I wrote a delphi program generating a gpx file as input for a "poor man's guidance system" for aerial spray by means of ultralight plane.
By and large, it produces route (parallel swaths) using gpx file as output.
The route's engine is based on the "Vincenty" algorithm which works fine for any wgs84 computation but
I can't get the accuracy of grid generated by ExpertGPS of Topografix (requirement).
I assume a 2D computation on the ellipsoïd :
1) From the start rtept (route point), compute the next rtept given a bearing and an arbitrary distance (swath length).
2) Compute the next rtept respective respective to previous bearing (90° turn) and another arbitrary distance (swath distance).
3) Redo 1) with the last rtept as starting point but in the opposite direction, and so on.
What's wrong with it ?
You do not describe your Pascal implementation of Vincenty's earth ellipsoid model so the following is speculation:
The model makes use of numerous geometrical trig functions-- ATAN2,
COS, SIN etc. Depending whether you use internal Delphi functions
or your own versions, there is the possibility of lack of precision
in calculations. The precision in the value of pi used in your
calculations could affect the precision you require.
Floating point arithmetic can cause decimal place errors. It will
make a difference whether you use single, double or real. I
believe some of the internal Delphi functions have changed with
different versions so possibly the version of Delphi you are
using will affect how the internal function is implemented.
If implemented accurately, Vincenty’s formula is supposed to be
accurate to within 0.5mm. Amazing accuracy. If there are rounding
errors or lack of precision in your Delphi implemention, the positional
errors can be significantly larger.
Consider the accuracy of your GPS information. Depending on how
many satellites are being used by the GPS receiver at any one time,
the accuracy of the positional information changes. Errors on
the order of 50 feet or more is possible. Additionally, the refresh
of positional information on the GPS receiver is not necessarily
instantaneous; therefore if the swath 'turns' occur rapidly, you
will have to ensure the GPS has updated at the turning point.
Your procedure to calculate the pattern seems reasonable so look
at your implementation of Vincenty's algorithm in your Delphi code.
This list is not exhaustive, I imagine others can improve it
dramatically. What I mention is based on my experience with GPS and
various versions of Delphi and what I could recall off the top of my head.
Something you might try is compare your calculations of
distance/bearing using your implementation of the algorithm with
examples provided on the Internet. There are several online
calculators. If you have not been there, the Aviation Formulary
is an excellent place to find examples of other navigational tricks.
http://williams.best.vwh.net/avform.htm . A comparison will
allow you to gain confidence in the precision of the Delphi
implementation of Vincenty's algorithm with data calculated by
mathematicians. Simply, your implementation of Vincenty may not be
precise. Then again, the error may be elsewhere.
I am doing farm GPS guidance similar for ground rig just with Android. Great for second tractor to help follow previous A B tracks especially when they disappear for a bit .
GPS accuracy repeat ability from one day to next will give larger distance. Expensive system's use dGPS2cm-10cm.5-30metres different without dGPS. Simple solution is recalibrate at known location. Cheaper light bars use this method.
Drift As above except relates to movement during job. Mostly unnoticeable <20cm 3hrs. Can jump 1-2metres rarely. I think when satellite connect or disconnect. Again recalibrate regularly at known coordinates ,i.e. spray fill point
GPS accuracy. Most phone update speed 1hz. 3? seconds between fixes at say 50km/hr , 41.66m between fixes. On ground rig 18km hrs but will be tracks after first run. Try a Bluetooth GPS 10hz check update speed and as mentioned fast turns a problem.
Accuracy of inputs and whether your guidance uses dGPS will make huge difference.
Once you are off your line say 5 metres at 100metres till next point, then at 50 metres your still 2.5 metres off unless your guidance takes you back to the route not the next coordinates.
I am not using Vincenty as I can 'bump'back onto line manually and over 1km across difference <30cm according to only reference I saw however I am taking 2 points and create parrallel points across.
Hope these ideas help your situation.
Related
I'm interested in developing a semi-autonomous RC lawnmower.
That is, the operator would decide when to stop, turn, etc., but could request "slightly overlap previous cut" and the mower would automatically do so. (Having operated high-end RC mowers at trade shows, this is the tedious part. Overcoming that, plus the high cost -- which I believe is possible -- would make a commercial success.)
This feature would require accurate horizontal positioning. I have investigated ultrasonic, laser, optical, and GPS. Each has its problems in this application. (I'll resist the temptation to go off on these tangents here.)
So... my question...
I know GPS horizontal accuracy is only 3-4m. Not good enough, but:
I don't need to know where I am on the planet. I only need to know where I am relative to where I was a minute ago.
So, my question is, is the inaccuracy consistent in the short term? if so, I think it would work for me. If it varies wildly by +- 1.5m from one second to the next, then it will not work.
