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Archive for the ‘GPS’ tag

Bed Time Stories

January 8th, 2009 at 12:30 am

First of all, shouts to my “peeps” (meine Leuts!) who faithfully read this crap. Especially Bess, who gets her name mentioned right back. But you’re seriously gonna struggle through this one. I don’t know where I got it.

Sometimes when I jump into bed, instead of falling asleep, my mind just starts rattling off all the crazy random stuff it’s been turning over all day. Or week. Tonight is one of those nights, and I figured I’d let it out, since it’s more of a pondering point than a thought. It’s a little musing in the arena of statistics (hey, I loved Discrete Mathematics in college!). Here’s the story.


I took my little GPS receiver with me to Europe, and as a result, I got some pretty nifty logs. All over the places I went, I’ve got an overlay for a Google map that shows me exactly where I was and when. I suppose to some, that’s kind of creepy, but moving on.

Because GPS was developed by the military for, um, military purposes, it’s actually quite an incredible system. Wikipedia has a lengthy article on the technical workings of GPS, but the key thing is this: most civilian GPS receivers in the last few years are accurate to a few meters - about 16ft. If you’re really geek, the Wikipedia article also explains in depth why civilian GPS measurements are inherently inaccurate.

The GPS receiver then generally knows exactly where it is at any given moment in time - you just have to ask it. So along with the receiver, I brought a logger. The logger’s job was to record where the GPS says it was at any given moment, and this is where we get to the statistics. Since it would be very technically challenging to record absolutely every positional data point the receiver can produce, we have to sample it, much like a digital audio recording is actually a sampling of an analog signal.

The Experiment

I setup my logger to poll the receiver at regular intervals. Depending on where we were going and what we were doing, I varied that poll rate from one second to five minutes. Obviously the more frequent polling times produce more accurate logs, but they also result in significantly more data. The flight from Atlanta to Zürich, for example, at a one-second poll rate would have produced over 34,200 data points! But since we were traveling in a relatively predictable manner, I scaled it back to just a few hundred data points.

Okay, I’m getting to the point, I promise.

Generally, this means that a GPS receiver can report its current location with an error of up to 16 feet. And that 16 feet could be in any direction, as if the receiver were in the center of a 32-foot diameter Bubble Boy hamster ball. But the reverse of that statement is also true: a receiver may report its location with an error as little as zero feet - it could be dead on the money. I observed this effect in practice by looking at my GPS logs superimposed on a map. Sometimes the log point was exactly where I remember standing, and sometimes it was a ways off.

I used my GPS sometimes to measure how far I had traveled that day as well, sometimes walking as much as six or seven miles in one day. But the idea that the GPS is often inaccurate by a meter or more got me to thinking. With all that information in mind, consider this:

The Question

While on an excursion, would the GPS location samples, over time, average out to a spot-on measurement of distance traveled? Would the accuracy of the GPS samples increase with more frequent samplings or less frequent samplings? Would the samplings average more accurately over time, grow infinitely more exaggerated, or would the error level off in time, reaching a point of diminishing inaccuracy? Finally, what impact would my route have on the GPS’s measurements? Would a straight line path (such as an overseas flight) produce more or less accurate averages than a route that randomly meanders through the streets of an open market?

My comments after the break, but please, leave yours!

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-- Weather When Posted --

Location: Atlanta, De Kalb-Peachtree Airport

Temperature: 42.8°F, Humidity: 57%

Written by jarrod.carlson

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Day Ten: Homeward Bound

December 17th, 2008 at 4:20 pm


We say goodbye to Jan and Europe

We say goodbye to Jan and Europe

Wake up. Take shower. Get dressed. Eat food. Pack shit. Say goodbye. Load car. Drive some. Refuel car. Return car. Check in. Clear customs. Clear security. Visit duty-free. Find gate. Make brown. Board plane. Sit down. Enjoy flight.

