http://velodynelidar.com/docs/datasheet/63-9194_Rev-G_HDL-64...
Thats the one LIDAR Uber seems to have matching pictures.
5Hz - 20Hz full round sampling rate, lets assume 15 Hz.
The resolution in the horizontal plane is dependent on rotational speed, so at 15 Hz it should be 0,26 degrees.
(0,35/20*15 = 0.26)
For the woman height the angular resolution is 0.4 degrees no matter the rotation speed.
Id est, she would have been atleast one pixel wide from 400 feet and about 2 pixels high and growing in size if we assume 2' wide.
(Not counting bike).
I really see no exuse for Uber messing this up that bad. The LIDAR can't have missed a potential "obstacle" when it got closer, even if the car wouldn't classify it as a human.
Frame Distance Angular Size of Target Pixel Size
0.00 400.00 0.29 1.10
1.00 396.09 0.29 1.11
2.00 388.27 0.30 1.14
3.00 376.53 0.30 1.17
4.00 360.89 0.32 1.22
5.00 341.33 0.34 1.29
6.00 317.87 0.36 1.39
7.00 290.49 0.39 1.52
8.00 259.20 0.44 1.70
9.00 224.00 0.51 1.97
10.00 184.89 0.62 2.38
11.00 141.87 0.81 3.11
12.00 94.93 1.21 4.64
13.00 44.09 2.60 10.00
These are NOT big targets, they could easily have been mistaken for noise and filtered out. All of the LIDAR data I've ever seen has been fairly noisy and did require filtering to get usable information from it. And given the number of frames they get maybe their filtering was just too aggressive.
But, as it got closer and what the computer though was noise was on about the same place a sane obstacle finder should have given a posetive match. Maybe at 30 - 40 m worst case?
At 142 feet the woman probably had (assuming she was 5.5'):
asind(5.5/142) = 2.21* => 2.21/0.4 = 5.5
So between 5 and 6 "scanlines" going from left to right over her.
Assuming she was 2' wide that's 0.8 degrees which would be 2 to 3 pixels in breadth according to your spread sheet.
That's between 10 and 18 pixels (voxels?) that stand out clearly from the flat road around it, exluding the bike.
If you wan't to get an idea of how LIDAR data looks Velodyne has free samples and a viewer for less resolution models.
http://velodynelidar.com/downloads.html
It pretty hard to identify obstacles far off, but you will still see there is something there. It's especially easy to identify obstacles that are vertical.
As she got closer, she would eventually show up clearly on the LIDAR data. But since the car never slowed down or went left, it didn't notice her at all even at point blanc (or did see her but failed to do anything about it).
Yeah, I'm willing to accept SOMETHING bad happened here, as I said I really just wanna dissuade people from the notion that LIDARs will see all obstacles all of the time. Not going to say the car acted perfectly and it was sensor failure, but definitely willing to say that the LIDAR probably COULD see her but not as well as people would assume.
Really, I think this was a case of the car over driving their effective sensor range, same as what happens when you're on a dark road and a deer runs into the middle of the road, you simply can't react fast enough by the time you realize the danger is there. Computers are fast but they aren't perfect.
What I'd be particularly interested in was if the computer saw her and if it did the calculation - I can't stop safely in this distance, and decided to just hit the obstacle because it was "safer". At that point we start getting into ethics and this problem gets a lot murkier.
Updating this with math not done at midnight:
This is based on the velodyne LIDAR specs I could find last night with some quick googling: - 400' range - .04 degree angular resolution - 15hz max update rateIf you have more accurate real world experience with these sensors and can share more accurate performance characteristics I can update.
These calculations were done assuming a vehicle moving at 40 mph. The stopping distance at that speed is about 110ft. I computed the pixel size by assuming 1 measurement = 1 pixel giving me 9000 pixels per 360 degrees.