Design, Analyze, and Implement Radar Sensors' … Sensors' Alignment Algorithm with MATLAB Delphi E&S Liang Ma 05/13/2014 Delphi ConfidentialDelphi E&S Three main properties …

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Design, Analyze, and Implement

Radar Sensors' Alignment Algorithm

with MATLAB

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Liang Ma

05/13/2014

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Three main properties of radar targets: Range Range rate Azimuth

Delphi Electronically Scanning Radar

Main features: Adaptive Cruise Control Collision Mitigation Rear and Side Detection System

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Alignment Algorithm

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Alignment

Static Alignment Dynamic Alignment

Horizontal

AlignmentVertical

Alignment

Auto

Alignment

Service

Alignment

Factory

Alignment

Radar sensor misalignment angle is the angle difference between real radar boresight and designed

radar boresight. Lateral offset = range * sin(azimuth)

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Least Square solver for Dynamic Alignment

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18 m/s

azimuth

range𝐴 𝑎𝑧𝑖𝑚𝑢𝑡ℎ ∗ 𝑥 = 𝐵(𝑟′)

Det 1 Det 3Det 2 Det 4

𝑥 = 𝐴\B

Combine all the equations/detections:

Host Vehicle

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Simulation results ( No noise added, injected misalignment angle : 0.3 degree)

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5 10 15 20 25 30 35 400.3

0.3

0.3

0.3

0.3

0.3

0.3

Speading angle of azimuth in degree

Mis

alig

nm

ent

anlg

e :

degre

eRaw Misalignment Angle Updates. Median: 0.3 degree

Input host speed, radar targets’

real time azimuth, range and range

rate, then simulate the LS solver

alignment algorithm with MATLAB.

The simulation results shows that

there is no error on the calculated

misalignment angle. This algorithm

is effective.

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Cont. (Add azimuth noise : 0.3°*randn + 0.1° )

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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Updates Number

Mis

alig

nm

ent

anlg

e :

degre

e

Raw Misalignment Angle Updates. Median: 0.39781 degree

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5 10 15 20 25 30 35 40-15

-10

-5

0

5

10

15

Speading angle of azimuth in degree

Mis

alig

nm

ent

anlg

e :

degre

e

Raw Misalignment Angle Updates. Median: 0.28177 degree

Cont. (Add range-rate noise : 0.1*randn )

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The greater the angle spreading, the less the noise, why ?

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A Matrix Condition Number ( cond(A) )

5 10 15 20 25 30 35 400

5

10

15

20

25

A matrix Condition Number V.S. Azimuth Spreading angle

Azimuth Angle Spreading in Degree

A m

atr

ix C

onditio

n N

um

ber

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Condition number is a

relative error magnification

factor.

Ref. : Cleve Moler, ‘Numerical Computing’ e-book

Cond(A) keeps decreasing with the increasing angle spreading of detections’ azimuth.

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Real Vehicle Logs Processing Results (600+ logs, 80+ GB, 3 days’ testing)

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 105

0

0.5

1

1.5

Updates number

Mis

alig

nm

ent

angle

in d

egre

es

Smoothed Misalignment Angle

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Cont.

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 105

-10

-5

0

5

10

Raw misalignment angles

Updates number

Mis

alig

nm

ent

angle

in d

egre

e

-15 -10 -5 0 5 10 15 200

5000

10000

15000

Histogram of raw angle updates

Misalignment angle in degrees

Incid

ent

num

ber

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Implement with Matlab Coder

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Verify Generated Code

% [YC_output, YC_Cals, YC_Params] = yawRateComp(YC_input, YC_output, YC_Cals, YC_Params);

% MATLAB Specs found here

[YC_output, YC_Cals, YC_Params] = yawRateComp_mex(YC_input, YC_output, YC_Cals,

YC_Params); % Verify generated code here and accelerate

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Coder Code Performance

Reliable. Coder code has been used in production code for half a year and no bug is found;

Efficient. This improved alignment algorithm with coder code can run as fast as previous old algorithm with hand code.

Easy to integrate.

Conclusions:

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Summary

Radar Sensors’ Alignment Algorithm design, simulation, data analysis, and implementation are done together within Matlab only;

One algorithm engineer can completely responsible with one algorithm block. Save time to coordinate with software engineer.

In the future, Matlab plus Coder will be popular in algorithm development area.

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