design, analyze, and implement radar sensors' alignment ...€¦ · delphi confidential cont....
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Delphi Confidential
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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