What is the unit in which core location framework gives the "Accuracy" (distance) for iBeacons. According to my knowledge it should be in Meters. But, in my app I have placed some beacons in distance of 19 Meters (63 foot) and the accuracy value of beacon from the framework is coming to be greater than 25 also sometimes.
The unit of CLBeacon.accuracy is in meters, but as you have witnessed, it is only a rough estimate. At short distances of 3 meters or less, the estimate will usually be within a meter. At longer distances it can be off by 10 meters or more.
This error is due to radio noise, multipath and attenuation. Estimation errors are a fundamental limitation of the technology, so you must set expectations appropriately.
Read more here: http://developer.radiusnetworks.com/2014/12/04/fundamentals-of-beacon-ranging.html
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I'm trying to decide whether it makes cpu processing time sense to use the more complex Haversine formula instead of the faster Pythagorean's formula but while there seems to be a pretty unanimous answer on the lines of: "you can use Pythagora's formula for acceptable results on small distances but haversine is better", I can not find even a vague definition on what "small distances" mean.
This page, linked in the top answer to the very popular question Calculate distance between two latitude-longitude points? claims:
If performance is an issue and accuracy less important, for small distances Pythagoras’ theorem can be used on an equirectangular projection:*
Accuracy is somewhat complex: along meridians there are no errors, otherwise they depend on distance, bearing, and latitude, but are small enough for many purposes*
the asterisc even says "Anyone care to quantify them?"
But this answer claims that the error is about 0.1% at 1000km (but it doesn't cite any reference, just personal observations) and that for 4km (even assuming the % doesn't shrink due to way smaller distance) it would mean under 4m of error which for public acces GPS is around the open-space best gps accuracy.
Now, I don't know what the average Joe thinks of when they say "small distances" but for me, 4km is definitely not a small distance (- I'm thinking more of tens of meters), so I would be grateful if someone can link or calculate a table of errors just like the one in this answer of Measuring accuracy of latitude and longitude? but I assume the errors would be higher near the poles so maybe choose 3 representative lattitudes (5*, 45* and 85*?) and calculate the error with respect to the decimal degree place.
Of course, I would also be happy with an answer that gives an exact meaning to "small distances".
Yes ... at 10 meters and up to 1km meters you're going to be very accurate using plain old Pythagoras Theorem. It's really ridiculous nobody talks about this, especially considering how much computational power you save.
Proof:
Take the top of the earth, since it will be a worst case, the top 90 miles longitude, so that it's a circle with the longitudinal lines intersecting in the middle.
Note above that as you zoom in to an area as small as 1km, just 50 miles from the poles, what originally looked like a trapezoid with curved top and bottom borders, essentially looks like a nearly perfect rectangle. In other words we can assume rectilinearity at 1km, and especially at a mere 10M.
Now, its true of course that the longitude degrees are much shorter near the poles than at the equator. For example any slack-jawed yokel can see that the rectangles made by the latitude and longitude lines grow taller, the aspect ratio increasing, as you get closer to the poles. In fact the relationship of the longitude distance is simply what it would be at the equator multiplied by the cosine of the latitude of anywhere along the path. ie. in the image above where "L" (longitude distance) and "l" (latitude distance) are both the same degrees it is:
LATcm = Latitude at *any* point along the path (because it's tiny compared to the earth)
L = l * cos(LATcm)
Thus, we can for 1km or less (even near the poles) calculate the distance very accurately using Pythagoras Theorem like so:
Where: latitude1, longitude1 = polar coordinates of the start point
and: latitude2, longitude2 = polar coordinates of the end point
distance = sqrt((latitude2-latitude1)^2 + ((longitude2-longitude1)*cos(latitude1))^2) * 111,139*60
Where 111,139*60 (above) is the number of meters within one degree at the equator,
because we have to convert the result from equator degrees to meters.
A neat thing about this is that GPS systems usually take measurements at about 10m or less, which means you can get very accurate over very large distances by summing up the results from this equation. As accurate as Haversine formula. The super-tiny errors don't magnify as you sum up the total because they are a percentage that remains the same as they are added up.
Reality is however that the Haversine formula (which is very accurate) isn't difficult, but relatively speaking Haversine will consume your processor at least 3 times more, and up to 31x more computational intensive according to this guy: https://blog.mapbox.com/fast-geodesic-approximations-with-cheap-ruler-106f229ad016.
For me this formula did come useful to me when I was using a system (Google sheets) that couldn't give me the significant digits that are necessary to do the haversine formula.
