Comparing analytical and and numerical simulations of the radar micro-Doppler signatures of multi-rotor UAVs

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Comparing analytical and numerical simulations of

the radar micro-Doppler signatures of multi-rotor

UAVs

Peter Speirs1

, Arne Schröder1

, Matthias Renker2

, Peter Wellig2

and Axel Murk1 1

Institute for Applied Physics, University of Bern, Switzerland

2

armasuisse W+T, Switzerland

07.12.2018

Electromagnetic Waves and Wind Turbines 2018, Tu Delft, The Netherlands

Intoduction

In this talk, I will be discussing:

1. How well we (authors) can currently simulate UAV RCS. 2. How necessary is it to simulate/measure multiple similar UAV

models?

3. How much detail do we need in the UAV models? — For RCS measurements?

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Intoduction

models?

— For micro-Doppler?

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Intoduction

models?

— For micro-Doppler?

Talk outline:

> Motivation and introduction

> Measurement results

> Comparisons between RCS simulations and measurements

> Comparison between simple and complex UAV models

> Doppler simulations

> Requirements for machine learning?

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The UAVs measured

Quadcopters:

DJI Phantom 2

DJI Phantom 3

DJI Phantom 4 Parrot AR Drone 2.0

Hexacopter:

DJI S900

DJI images from Parrot image from

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Measurement results

> Measurements performed in an anechoic chamber. All at 10 GHz, 10 kHz BW.

> Phantom 3 and 4 with a camera below, others without.

> Phantom 2 measurements VV, 135-225◦, all others HH, 360◦, rotated by a turntable

> Step size of 0.25◦

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Measurement results

> Measurements performed in an anechoic chamber. All at 10 GHz, 10 kHz BW.

> Phantom 3 and 4 with a camera below, others without.

> Phantom 2 measurements VV, 135-225◦, all others HH, 360◦_{, rotated by a turntable}

> Step size of 0.25◦

Phantom 2 in the anechoic chamber.

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The UAVs simulated

Three different classes of UAVs simulated: quadcopters, hexacopters and octocopters. Note that the images are not to scale.

Quadcopter Hexacopter Octocopter

Photo Comple x model No model Simple model

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The UAVs simulated

What are the model simplifications?

Quadcopter Hexacopter and Octocopter

Key differences:

> Dielectric body neglected.

> Switch from a Finite Element Method (FEM) solver to Method of Moments (MoM) solver.

> Rotors replaced with rectangles.

> Motors replaced with cylinders.

Key differences:

> Only large components kept: landing gear, arms, battery, rotors, motors, top and bottom plates.

> Hexacopter model based on the octocopter model, with components shortened and geometry adjusted to approximate the DJI S900.

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The UAVs simulated

What are the model simplifications?

Quadcopter Hexacopter and Octocopter

Key differences:

> Dielectric body neglected.

> Switch from a Finite Element Method (FEM) solver to Method of Moments (MoM) solver.

> Rotors replaced with rectangles.

> Motors replaced with cylinders.

Key differences:

> Only large components kept: landing gear, arms, battery, rotors, motors, top and bottom plates.

> Hexacopter model based on the octocopter model, with components shortened and geometry adjusted to approximate the DJI S900.

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Simulation method

> Simulations in Ansys HFSS.

> Hexacopter, octocopters and simplified quadcopter:

— HFSS Integral Equation (MoM) solver, treating all materials as perfect electrical conductors.

> Complex quadcopter:

— HFSS FEM solver, allowing the dielectric treatment of the plastic hull.

> All simulations at 10 GHz.

Model Elements Time Memory

Quad.* 802 638 28 hrs 326 GB†

Simple quad. 16 655 12 mins 2.6 GB Simple hexa.‡ 238 714 9 hrs 49.6 GB

Octo.§ 387 554 29.5 hrs 98.1 GB Simple octo.‡,k 238 820 6.4 hrs 31.5

*0− 90◦_{only - simulation performed in 4}

parts.

†_{This exceeds system memory, so some}

disk caching included in time.

‡₀

− 180◦only - rotational symmetry.

§₀

− 180◦only - simulation performed in 2 parts.

k

Running on 8 cores. All others on 4.

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Comparing simulation and measurement

Phantom 2

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Comparing simulation and measurement

Phantom 3

Measurement with camera, simulation without.

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Comparing simulation and measurement

Phantom 4

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Comparing simulation and measurement

Parrot

No camera.

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Comparing simulation and measurement

Hexacopter

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Comparing simple and complex models

Quadcopter

HH (co-polar) HV (cross-polar)

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Comparing simple and complex models

Octocopter

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Static RCS Summary

> Complex model statistics compare well with measurements. Absolute RCS values compare less well, but not terrible.

> Quadcopter simple and complex model absolute co-polar RCS values compare well, cross-polar less well. Statistics not well reproduced.