I have tried to find this information but have had no success (possibly because of the ubiquity of other GPS-accuracy discussion), so I appreciate any guidance.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Edit ~~~~~~~~~~~~~~~~~~~~~~
It's looking to me like GPS is not just skewed but granular. I'd be interested in hearing from anyone who can give better insight into this, but for now I'm going to explore other options.
I realized that even though my intended application is "outdoor", this question is technically in the field of "indoor positioning systems" so I am adding that tag.
My latest thinking is to have 3 "intelligent" high-dB ultrasonic (US) speaker units. The mower emits RF requests for a tone from each speaker in rapid sequence, measuring the time it takes to "hear" each unit's response, thereby calculating distance to each of these fixed point and using trilateration to get position. if the fixed-point speakers are 300' away from the mower, the mower may have moved several feet between the 1st and 3rd response, so this would have to be allowed for in the software. If it is possible to differentiate 3 different US frequencies, they could be requested/received "simultaneously". Though you still run into issues when you're close to one fixed unit and far from another. So some software correction may still be necessary. If we can assume the mower is moving in a straight line, this isn't too complicated.
Another variation is the mower does not request the tones. The fixed units send RF "here comes tone from unit A" etc., and the mower unit just monitors both RF info and US tones. This may simplify things somewhat, but it seems it really requires the ability to determine which speaker a tone is coming from.
This seems like the kind of thing you could (and should) measure empirically. Just set a GPS of your liking down in the middle of a field on a clear day and wait an hour. Then come back and see what you find.
Because I'm in a city, I can't run out and do this for you. However, I found a paper entitled iGeoTrans – A novel iOS application for GPS positioning in geosciences.
That includes this figure which duplicates the test I propose. You'll note that both the iPhone4 and Garmin eTrex10 perform pretty poorly versus the accuracy you say you need.
But the authors do some Math Magic™ to reduce the uncertainty in the position, presumably by using some kind of averaging. That gets them to a 3.53m RMSE measure.
If you have real-time differential GPS, you can do better. But this requires relatively expensive hardware and software.
Even aside from the above, you have the potential issue of GPS reflection and multipath error. What if your mower has to go under a deck, or thick trees, or near the wall of a house? These common yard features will likely break the assumptions needed to make a good averaging algorithm work and even frustrate attempts at DGPS by blocking critical signals.
To my mind, this seems like a computer vision problem. And not just because that'll give you more accurate row overlaps... you definitely don't want to run over a dog!
In my opinion a standard GPS is no way accurate enough for this application. A typical consumer grade receiver that I have used has a position accuracy defined as a CEP of 2.5 metres. This means that for a stationary receiver in a "perfect" sky view environment over time 50% of the position fixes will lie within a circle with a radius of 2.5 metres. If you look at the position that the receiver reports it appears to wander at random around the true position sometimes moving a number of metres away from its true location. When I have monitored the position data from a number of stationary units that I have used they could appear to be moving at speeds of up to 0.5 metres per second. In your application this would mean that the lawnmower could be out of position by some not insignificant distance (with disastrous consequences for your prized flowerbeds).
There is a way that this can be done, as has been proved by the tractor manufacturers who can position the seed drills and agricultural sprayers to millimetre accuracy. These systems use Differential GPS where there is a fixed reference station positioned in the neighbourhood of the tractor being controlled. This reference station transmits error corrections to the mobile unit allowing it to correct its reported position to a high degree of accuracy. Unfortunately this sort of positioning system is very expensive.
I am working on a project which determines the indoor position of an object which moves in 3D space (e.g. a quadcopter).
I have built some prototypes which use a combination of gyroscope, accelerometer and compass. However the results were far from being satisfactory, especially related to the moved distance, which I calculated using the accelerometer. Determining the orientation using a fusion of gyroscope and compass was close to perfect.
In my opinion I am missing some more sensors to get some acceptable results. Which additional sensors would I need for my purpose? I was thinking about adding one or more infrared cameras/distance sensors. I have never worked with such sensors and I am not sure which sensor would lead to better results.
I appreciate any suggestions, ideas and experiences.
The distance checking would decidedly help. The whole algorithm of any surface geo survey is based on the conception of start/final check. You know the start, then you add erroneous steps, and come to the finish that you know, too. But you have collected some sum error by the way. Then you distribute the error found among all steps done, with the opposite sign, of course.
What is interesting, in most cases you not only somewhat diminish the effect of arbitrary mistakes, but almost eliminate the systematical ones. Because they mostly are linear or close to linear and such linear distribution of found error will simply kill them.
That is only the illustration idea. Any non-primitive task will contain collecting all data and finding their dependencies, linearizing them and creating parametrical or correlational systems of equations. The solving of them you get the optimal changes in the measured values. By parametrical method you can also easily find approximate errors of these new values.