…nine endless hours pass…

There are still another few hours before we get off the plane at JFK! Then another two hours will pass until boarding the connecting flight to Atlanta. Then however long that flight is. Brian had slept nearly the entire trans-atlantic leg. Lucky bastard…

Written by jarrod.carlson

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Day Nine: Longest Post Ever!

December 16th, 2008 at 11:59 pm

Tuesday had arrived. The last day for me in Frankfurt, and in fact, all of Europe. The thought made me a little sad as I woke up, freezing on the floor of Philipp’s apartment. What a night.

Of course I owe Philipp a great deal of gratitude, so I hope that if he’s reading this he takes no offense. But the floor was cold, and as Philipp left for work in the morning, I realized that I had spent more time in the night trying to stay warm than actually sleeping. And then I realized I was lying on - and not in - a sleeping bag Philipp had left out for me. Ha!

Well I still owe you many thanks, Philipp, for your hospitality.

Following an extra hour of sleep under the warmth of the other sleep sack, I got the day started at the early hour of 11:00. I felt guilty for having slept in the extra time, but I couldn’t think of anywhere else I’d rather be, so I just enjoyed it. I’m on vacation, after all.

I have to admit, though, that I was a bit stumped by the shower. Jessy’s shower had only one wall and no curtain, but at least the shower head was mounted high on the wall. Here, there were no walls, and the hand held sprayer only reached about shoulder height. So I guess I’ll be squatting for my shower? How do Germans usually do this?!?

My first order of business was to get things packed up and stowed away. In doing so, I discovered an extra set of.. “essentials” stashed in my back pack (in the event of lost luggage). Great! That would save me the trouble of washing clothes.

So on to my second task instead - the grocery. I needed some food stuffs to bring home to the states, and there was a REWE just across the street, and since Philipp had left me a key, I made for it. I picked up as much candy, chocolate, wine, and whatever else I thought I could carry home and pack into my luggage.

Next, I was hungry. I reasoned that this might be my last chance at a real, authentic Döner Kebab, and this was probably the best place to get it, so I headed for the international cuisines of the Hauptbahnhof. There I found “Max & Moritz” and had myself a Kebob. Sorry you missed that one, Brian, but I’m sure you’re enjoying your €70 company lunch in Göttingen, too.

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Written by jarrod.carlson

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Day Eight: I’ve Been Lost, and Found

December 15th, 2008 at 10:45 pm

When I last wrote, I had been in a Starbucks bu the Hauptbahnhof, thinking of what to do next. I had checked my bags at a locker in the station and gone on for the day in the city.

Since it was about lunch time, I decided to find food, and proximity to the Hauptbahnhof should provide a multitude of options. So I just began walking in some non-particular direction. I should have a GPS log to look at later.

The search quickly made me realize how different Frankfurt is than other towns I’ve seen on this trip and in past trips.

For one, it’s an understatement that this is a commuter town. The population nearly doubles by day, from what I hear. This also, unfortunately, means it has one of the most complex public transportation systems imaginable. They have Regional and Regional Express trains, S-Bahn and S-Bahn Express trains, U-Bahn subway trains, tram cars on the street, buses, and even public taxis! The network map looked like a bowl of spaghetti, dropped carelessly on the floor.

And that is exactly what I found for lunch - Spaghetti alla Matriciana - but not dropped on the floor. It seemed to be a reasonably authentic Italian restaurant (who’s name I cannot remember). I believe it was just north west of the train station. It was delicious, but even better was the beer. A private label, I gathered, called Pfugstäder.

After eating, I decided to tackle the transit system and go find the Christkindlmarkt - Frankfurt is supposed to have one of the biggest and best.

This long exposure of the market in Frankfurt pleases me

This long exposure of the market in Frankfurt pleases me

The market was (predictably) in the squares in and around Römer Platz - or just Dom. I walked through it a bit and was disappointed at how small it was, and filled only with food and drinks, which I did not want. I ventured down to the river and over the bridge to take some photos.

