Radar Beats GPS In Court — Or Does It?

TechnologyResource writes "More than two years ago in California, a police officer wrote Shaun Malone a ticket for going 62mph in a 45-mph zone. Malone was ordered to pay a $190 fine, but his parents appealed the decision, saying data from a GPS tracking system they installed in his car to monitor his driving proved he was not speeding. What ensued was the longest court battle over a speeding ticket in Sonoma county history. The case also represented the first time anyone locally had tried to beat a ticket using GPS. The teen's GPS pegged the car at 45 mph in virtually the same location. At issue was the distance from the stoplight — site of the first GPS 'ping' that showed Malone stopped — to the second ping 30 seconds later, when he was going 45 mph. Last week, Commissioner Carla Bonilla ruled the GPS data confirmed the prosecution's contention that Malone had to have exceeded the speed limit and would have to pay the $190 fine. 'This case ensures that other law enforcement agencies throughout the state aren't going to have to fight a case like this where GPS is used to cast doubt on radar,' said Sgt. Ken Savano, who oversees the traffic division. However, Commissioner Bonilla noted the accuracy of the GPS system was not challenged by either side in the dispute, but rather they had different interpretations of the data. Bonilla ruled the GPS data confirmed the prosecution's contention that Malone had to have exceeded the speed limit."

30 seconds is a low sample rate

[SlashSim]

I expect sampling as close to continually as possible would make for a tighter defense, 30 seconds is pretty coarse to predict a spot speed.

Re:Standard Calculus

[olden]

Seconded. Furthermore, even if the GPS averaged on a much smaller interval, quoting http://www.pressdemocrat.com/article/20081206/NEWS/812060371/1334/NEWS [pressdemocrat.com]:
"The distance between the radar reading and when he was recorded going 45 mph is great enough that Malone could have easily slowed down, Heppe testified."
Game over son, you lost.

Re:Standard Calculus

[pyr02k1]

The problem of this calculus you mention wasnt the speed at the end, nor even the beginning. we're missing a piece of information to properly go through this. distance. it says at a stop light, he was 0, then the next ping was 45. but the problem becomes distance covered in that 30 seconds. tie in the math, etc. if it says 45 on the ping, thats worthless. we need to know how far he traveled in 35 seconds to get an average speed, and, for the sake of argument, his vehicles 0-60 speed as well to get the stats on how quickly he could have possibly gone up to 60, nearly where they "clocked" him. obviously, his average speeds worthless, and his speed 30 seconds after his initial of 0 is worthless. we need the distance traveled in that 30 seconds. And TFA says "virtually" the same location. For all we know, he spotted the cop, hit his brakes and was doing 45 when he was pinged. Distance is key ... notice how TFA forgets that wonderful detail. And, I'm sure as a teenager, with a GPS, he knew that if he hit 70, theyd get an email alert. Heck, he probably knew that if he wanted to, he could go 69, wait for a ping, if he had timed them right, speed up to 100 and brake to 69 again, all before the second ping... I guess the parents forgot that Teenager + Technology is generally > Parents + technology

Re:Sounds like california

[MichaelSmith]

The margin of error is for your speedometer, not for you to knowingly drive over the limit.

(tolerance is 3% here in Victoria, Australia);

Re:Standard Calculus

[Anonymous Coward]

"It recorded Malone sitting at a stoplight at Frates Road and 30 seconds later going 45 mph 2,040 feet farther down the road, according to Heppe."

d=rt so we have 2040 = x * 30 so 2040/30 = x x=68!

Yep - GPS proves he was speeding.

Re:Standard Calculus

[tokul]

My gps can tell me my speed at the exact moment

No, it does not. GPS only tells you your average speed between two GPS pings. Ping 1 - you are at X, ping 2 - you are at Y, your current speed is how fast you must move in order to get from X to Y in time between ping1 and ping2.

Re:Amazing

[Anonymous Coward]

no it doesn't. IF it's an average over 30 seconds (which seems a stupid way to record data, and VERY unlikely to exactly match the speed limit the way it has), ALL it means he travelled .375 miles in those 30 seconds. He could do this by averaging 90 over 15 seconds and remaining stopped for 15 seconds, or accelerating to above 45 mph (since he was stopped [for at least 30 seconds if these are averages] at the beginning of this run).

Basically, we don't have all the data necessary. I have to assume the people arguing the case did, as there's no way to know. Like another poster said: we don't know how far he got from that stoplight in 30 seconds and what portion of the 30 seconds he was just stopped at the stoplight still.

