Realistic Modelling of Ultrasound Sensing for Autonomous Vehicles

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Thesis in Electrical Engineering

Department of Electrical Engineering, Linköping University, 2019

Realistic Modelling of

Ultrasound Sensing for

Autonomous Vehicles

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ii

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vi

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viii

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1

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2

Equipment and

Experimental Setups

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3

Background Theory

𝑐 γ ℃ 𝑐 = √𝛾𝑅𝑇

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14 𝑍 𝑋𝑙 𝑋𝐶 𝑍 = 𝑅 + 𝑗(𝑋𝑙 − 𝑋𝐶) 𝑋𝑙 𝑋𝑐 𝑋𝑙 = 𝜔𝐿 𝑋𝐶= 1/𝜔𝐶 ω 𝑍 = 𝑉𝑝 𝐼𝑝

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|𝑍| = | |

₁

𝑗𝜔𝐶

𝑜𝑝

+

1 𝑅

1

+ 𝑗𝜔𝐿

1

+

_𝑗𝜔𝐶

1

1 | |

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16 𝑦 = 𝑎𝑥 + 𝑏 {(𝑥1, 𝑦1), (𝑥2, 𝑦2) … (𝑥𝑁, 𝑦𝑁)} 𝑎 𝑏 𝐸(𝑎, 𝑏) = ∑(𝑦𝑖− (𝑎𝑥𝑖+ 𝑏))2 𝑁 𝑖=1 𝜕𝐸 𝜕𝑎= 0 𝑎𝑛𝑑 𝜕𝐸 𝜕𝑏 = 0

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𝑟

1

4𝜋𝑟2 ∝ 𝐼 ∝ 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 2

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18

4

Testbench Validation by

Speed of Sound

Measurements

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20 µ

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𝑑 = 𝑣𝑡 + 𝑜𝑓𝑓𝑠𝑒𝑡

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22 µ

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5

Impedance Measurement

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26 𝑉𝐵− 𝑉𝐴 𝑅 ≈ 2000 Ω Ι 𝐼 = 𝑉𝐵− 𝑉𝐴 𝑅 𝑍 = 𝑉𝐴 𝐼

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measurement error introduced by the input impedance of the PicoScope is negligible since

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28 Ω

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|𝑍| = 𝑋𝐶= 1 𝜔𝐶 =

1 2𝜋𝑓𝐶

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44 |𝑍𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛_𝜔| = |

1 𝑗𝜔𝐶|

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𝑒 = ∑ |𝑍𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡_𝜔− |𝑍𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛_𝜔|| 2𝜋𝑓𝑁

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6

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52 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = 20 × 𝑙𝑜𝑔10( 2 × |𝑋(𝑓)| 𝑁 ) 𝑑𝐵 𝑋𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑋𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑌𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑌𝑜𝑟𝑖𝑔𝑛𝑎𝑙 𝑌𝑜𝑟𝑖𝑔𝑛𝑎𝑙= 𝑌𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 × 𝑋𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑋𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑

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68 20 + 30₂ 𝑥 = 30 2 30 − 2𝑥 𝑥 ≈ 12.3529 𝑐𝑚, 30 − 2𝑥 ≈ 5.2941 𝑐𝑚 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑤ℎ𝑜𝑙𝑒 𝑝𝑎𝑡ℎ = 2 × √152_{+ (30 − 2𝑥)}2_{+ 4 × √35}2_{+ 𝑥}2_{≈ 180.2776 𝑐𝑚} 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 =180.2776 × 10 −2 344 × 10 3_{≈ 5.2406 𝑚𝑠}

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ϴ

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8

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0.09 𝑑𝐵 = 10 log(𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑃𝑟𝑒𝑎𝑙𝑖𝑡𝑦 ) 𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑃𝑟𝑒𝑎𝑙𝑖𝑡𝑦 = 2(0.09 𝑑𝐵10 )_{≈ 1.006} 𝑈2_{∝ 𝑃} 𝑈𝑟𝑒𝑎𝑙𝑖𝑡𝑦≈ 𝑈𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 1.003

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Conclusions and Future

Work

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REFERENCE

Bibliography

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