On my way back through the market, I realized my error. I should have gone left at Albuquerque. To the other side of the street was an incredibly expansive street market weaving in and down every side street for blocks! Wow! I had previously found only a small tributary of this enormous market. It was a kind of bendy, twisty, shopping mall, with tastes, smells, and sights everywhere. A man could spend hours visiting all the carts and examining all the wares for sale.

So that’s exactly what I did. But unfortunately, by this time, my phone was beginning to run low on power, so I couldn’t leave it on to track my whereabouts. Although I literally walked around the same three-block market for over three hours and almost never saw anything twice!

Beautiful sunset

Beautiful sunset

As the sun began to set, the beautifully restored medieval architecture glowed with a bright orange light, caused by the city’s pollution - not entirely unlike suburban Atlanta. I helped myself to a few “artsy” photos.

Not long after the sun had set, I made back for the train station. It was time to meet up with Philipp, who would be offering me his floor for a free stay tonight. I took the S-Bahn train to Niederrad Bahnhof, where Philipp picked me up in his black Ford Focus “Caravan”, as he called it. I guess that’s the fancy German term for hatchback.

After reaching his place and dropping my bags, it was dinner time. Philipp suggested the Paulaner Haus am Dom, and I couldn’t refuse. This place was essentially the Hofbrauhaus, but for Paulaner. So that is where we went. I ordered a round of tall Paulaner Hefeweizen for the two of us and for myself the Wienerschnitzel. God it was tasty! Maybe it was all the walking around… Philipp ordered something resembling the entire hind leg of a pig - Schweinsaxen I think.

After dinner, it was time to retire. I made up my spot on the floor and settled in for a cold night - the heat had been off in Philipp’s apartment all weekend! Read the rest of this entry »

Written by jarrod.carlson

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Day Seven: Top Amazing Gear Race

December 14th, 2008 at 10:02 pm

The Black Forst

Captain Ludvig at the helm gives the 320i a Top Gear review

By the powers invested in some higher authority, we woke up Sunday morning, not hung over. Though I may not have been hung over, I was not on stable ground. I had completely expected the morning to be painful, but it was not. The world was still spinning a bit when I looked far into the distance, but that was little price to pay for the evening we’d just brought to a close not six hours before. And soon we would be headed for Bad Kreuznach and I could sleep in the car.

In Karlsplatz we picked up what was supposed to be a Ford Mondeo or Volkswagon Jetta. Sixt, however, had given them all away and offered us instead a BMW 320i instead.

Thrilled, we made for the Autobahn. Once on the road, I setup my camera on the dash and we did a little Top Gear style review of the car. Brian seems pleased, but perhaps that was because he had the pleasure of driving. From the passenger seat, I quickly began to despise the car.

The seat was obnoxious. You could only raise the seat by getting out of it - hardly practical at 120 km/h. It was awkwardly angled as well, so I couldn’t get my bum comfortably positioned. And there was nowhere to put my arms.

Besides that, the ride was incredibly stiff. Every little bump in the road made my guts jolt about like James May in his high speed boat ride. My bottom was sore by the time we’d reached out destination. Thankfully, I’d been too tired to care and simply slept most of the journey.

Road Trip from München to Bad Kreuznach in a rented BMW 320i

Road Trip from München to Bad Kreuznach in a rented BMW 320i

There were, however, a few parts for which I was awake. Wide awake.

Being the Autobahn, there is no speed limit in certain sections. So when the opportunity presented itself, Brian gave it the beans, so to speak. I took some proper video of us dashing along at ~220 km/h (~128 mph). Not surprisingly, those bouts of high speed were pretty exciting.

Secondly, our route (shown on my slick GPS map!) took us through the Black Forest, which was presently not black at all. In fact quite the opposite - all white and gray. Everything was glazed in snow, and the deeper we went, the denser the fog became. Soon, we were unable to see off the road at all, and in front of us, we could only see about 100m. Or less. The fog was in some patches so thick, it had became dark, like a thunderstorm cloud. Fog so thick the sun cannot shine through it. But it eventually gave way and we left the forest. And I returned to my dazing and drifting to and from sleep.

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Written by jarrod.carlson

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