Re:Standard Calculus

[pyr02k1]

i only caught the part on the pressdemocrat link. missed a whole other link :D take one thing into account now, the rough 0-60 speed of a car, that can do 0-60 in 6.8 seconds. it would travel around 300 ft if the speed was exactly the same the whole distance to 60. thats the other part we need in this equation and we're golden. if it took him 300 ft to get to 60 at 6.8 seconds. he has 23.2 seconds to continue 1700 ft. so he'd of been doing, 73 :D now figure in his car was really slower then that, but 65 would be about right in the end result. no matter the year of celica, i doubt it was doing 0-60 in 6.8, unless mommy and daddy paid a load of cash to make it go faster... he sped. i think if gps proved he wasnt speeding, it'd of been nice. but they spent all this time fighting a case, where he was speeding anyways. oy vey

Re:Standard Calculus

[Dachannien]

Actually, you did your math wrong. 2040 feet / 30 seconds = 46.4 miles per hour.

The thing is, that's the average speed over the 2040 feet. As was mentioned above, given the initial condition of v(0) = 0, this means that at some point in the intervening distance, the kid must have been going significantly more than 45 mph.

The final condition of v(30 seconds) = 45 mph would increase the peak speed even more.

Re:Standard Calculus

[kdemetter]

yes , well , then these pings are very close together , because it near exactly matches the speed my car is going .
Offcourse , it may be off by some , but the same is true for the radar.

If i went 62mph , at a given time , i would be able to see that on my gps . It won't show as 45mph.

The path travelled

[Anonymous Coward]

Since the article didn't give enough information (and manages to misspell one of the street names), I googled around and figured out the path taken (from http://www.pressdemocrat.com/article/20071002/NEWS/710020308?Title=Case-pits-police-radar-against-GPS-in-teen-s-car# [pressdemocrat.com]): http://maps.google.com/maps/ms?hl=en&gl=us&ie=UTF8&oe=UTF8&msa=0&msid=105238595049957684644.000477c5e46e20fe9dff3&ll=38.2325,-122.591393&spn=0.010956,0.010257&z=16 [google.com]

The first point is when he was stopped at the intersection, the middle is (probably) where the cop got him on radar, and the end is where the GPS clocked him at 45 MPH.

I estimate that's about 2.2k feet from a dead stop in 30 seconds, which puts his average speed at 50. It's pretty much a given he was speeding when the cop radar'd him and he put on the braked.

Re:Standard Calculus

[raynet]

Actually that depends on the GPS. Mine updates the speed and heading information every second but stores the information only every 15 seconds. So each saved record contains the average speed for the past second, not the average speed of the 15 second interval.

Re:Standard Calculus

[teg]

2040 over 30 is 68! I'm sure I'm missing something here.

Yes, he is converting from feet over seconds to mph at the same time.

Re:Standard Calculus

[Anonymous Coward]

2040 ft / 30 seconds != 68 miles/hr. it equals 68 feet/second, which is 46.36 mph. Still speeding though since he was stopped at the beginning, so he couldn't have been maintaining that 46mph the entire time and would have to have gone faster than that. 46 mph is still speeding anyway ;)

It uses Doppler shift

[Alef]

A GPS typically calculates velocity from Doppler shift of the D-band signal. This give higher accuracy since the position reading is somewhat unreliable. It also means you can (in principle) get the velocity information virtually instantaneously without having to sample two locations. However, in reality a lot of averaging and filtering is going on, and I think many receivers weighs in both position deltas and Doppler shift in the equations, so the reading is going to have at least some lag.

(Reference [aprs.net])

Re:Standard Calculus

[msauve]

Wondering where you got average speed from ?

Average speed is easily calculated, based on the statement from this article [pressdemocrat.com]:

"It recorded Malone sitting at a stoplight at Frates Road and 30 seconds later going 45 mph 2,040 feet farther down the road,"

That would be 2040 ft / 30 sec === 0.386 mi / 0.0833 hr = 46.4 MPH

I personally think this article does not have enough info to make any meaningful decisions from.

No, but it does provide "related links" to other articles which do provide sufficient detail. He started at 0 MPH, ended at 45 MPH, and averaged 46.4 MPH. That can't be done without exceeding the speed limit of 45 MPH.

Re:Standard Calculus

[natehoy]

Most of these tracking units are calculating speed in "near real time" based on GPS readings every second or so, and are pretty accurate. The ones that TRACK your speed, like the one the kid had, send the current speed and position in a "ping" every 30 seconds.

So, in all likelihood, the data was accurate for the time it was sent - it wasn't an average over 30 seconds, it was a snapshot of an accurate speed every 30 seconds.

However, this proves nothing, since he was at zero at the light, 45 a half minute later, then got flagged for speeding at neither of those times. He could have been mashing the pedal from the stoplight and been on his way to 62 when the snapshot read 45.

More telling would have been the logs from his driving in general.

Re:Sounds like california

[bickerdyke]

The error margins of speedometers (at least here) have to be calibratet to err on the safe side. It may show 10%+4km/h faster than your actual speed, but never ever slower.

http://en.wikipedia.org/wiki/Speedometer#International_agreements [wikipedia.org]

Re:Standard Calculus

[jmauro]

You're screwing up the part of the Uncertainty principle that most people do. It's not position v. velocity accuracy, but position v momentum. For most large things like planets, cars, insects, and protozoa the mass part of the momentum calculation can drive the accuracy error of measuring both down to about zero. The Uncertainty principle only really matters for really small things like molecules, atoms, and quarks where the mass doesn't overwhelm the equation.