I'm successfully using pitch detection features of ml5:
tutorial: https://ml5js.org/reference/api-PitchDetection/
model: https://cdn.jsdelivr.net/gh/ml5js/ml5-data-and-models/models/pitch-detection/crepe/
The issue:
No pitch above ±2000Hz is detected. I tried multiple devices and checked that the sounds are visible on sonograms so it's does not seem to be a mic issue.
I assumed it may be a result of sampling rate limitations / resampling done by the library, as the Nyquist frequency (max "recordable" frequency) is that of half of the sampling rate.
I hosted the ml5 sources localy and tried modifying the PitchDetection class
There I see the sampling rate seems to be resampled to 1024Hz for performance reasons. This does not sound right though as if I'm not mistaken, this would only allow detection of frequencies up to 512hz. I am definitely missing something (or a lot).
I tried fiddling with the rates, but increasing it to, say 2048 causes an error:
Error when checking : expected crepe_input to have shape [null,1024] but got array with shape [1,2048].
My question is:
Is there something in ml5 PitchDetection class I can modify, configure (perhaps a different model) to detect frequencies higher than 2000Hz using crepe model?
After more investigation, turns out the CREPE model itself supports up to ~1997Hz (seen in code) or 1975.5 Hz (seen in paper)
The paper about CREPE:
https://arxiv.org/abs/1802.06182
States:
The 360 pitch values are denoted as c1, c2..., 360 are selected so that they cover six octaves with 20-cent intervals between C1 and B7, corresponding to 32.70 Hz and 1975.5 Hz
The JS implementation has this mapping which maps the 360 intervals to 0 - 1997Hz range:
const cent_mapping = tf.add(tf.linspace(0, 7180, 360), tf.tensor(1997.3794084376191))
This means, short of retraining the model I'm probably out of luck at using it for now.
Edit:
After a good nights sleep I found a simple solution which works for my simple application.
In it's essence, it is to resample my audio buffer so it has 2 times lower pitch. CREPE than detects a pitch of 440Hz as 220Hz, and I just need to multiply it by 2.
The result is still more consistently correct than YIN algorithm for my real time, noisy application.
At first blush this presumably means -
(1) looking only at lower IR frequencies,
(2) select a IR frequency cut-off for low frequency buckets of the u/v FFT grid
(3) Once we have that, derive the power distribution - squares of amplitudes - for that IR range of frequency buckets the camera supports.
(4) Fit that distribution against the Rayleigh-Jones classical Black Box radiation formula:
(https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law#Other_forms_of_Rayleigh%E2%80%93Jeans_law)
(5) Assign a Temperature of 'best fit'.
The units for B(ν,T) are Power per unit frequency per unit surface area at equilibrium Temperature
Of course, this leaves many details out, such as (6) cancelling background, etc, but one could perhaps use the opposite facing camera to assist in that. Where buckets do not straddle the temperature of interest, (7) use a one-sided distribution to derive an inferred Gaussian curve to fit the Rayleigh-Jeans curve at that derived central frequency ν, for measured temperature T.
Finally (8) check if this procedure can consistently detect a high vs low surface temperature (9) check if it can consistently identify a 'fever' temperature (say, 101 Fahrenheit / 38 Celcius) pointing at a forehead.
If all that can be done, (10) Voila! a body fever detector
So those who are capable can fill us in on whether this is possible to do so for eventual posting at an app store as a free Covid19 safe body temperature app? I have a strong sense there's quite a few out there who can verify this in a week or two!
It appears that the analog signal assumed in (1) and (2) are not available in the Android digital Camera2 interface.
Android RAW image stream, that is uncompressed YUV, is already encoded Y green monochrome, and U,V are blue and red shifts from zero for converting green monochrome to color.
The original analog frequency / energy signal is not immediately accessible. So adaptation is not possible (yet).
I'm trying to track the distance a user has moved over time in my application using the GPS. I have the basic idea in place, so I store the previous location and when a new GPS location is sent I calculate the distance between them, and add that to the total distance. So far so good.
There are two big issues with this simple implementation:
Since the GPS is inacurate, when the user moves, the GPS points will not be a straight line but more of a "zig zag" pattern making it look like the user has moved longer than he actually have moved.
Also a accuracy problem. If the phone just lays on the table and polls GPS possitions, the answer is usually a couple of meters different every time, so you see the meters start accumulating even when the phone is laying still.