The utmost base of these methods is the lesser squares method of Gauss. The more concrete methodics can be found in old books on geodesy/geomatic/triangulation/ geodesy nets. The books after introduction of GPS are for nothing, because everything was terribly simplified by it. Look for the books with matrix formulaes for lesser squares solutions.
Sorry if I had translated some terms into English with errors.
As per the title. I want to, given a Google maps URL, generate a twistiness rating based on how windy the roads are. Are there any techniques available I can look into?
What do I mean by twistiness? Well I'm not sure exactly. I suppose it's characterized by a high turn -to-distance ratio, as well as high angle-change-per-turn number. I'd also say that elevation change of a road comes in to it as well.
I think that once you know exactly what you want to measure, the implementation is quite straightforward.
I can think of several measurements:
the ratio of the road length to the distance between start and end (this would make a long single curve "twisty", so it is most likely not the complete answer)
the number of inflection points per unit length (this would make an almost straight road with a lot of little swaying "twisty", so it is most likely not the complete answer)
These two could be combined by multiplication, so that you would have:
road-length * inflection-points
--------------------------------------
start-end-distance * road-length
You can see that this can be shortened to "inflection-points per start-end-distance", which does seem like a good indicator for "twistiness" to me.
As for taking elevation into account, I think that making the whole calculation in three dimensions is enough for a first attempt.
You might want to handle left-right inflections separately from up-down inflections, though, in order to make it possible to scale the elevation inflections by some factor.
Try http://www.hardingconsultants.co.nz/transportationconference2007/images/Presentations/Technical%20Conference/L1%20Megan%20Fowler%20Canterbury%20University.pdf as a starting point.
I'd assume that you'd have to somehow capture the road centreline from Google Maps as a vectorised dataset & analyse using GIS software to do what you describe. Maybe do a screen grab then a raster-to-vector conversion to start with.
Cumulative turn angle per Km is a commonly-used measure in road assessment. Vertex density is also useful. Note that these measures depend upon an assumption that vertices have been placed at some form of equal density along the line length whilst they were captured, rather than being manually placed. Running a GIS tool such as a "bendsimplify" algorithm on the line should solve this. I have written scripts in Python for ArcGIS 10 to define these measures if anyone wants them.
Sinuosity is sometimes used for measuring bends in rivers - see the help pages for Hawths Tools for ArcGIS for a good description. It could be misleading for roads that have major
changes in course along their length though.
I have the following problem: I have 2 signals over time. They are from the same source so they should be the same. I want to check if they really are.
Complications:
they may be measured with different sample rates
the start / end time do not correlate. The measurement does not start at the same time and end at the same time.
there may be an time offset between the two signals.
My thoughts go along Fourier transformation, convolution and statistical methods for comparison. Can someone post me some links where I can find more information on how to handle this?
You can easily correct for the phase by just shifting them so their centers of mass line up. (Or alternatively, in the Fourier domain just multiplying by the inverse of the phase of the first coefficient.)
Similarly, if you want to line up the images given only partial data, you can just cross correlate and take the maximal value (which is again easy to do in the Fourier domain).
That leaves the only tricky part of this process as dealing with the sampling rates. Now if you know a-priori what the sample rates are, (and if they are related by a rational number), you can just use sinc interpolation/downsampling to rescale them to a common sampling rate:
https://ccrma.stanford.edu/~jos/st/Bandlimited_Interpolation_Time_Limited_Signals.html
If you don't know the sampling rate, you may be a bit screwed. Technically, you can try just brute forcing over all the different rescalings of your signal, but doing this tends to be either slow or else give mediocre results.
As a last suggestion, if you just want to match sounds exactly you can try using the cepstrum and verifying that the peaks of the signal are close enough to within some tolerance. This type of analysis is used a lot in sound and speech recognition, with some refinements to make it operate a bit more locally. It tends to work best with frequency modulated data like speech and music:
http://en.wikipedia.org/wiki/Cepstrum
Fourier transformation does sound like the right way.
There is too much mathematical information for me to just start explaining here so if you really wanna know what's going on with that (cause I don't think you can just use FT without understanding it) you should use this reference from MIT OpenCourseWare: http://ocw.mit.edu/courses/mathematics/18-103-fourier-analysis-theory-and-applications-spring-2004/lecture-notes/
Hope it helped.
If you are working with a linux box and the waveforms that need to be processed have already been recorded, you can try to use the file command to display details about the recording. It gives you the sampling rate when it is invoked on a wav file, though I am not sure what format you are recording in.
If the signals are time-shifted with respect to each other, you may try to convolve one with a delta function with increasing delays and then comparing. On MATLAB, conv and all should be good enough.