Think about it this way in normal everyday life we're not losing a car because it has a speedometer or the Earth because some one is keeping track of a year. For things like traffic tickets the accuracy of both speed and position are extremely accurate.

Re:Standard Calculus

[Anonymous Coward]

I'm certain I drive a European car, you insensitive clod!

Re:Standard Calculus

[jbengt]

Good point, I hadn't thought of that
One of the earlier articles olden linked above says "the GPS recorded Malone sitting at a stoplight at Frates Road and 30 seconds later going 45 mph 2,040 feet farther down the road, according to Heppe". This makes his (time) average speed about 46.4 mph.
If we assume that the light did change to green immediately, then if he uniformly accelerated from 0 to 60 for 9-1/2 seconds (averaging 31 mph) and then decelerated at a constant rate from 62 to 45 (averaging 53.5 mph) for the next 20-1/2 seconds, he would have averaged about 46.4 mph. My guess would be that he accelerated a little slower than that, stayed at high speed until he saw the cop, then braked quickly. Either way, it would have been very possible for him to have hit 62 or above. Not to mention that properly maintained radar is probably much higher accuracy than GPS.
Radar readings are not infallible, though. The question I still have, though, is where did the officer stop him? If it was near or after the 45 mph ping, then there would be some doubt in my mind.

Re:Sgt is an idiot

[ceoyoyo]

Algebra would have done just fine in this case.

Re:Sounds like california

[VGPowerlord]

If you mean not coming to a complete stop at a stop sign, is that a serious offense? There'll be a lot of wasted fuel if everyone stopped at every stop sign.

Well, see, if you weren't required to stop completely, that corner would have a Yield sign instead.

Re:Standard Calculus

[GoRK]

The real answer here is it depends a great deal on the GPS itself, then it depends on how whatever software is reporting and logging this information post processes it.

GPS itself is capable of reporting an instantaneous velocity vector calculated by measuring the doppler shift from each satellite. (Comes in as a GPVTG sentence in the NMEA data) So if the receiver is tracking a lot of satellites with a good distribution and there isnt a lot of multipath problems, the accuracy of this vector is ridiculously good. Also, a receiver may not support GPVTG.

Now you can also get velocity data from a GPRMC (ie normal position data) sentence too. According to the specification, the bearing here is supposed to be calculated based on position track angle (presumably so that you dont have to be moving to have a GPS bearing).. The spec seems silent to the origin of the speed reported in this sentence -- seems like it could be calculated as track speed (average speed over the interval) but could easily be reported as instantaneous speed as well.

Of course I haven't tested any, but I imagine in practice, GPS receivers would normally report track/position averaged data in GPRMC and instantaneous data in GPVTG. Any software that is supposed to present this data to a user would have to determine how to aggregate and filter it to provide for its intended purpose. If you really intend to beat a speeding ticket with GPS I would suggest that you need data points of either type (instantaneous or averaged) with at least 1Hz if not 5Hz granularity along with knowledge of what the data represents and how the raw data is filtered and processed. This 30s interval business in this case is just dumb, and nobody ever bothered to determine anything about the nature of the data it seems.

They knew they were guilty the whole time

[whoda]

The kids dad was the one who fought this the whole time.
The dad got the GPS because of prior infractions by his son.
The kid got 2 other motor-vehicle infractions while this case was proceeding.
Halfway through the case, the dad changed their defense from "The radar gun was wrong", to "It was an illegal speed trap."

They knew they were going to lose the whole time, they just hoped the county wouldn't put out the money.
Example:
They waited until the county had paid the expenses for an expert to come fly cross country and testify. Right before he was to testify, the kids lawyer got a continuation so the expert had to go home and get paid again to come out later.

Re:Sgt is an idiot

[jbengt]

Correct me if I'm wrong . . .

You are wrong [gpsinformation.net]

Re:It uses Doppler shift

[systemeng]

I worked on a low cost military training system that used some older civilian GPS hardware. Our GPS's provided instantaneous velocity at 1Hz and instantaneous position at 1Hz. The velocity tended to be much better than the position in noisy GPS conditions. You can also use the velocity to kalman filter the position leading to increased position accuracy. It's hard to tell what a GPS is displaying but internally, the velocity measurement is very accurate but at too low a time resolution for some situations involving moving vehicles. If the GPS in the article was logging at 30 second intervals, it would be very difficult to know anything about the instantaneous speed of the vehicle in question. That my $.02

Re:Standard Calculus

[Rallion]

You state that you ASSUME he accelerated in only 6 seconds, and decelerated in only 1. These are feasible, and maybe even likely.

You also assume that he started accelerating at the same instant as the first reading and decelerated only in the last second. While still possible, this is extremely unlikely.

It's interesting to me that despite these assumptions, you still say "at most 52 MPH." It would actually be much more accurate to say "at least 52 MPH, but probably more."