> Hexacopter simple and complex models compare well, albeit with some smaller variations in statistics. 11

Doppler simulations

Target assumptions: > 10 cm length blade > Rotating at 20 Hz > PRF of 10.24 kHz > Radar at 10 GHz Short-time Fourier transform:

> Blackman window of length 101 used (corresponding to 9.86 ms)

> Zero-padded to length 3072.

Analytic blade1

:

1_{Model from: Martin, J. and Mulgrew, B., Analysis of the theoretical radar return signal from aircraft propeller blades, IEEE International Radar}

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Doppler simulations

> Doppler return from rotor movement can be simulated in HFSS by calculating the complex far-field electric field for stepped rotor positions.

> When sequenced, these values can be treated as the time-domain signal at the receiver.

Analytic blade: Simple rotor: Complex rotor:

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Doppler simulations

> Complex quadcopter model, but using MoM solver and assuming a PEC hull.

> Simplified quad- and hexacopter model and full octocopter model results are bistatic, resulting in a reduction in Doppler velocity by a factor of 2. Patterns the same though.

Full (PEC) quadcopter: Simplified quadcopter:

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Simplified UAV models

> Do we really need this complexity? Would a simple analytic approximation be enough?

> To test this, attempt to use machine learning to identify the number of rotors in a UAV RCS signal.

> We have built a model from the analytic blade approximation that allows the variation of:

— Number of rotors

— Number of blades per rotor — Rotor size

— UAV size

— UAV orientation (yaw, pitch, roll, elevation relative to radar)

— Individual rotor RPMs — Rotor starting positions — UAV radial velocity — Radar frequency

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Simplified UAV models

— Number of rotors

— Number of blades per rotor — Rotor size

— UAV size

— UAV orientation (yaw, pitch, roll, elevation relative to radar)

— Individual rotor RPMs

— Rotor starting positions

— UAV radial velocity — Radar frequency

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Simplified UAV models

> Have created training sets of 250x4 and 500x4 different sample signals, with the above parameters randomised.

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Simplified UAV models

> Have created training sets of 250x4 and 500x4 different sample signals, with the above parameters randomised.

Examples:

Single rotor Quadcopter

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Convolutional Neural Network

> One approach to the machine learning problem is to apply a Convolutional Neural Network directly to the (absolute values of) a time-frequency representation, treating them as images.

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Convolutional Neural Network

> This was tried with both wavelet and short-time Fourier transforms (STFTs).

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Convolutional Neural Network

> Lower resolution than usual to make problem tractable:

— STFT: 128x923, 8 bit — Wavelet: 236x1536, 8 bit

STFT _Wavelet

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Convolutional Neural Network

> Tried various different CNNs, but the most sucessful was: (show screehshot of code)

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Convolutional Neural Network

> Trained the network on 4x100 images

STFT Wavelet

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Convolutional Neural Network

> Trained the network on 4x100 images

> Results when applied to data (4x150 images)

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Convolutional Neural Network

Applying to simulated RCSs Quadcopter STFT Wavelet Simple Quadcopter STFT Wavelet Hexacopter

STFT Wavelet _STFT Octocopter Wavelet

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Convolutional Neural Network

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Convolutional Neural Network

STFT Wavelet _STFT Octocopter _Wavelet

Unfortunately, classifier says 1 rotor for all, both wavelet and STFT.

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Regression method

Applying to simulated RCSs

> More computationally efficient is some kind of classification or regression method. Here use Matlab’s❢✐"#❡♥&❡♠❜❧❡ function.

> To apply this, need some set of features to classify on:

— The ‘human’ classification features from [1].

— A custom set based on convolution with the signal from a single rotor. Based on finding the 8 peak frequencies, their amplitudes, and the number of repetitions of the signal at each peak.

[1] Kim, Y. and Ling, H., Human Activity Classification Based on Micro-Doppler Signatures Using a Support Vector Machine, IEEE Transactions on Geoscience and Remote Sensing:47 1328-1337, May 2009.

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Regression method

> Trained on both 4x250 samples from both descriptor sets, and tested against the remaining 4x250 samples, getting:

‘Human’ descriptors: Convolution descriptors:

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Regression method

> Trained on both 4x250 samples from both descriptor sets, and tested against the remaining 4x250 samples, getting:

‘Human’ descriptors: Convolution descriptors:

> Unfortunately, determines each simulated signal to be a hexacopter.

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Summary

RCS simulation:

> We can approximately reproduce the RCS statistics for quadcopter UAVs in simulation, but we do not currently accurately reproduce the absolute RCS.

> And there are some issues with the hexacopter, although these may be measurement issues. Simulation simplification:

> Current simplified models can reproduce the mean values of the complex model simulated RCS, But not the statistical properties.

Doppler simulations:

> Simplification model reproduces some features, but not all.

> So far it appears that more than just the analytic model is necessary to produce a usable model for this machine learning application.

> But still at the very early stages of this work.

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Thank you! Questions? peter.speirs@iap.unibe.ch