Both of these makes the tracking useless of coruse, since the number I'm providing is nowwhere near accurate enough.
But I guess that this problem is solvable since there are a lot of fitness trackers and similar out there that does track distance from GPS. I guess they do some kind of interpolation between the GPS values or something like that? I guess that won't be 100% accurate either, but probably good enough for my usage.
So what I'm after is basically a algorithm where I can put in my GPS positions, and get as good approximation of distance travelled as possible.
Note that I cannot presume that the user will follow roads, so I cannot use the Google Distance Matrix API or similar for this.
This is a common problem with the position data that is produced by GPS receivers. 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. If you simply integrate the distance moved between samples then you will get a very large apparent distance travelled.for a stationary device.
A simple algorithm that I have used quite successfully for a vehicle odometer function is as follows
for(;;)
{
Stored_Position = Current_Position ;
do
{
Distance_Moved = Distance_Between( Current_Position, Stored_Position ) ;
} while ( Distance_Moved < MOVEMENT_THRESHOLD ) ;
Cumulative_Distance += Distance_Moved ;
}
The value of MOVEMENT_THRESHOLD will have an effect on the accuracy of the final result. If the value is too small then some of the random wandering performed by the stationary receiver will be included in the final result. If the value is too large then the path taken will be approximated to a series of straight lines each of which is as long as the threshold value. The extra distance travelled by the receiver as its path deviates from this straight line segment will be missed.
The accuracy of this approach, when compared with the vehicle odometer, was pretty good. How well it works with a pedestrian would have to be tested. The problem with people is that they can make much sharper turns than a vehicle resulting in larger errors from the straight line approximation. There is also the perennial problem with sky view obscuration and signal multipath caused by buildings, vehicles etc. that can induce positional errors of 10s of metres.
Have done fft (see earlier posting if you are interested!) and got a result, which helps me. Would like to analyse the noisiness / spikiness of an array (actually a vb.nre collection of single). Um, how to explain ...
When signal is good, fft power results is 512 data points (frequency buckets) with low values in all but maybe 2 or 3 array entries, and a decent range (i.e. the peak is high, relative to the noise value in the nearly empty buckets. So when graphed, we have a nice big spike in the values in those few buckets.
When signal is poor/noisy, data values spread (max to min) is low, and there's proportionally higher noise in many more buckets.
What's a good, computationally non-intensive was of analysing the noisiness of this data set? Would some kind of statistical method, standard deviations or something help ?
The key is defining what is noise and what is signal, for which modelling assumptions must be made. Often an assumption is made of white noise (constant power per frequency band) or noise of some other power spectrum, and that model is fitted to the data. The signal to noise ratio can then be used to measure the amount of noise.
Fitting a noise model depends on the nature of your data: if you know that the real signal will have no power in the high frequency components, you can look there for an indication of the noise level, and use the model to predict what the noise will be at the lower frequency components where there is both signal and noise. Alternatively, if your signal is constant in time, taking multiple FFTs at different points in time and comparing them to get a standard deviation for each frequency band can give the level of noise present.
I hope I'm not patronising you to mention the issues inherent with windowing functions when performing FFTs: these can have the effect of introducing spurious "noise" into the frequency spectrum which is in fact an artifact of the periodic nature of the FFT. There's a tradeoff between getting sharp peaks and 'sideband' noise - more here www.ee.iitm.ac.in/~nitin/_media/ee462/fftwindows.pdf
Calculate a standard deviation and then you decide the threshold that will indicate noise. In practice this is usually easy and allows you to easily tweak the "noise level" as needed.
There is a nice single pass stddev algorithm in Knuth. Here is link that describes an implementation.
Standard Deviation
calculate the signal to noise ratio
http://en.wikipedia.org/wiki/Signal-to-noise_ratio
you could also check the stdev for each point and if it's under some level you choose then the signal is good else it's not.
wouldn't the spike be
treated as a noise glitch in SNR, an
outlier to be discarded, as it were?
If it's clear from the time-domain data that there are such spikes, then they will certainly create a lot of noise in the frequency spectrum. Chosing to ignore them is a good idea, but unfortunately the FFT can't accept data with 'holes' in it where the spikes have been removed. There are two techniques to get around this. The 'dirty trick' method is to set the outlier sample to be the average of the two samples on either site, and compute the FFT with a full set of data.
The harder but more-correct method is to use a Lomb Normalised Periodogram (see the book 'Numerical Recipes' by W.H.Press et al.), which does a similar job to the FFT but can cope with missing data properly.