I know that the precision of the GPS depends a lot on the quality of it but if you know aproximatively the precision of a GPS tracking depending on the number of satellites I would be very thankful.
The number of satellites has a counterituitivly low impact on GPS precision.
On a theoretical basis, 3 Satellites will provide a perfect fix, in reality it will create a pyramid-shaped area of confidence space, that when projected onto a Map will be an error triangle.
More satellites will add more facettes to the confidence space, but after projection onto a 2D map this will give only a modes reduction of error area.
The biggest benefit of more satellites is the possibility to discard outliers - this is especially true in built-up areas where a reflected signal can create a wildly wrong area with a high confidence. If you have, say, 5 satellites with 4 agreeing well and one outlier, you have a good argument to discard it.
This works out to a situation with 4 satellites and good signal providing a much better fix than 7 satellites with bad signal.
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I have 2 movable points. When the distance between them exceeds 10 ft, I want to get an alert. Is this possible? What is the minimum distance that is measurable?
Maybe this will help you further.
How accurate is GPS?
It depends. GPS satellites broadcast their signals in space with a certain accuracy, but what you receive depends on additional factors, including satellite geometry, signal blockage, atmospheric conditions, and receiver design features/quality.
For example, GPS-enabled smartphones are typically accurate to within a 4.9 m (16 ft.) radius under open sky (VIEW SOURCE AT ION.ORG). However, their accuracy worsens near buildings, bridges, and trees.
Most GPS systems report "accuracy" in units of meters, with the figure varying over orders of magnitude. What does this figure mean? How can it be translated to an error function for estimation, i.e. the probability of an actual position given the GPS reading and its reported accuracy?
According to the Wikipedia article on GPS accuracy, a reading down to 3 meters can be achieved by precisely timing the radio signals arriving at the receiver. This seems to correspond with the tightest error margin reported by e.g. an iPhone. But that wouldn't account for external signal distortion.
It sounds like an error function should have two domains, with a gentle linear slope out to the reported accuracy and then a polynomial or exponential increase further out.
Is there a better approach than to tinker with it? Do different GPS chipset vendors conform to any kind of standard meaning, or do they all provide only some kind of number for the sake of feature parity?
The number reported is usually called HEPE, Horizontal Estimated Position Error. In theory, 67% of the time the measurement should be within HEPE of the true position, and 33% of the time the measurement should be in horizontal error by more than the HEPE.
In practice, no one checks HEPE's very carefully, and in my experience, HEPE's reported for 3 or 4 satellite fixes are much larger than they need to be. That is, in my experience 3 satellite fixes are accurate to within a HEPE distance much more than 67% of the time.
The "assumed" error distribution is circular gaussian. So in principle you could find the right ratios for a circular gaussian and derive the 95% probability radius and so on. But to have these numbers be meaningful, you would need to do extensive statistical testing to verify that indeed you are getting around 95%.
The above are my impressions from working in the less accuracy sensitive parts of GPS over the years. Concievably, people who work on using GPS for aircraft landing may have a better sense of how to predict errors and error rates, but the techniques and methods they use are likely not available in consumer GPS devices.
We're building a GIS interface to display GPS track data, e.g. imagine the raw data set from a guy wandering around a neighborhood on a bike for an hour. A set of data like this with perhaps a new point recorded every 5 seconds, will be large and displaying it in a browser or a handheld device will be challenging. Also, displaying every single point is usually not necessary since a user can't visually resolve that much data anyway.
So for performance reasons we are looking for algorithms that are good at 'reducing' data like this so that the number of points being displayed is reduced significantly but in such a way that it doesn't risk data mis-interpretation. For example, if our fictional bike rider stops for a drink, we certainly don't want to draw 100 lat/lon points in a cluster around the 7-Eleven.
We are aware of clustering, which is good for when looking at a bunch of disconnected points, however what we need is something that applies to tracks as described above. Thanks.
A more scientific and perhaps more math heavy solution is to use the Ramer-Douglas-Peucker algorithm to generalize your path. I used it when I studied for my Master of Surveying so it's a proven thing. :-)
Giving your path and the minimum angle you can tolerate in your path, it simplifies the path by reducing the number of points.
Typically the best way of doing that is:
Determine the minimum number of screen pixels you want between GPS points displayed.
Determine the distance represented by each pixel in the current zoom level.
Multiply answer 1 by answer 2 to get the minimum distance between coordinates you want to display.
starting from the first coordinate in the journey path, read each next coordinate until you've reached the required minimum distance from the current point. Repeat.
I'm writing an application for iphone4 and I'm taking values from the accelerometer to compute the current movement from a known initial position.
I've noticed a very strange behavior: often times when I walk holding the cellphone for a few meters and then I stop, I register a negative peak of overall velocity when the handset decelarates. How is that possible if I keep moving in the same direction?
To compute the variation in velocity I just do this:
delta_v = (acc_previous + acc_now)/2 * (1/(updating_frequency))
Say you are moving at a constant 10 m/s. Your acceleration is zero. Let's say, for the sake of simplicity, you sample every 1 second.
If you decelerate smoothly over a period of 0.1 seconds, you might get a reading of 100 m/s/s or you might not get a reading at all since the deceleration might fall between two windows. Your formula most likely will not detect any deceleration or if it does, you'll get two values of -50 m/s/s: (0 - 100) / 2 and then (-100 + 0) / 2. Either way you'll get the wrong final velocity.
