -0.4315±0.7308i -0.4006±1.3757i -0.6505±2.1892i -0.7675±3.2639i 2.7573±2.0228i -0.0003±3.6903i -0.0620±4.1087i -0.7926±4.4204i 2.3294±4.0539i -0.0024±4.8227i -0.0684±9.2275i

-0.4315±0.7308i -0.4006±1.3757i -0.6505±2.1892i -0.7675±3.2639i -0.0003±3.6903i -0.0620±4.1087i -0.7926±4.4204i -0.0024±4.8227i

The values of the true NRFs obtained have been compared with the results obtained using Cauchy method [9]. The results match with the published results.

Further, the pole set is reduced to create a database for the object.

0 1 2 3 4 5

0 0.05 0.1 0.15

Frequency (GHz)

E-field magnitude (v)

0 degree 30 degree 60 degree

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