These are just 'crude' attempts (almost like hacking at the problem). There may be algorithms that are shift-invariant that may do a better job.
Hope that helps.
For example you measure the data coming from some device, it can be a mass of the object moving on the bridge. Because it is moving the mass will give data which will vibrate in some amplitude depending on the mass of the object. Bigger the mass - bigger the vibrations.
Are there any methods for filtering such kind of noise from that data?
May be using some formulas of vibrations? Have no idea what kind of formulas or algorithms (filters) can be used here. Please suggest anything.
EDIT 2:
Better picture, I just draw it for better understanding:
Not very good picture. From that graph you can see that the frequency is the same every
time, but the amplitude chanbges periodically. Something like that I have when there are no objects on the moving road. (conveyer belt). vibrating near zero value.
When the object moves, I there are the same waves with changing amplitude.
The graph can tell that there may be some force applying to the system and which produces forced occilations. So I am interested in removing such kind of noise. I do not know what force causes such occilations. Soon I hope I will get some data on the non moving road with and without object on it for comparison with moving road case.
What you have in your last plot is basically an amplitude modulated oscillation coming from a function like:
f[x] := 10 * (4 + Sin[x]) * Sin[80 * x]
The constants have been chosen to match your plot (using just a rule of thumb)
The Plot of this function is
That isn't "noise" (although may be some noise is there too), but can be filtered easily.
Let's see your data for the static and moving payloads ....
Edit
Based on your response to several comments, and based in my previous experience with weighting devices:
You are interfacing the physical world, not just getting input from a mouse and keyboard. It is very important for you understand the device, how it works and how it is designed.
You need a calibration procedure. You have to use several master weights to be sure that the device is working properly and linearly in the whole scale, and that the static case is measured much better than your dynamic needs.
You'll not be able to predict if you can measure with several loads in the conveyor until you do some experiments and look very carefully at the resulting plots
You need to be sure that a load placed anywhere in the conveyor shows the same reading. Or at least you should be able to correlate reading and position.
As I said before, you need a lot of info, and it seems that is not available. I always worked as a team with the engineers designing the device.
Don't hesitate to add more info ...
Have you tried filters with lowpass characteristics? There are different approaches for smoothing data (i.e. Savitzky-Golay, Gauss, moving average) but often, a simple N-point median filter is already sufficient.
It really depends on what you're after.
Take a look at this book:
The Scientist and Engineer's Guide to Digital Signal Processing
You can download it for free. In particular, check chapters 14 and 15.
If the frequency changes with mass and you're trying to measure mass, why not measure the frequency of the oscillations and use that as your primary measure?
Otherwise you need a notch filter which is tunable - figure out the frequency of the "noise" and tune the notch filter to that.
Another book to try is Lyons Understanding Digital Signal Processing
In order to smooth the signal, I'd average the previous 2 * n samples where n is the maximum expected wavelength of the vibrations.
This should cause most of the noise to be eliminated.
If you have some idea of the range of frequencies, you could do a simple average as long as the measurement period were sufficiently long to give you the level of accuracy you want to achieve. The more wavelengths worth of data you average against, the smaller the ratio of contributed error from a partial wavelength.
I'd suggest first simulating/modeling this in software like Matlab.
Data you'll need to consider:
The expected range of vibration frequencies
The measurement accuracy you want to achieve
The expected range of mass you'll want to measure
The function of mass to vibration amplitude
You should be able to apply the same principles as noise-cancelling microphones: put two sensors out, then subtract the secondary sensor's (farther away from the good signal source) signal from the primary sensor's (closer to the good signal source) signal.
Obviously, this works best if the "noise" will reach both sensors fairly equally while the "signal" reaches the primary sensor much more strongly.
For things like sound, this is pretty easy to do in the sensor itself, which makes your software a lot easier and more performant. Depending on what you're measuring, this might be easier to do with multiple sets of hardware and doing the cancellation in software.
If you can characterize the frequency spectra of the unwanted vibration noise, you might be able to synthesize a set of (near) minimum phase notch or band reject filter(s) to allow you to acquire your desired signal at your desired S/N ratio with minimized latency or data set size.
Filtering noisy digital signals is straight forward, as previous posters have noted. There are lots of references. You have not however stated what your objectives are clearly, so we cannot point you into a good direction. Are you looking for a single measurement of a single object on a bridge? [Then see other answers].
Are you monitoring traffic on this bridge and weighing each entity as it passes by? Then you need to determine when entities are on the sensor and when they are not. Typically, as long as the sensor's noise floor is significantly lower than the signal you're measuring this can be accomplished by simple thresholding.
Are you trying to measure the vibrations of the bridge caused by other vehicles? In which case you need either a more expensive sensor if you're having problems doing this, or a clearer measuring objective.