Something similar could happen at almost any scale, All you need is a short period of high acceleration or deceleration that you happen to sample and your figures are screwed.
Numerical integration is hard. Naive numerical integration of a noisy signal will essentially always produce significant errors and drift (like what you're seeing). People have come up with all sorts of clever ways to deal with this problem, most of which require having some source of reference information other than the accelerometer (think of a Wii controller, which has not only an accelerometer, but also the thingy on top of the TV).
Note that any MEMS accelerometer is necessarily limited to reporting only a certain band of accelerations; if acceleration goes outside of that band, then you will absolutely get significant drift unless you have some way to compensate for it. On top of that, there is the fact that the acceleration is reported as a discrete quantity, so there is necessarily some approximation error as well as noise even if you do not go outside of the window. When you add all of those factors together, some amount of drift is inevitable.
Well if you move any object in one direction, there's a force involved which accelerates the object.
To make the object come to a halt again, the same force is needed in the exact opposite direction - or to be more precise, the vector of the acceleration event that happened before needs to be multiplied with -1. That's your negative peak.
Not strictly a programming answer, but then again, your question is not strictly a programming question :)
If it's going a thousand miles per hour, its acceleration is 0. If it's speeding, the acceleration is positive. If it's slowing down, the acceleration is negative.
You can use the absolute number of the velocity to invert any negative acceleration, if that's needed:
fabs(delta_v); // use abs for ints
I'm using GPS units and mobile computers to track individual pedestrians' travels. I'd like to in real time "clean" the incoming GPS signal to improve its accuracy. Also, after the fact, not necessarily in real time, I would like to "lock" individuals' GPS fixes to positions along a road network. Have any techniques, resources, algorithms, or existing software to suggest on either front?
A few things I am already considering in terms of signal cleaning:
- drop fixes for which num. of satellites = 0
- drop fixes for which speed is unnaturally high (say, 600 mph)
And in terms of "locking" to the street network (which I hear is called "map matching"):
- lock to the nearest network edge based on root mean squared error
- when fixes are far away from road network, highlight those points and allow user to use a GUI (OpenLayers in a Web browser, say) to drag, snap, and drop on to the road network
Thanks for your ideas!
I assume you want to "clean" your data to remove erroneous spikes caused by dodgy readings. This is a basic dsp process. There are several approaches you could take to this, it depends how clever you want it to be.
At a basic level yes, you can just look for really large figures, but what is a really large figure? Yeah 600mph is fast, but not if you're in concorde. Whilst you are looking for a value which is "out of the ordinary", you are effectively hard-coding "ordinary". A better approach is to examine past data to determine what "ordinary" is, and then look for deviations. You might want to consider calculating the variance of the data over a small local window and then see if the z-score of your current data is greater than some threshold, and if so, exclude it.
One note: you should use 3 as the minimum satellites, not 0. A GPS needs at least three sources to calculate a horizontal location. Every GPS I have used includes a status flag in the data stream; less than 3 satellites is reported as "bad" data in some way.
You should also consider "stationary" data. How will you handle the pedestrian standing still for some period of time? Perhaps waiting at a crosswalk or interacting with a street vendor?
Depending on what you plan to do with the data, you may need to supress those extra data points or average them into a single point or location.
You mention this is for pedestrian tracking, but you also mention a road network. Pedestrians can travel a lot of places where a car cannot, and, indeed, which probably are not going to be on any map you find of a "road network". Most road maps don't have things like walking paths in parks, hiking trails, and so forth. Don't assume that "off the road network" means the GPS isn't getting an accurate fix.
In addition to Andrew's comments, you may also want to consider interference factors such as multipath, and how they are affected in your incoming GPS data stream, e.g. HDOPs in the GSA line of NMEA0183. In my own GPS controller software, I allow user specified rejection criteria against a range of QA related parameters.
I also tend to work on a moving window principle in this regard, where you can consider rejecting data that represents a spike based on surrounding data in the same window.
Read the posfix to see if the signal is valid (somewhere in the $GPGGA sentence if you parse raw NMEA strings). If it's 0, ignore the message.
Besides that you could look at the combination of HDOP and the number of satellites if you really need to be sure that the signal is very accurate, but in normal situations that shouldn't be necessary.
Of course it doesn't hurt to do some sanity checks on GPS signals:
latitude between -90..90;
longitude between -180..180 (or E..W, N..S, 0..90 and 0..180 if you're reading raw NMEA strings);
speed between 0 and 255 (for normal cars);
distance to previous measurement matches (based on lat/lon) matches roughly with the indicated speed;
timedifference with system time not larger than x (unless the system clock cannot be trusted or relies on GPS synchronisation :-) );
To do map matching, you basically iterate through your road segments, and check which segment is the most likely for your current position, direction, speed and possibly previous gps measurements and matches.
If you're not doing a realtime application, or if a delay in feedback is acceptable, you can even look into the 'future' to see which segment is the most likely.
Doing all that properly is an art by itself, and this space here is too short to go into it deeply.
It's often difficult to decide with 100% confidence on which road segment somebody resides. For example, if there are 2 parallel roads that are equally close to the current position it's a matter of creative heuristics.