gyroscopes which measure rate of rotation of angles when integrated produce angles right?
my question is how do i do this? what im doing so far is just adding all the angles ive detected and that seems to be very wrong
AngleIntegrated = GyroDegPersec * (1/GyroBandWidth);
suggestions are very welcome. thanks
You need to integrate with respect to time. So ideally you should sample the gyroscope at regular (fixed) time intervals, T, and then incorporate that sampling interval, T, into your integral calculation.
Note that T needs to be small enough to satisfy the Nyquist criterion.
You can integrate in discrete domain. Suppose the angular rate is da, it's time integral is a.
k is the discrete step number.
a(k) = a(k-1) + T*0.5*(da(k) + da(k-1))
For example, da(k) is current angular rate reading. da(k-1) is previoud angular rate reading. a(k-1) is the previous step's integration value(rotation angle). T is sampling rate. If the sensor outputs in every 1 millisecond, T becomes 0.001.
You can use this formula when k>0. The initial value, a(0), must be given.
Knowing that of course you can't count on having a correct value in the long run (by integration your error window will always increase over time) what I would do is reading the gyroscope, interpolating the current read and previous few ones to get a smooth curve (e.g. a parabola using current read and previous two) and then computing the integral of that parabola from last read time and current time.
Related
I'm trying to determine the total length of time that a square wave takes to linearly increase from frequency 1 to frequency 2.
Question 1:
If I start at, for example:
f1=0hz
f2=1000hz
step increase per cycle is 10hz
What is the total time that elapses for this linear increase of frequency to take place?
Question 2:
If I have:
f1=0hz
f2=1000hz
and I want the increase to take place over 5 seconds, for example,
how would I calculate the rate of interval increase per cycle to achieve this.
*(basically the inverse of question 1)
This is for a hobby project to make a faster stepper motor driver profile, for programming an Atmel microcontroller (in C [well, Atmel's Arduino "C"]).
Any thoughts would be helpful. Thank you in advance!
I found this sine wave that slowly ramps up frequency from f1 to f2 for a given time but this answers a slightly different question - and is for a Sine wave.
#T Brunelle,
Q1. Your time for a general frequency would be
t=(1/(delta f))*ln(f2/f1)
where f1 and f2 are start and end frequencies and (delta f) is the change per cycle. Obviously this won't work if f1 is 0, but then a zero-frequency oscillation doesn't make sense either.
This comes from solving (in practice, just multiplying together and using the chain rule):
df/d(phase)=(delta f)
and
d(phase)/dt=f
where "phase" increases by 1 each cycle.
Q2. Just invert the formula in Q1.
This assumes that the change is linear PER CYCLE (rather than PER TIME, as was in your linked page). In your case it is also independent of the waveform shape.
I've spent a few hours doing research on numeric integration and velocity/position estimation but I couldn't really find an answer that would be either understandable by my brain or appropriate for my situation.
I have an IMU (Inertial Measurement Unit) that has a gyro, an accelerometer and a magnetometer. All those sensors are in fusion, which means for example using the gyro I'm able to compensate for the gravity in the accelerometer readings and the magnetometer compensates the drift.
In other words, I can get pure acceleration readings using such setup.
Now, I'm trying to accurately estimate the position based on acceleration, which as you may know requires double integration, and there are various methods of doing that. But I don't know which would be the most appropriate here.
Could somebody please share some information about this?
Also, I'd appreciate it if you could explain it to me without using any complex math formulas/symbols, I'm not a mathematician and this was one of my problems when looking for information.
Thanks
You can integrate the accelerations by simply summing the acceleration vectors multiplied by the timestep (period of the IMU) to get the velocity, then sum the velocities times the timestep to get the position. You can propagate (not integrate) the orientation by using various methods depending on which orientation representation you choose (Euler angles, Quaternions, Attitude Matrix (DCM), Axis-Angle, etc..).
However you have a bigger problem.
Long story short: Unless you have a naval-quality IMU (USD$200,000+) you cannot simply integrate the accelerations and angular rates to get an accurate pose (position and orientation) estimates.
I assume you are using a low-cost (under USD$1,000) IMU - your accelerometer and gyro are subject to both noise and bias. These will make it impossible to get accurate pose by simply integrating.
In practice to do what you are intending it is required to fuse 'correcting' measurements of the position and optionally the orientation. The IMU 'predicts' the position/orientation, while another sensor model (camera features, gps, altimeter, range/bearing measurements) take the predicted position and 'correct' it. There are various methods of fusing this data, the most prolific of which is the Extended Kalman Filter or Error-State (Indirect) Kalman Filter.
Back to your original question; I would represent the orientation as quaternions, and you can propagate the quaternion orientation by using the error-quaternion derivative and the angular rates from your gyro.
EDIT:
The noise problem can be partially worked around by using a high pass
filter, but what kind of bias are you exactly talking about?
You should read up on the sources of error in MEMS accelerometers: constant alignment bias, random walk bias, white noise and temperature bias. As you said you can high-pass filter to reduce the effect of noise - however this is not perfect so there is significant residual noise. The double integration of the residual noise gives a quadratically-increasing position error. Even after removing the acceleration due to gravity there will be significant accelerations measured due to these error sources which will render the position estimate inaccurate within less than 1 second of integration.
i have a sinusoidal-like shaped signal,and i would like to compute the frequency.
I tried to implement something but looks very difficult, any idea?
So far i have a vector with timestep and value, how can i get the frequency from this?
thank you
If the input signal is a perfect sinusoid, you can calculate the frequency using the time between positive 0 crossings. Find 2 consecutive instances where the signal goes from negative to positive and measure the time between, then invert this number to convert from period to frequency. Note this is only as accurate as your sample interval and it does not account for any potential aliasing.
You could try auto correlating the signal. An auto correlation can be rapidly calculated by following these steps:
Perform FFT of the audio.
Multiply each complex value with its complex conjugate.
Perform the inverse FFT of the audio.
The left most peak will always be the highest (as the signal always correlates best with itself). The second highest peak, however, can be used to calculate the sinusoid's frequency.
For example if the second peak occurs at an offset (lag) of 50 points and the sample rate is 16kHz and the window is 1 second then the end frequency is 16000 / 50 or 320Hz. You can even use interpolation to get a more accurate estimation of the peak position and thus a more accurate sinusoid frequency. This method is quite intense but is very good for estimating the frequency after significant amounts of noise have been added!
100 periods have been collected from a 3 dimensional periodic signal. The wavelength slightly varies. The noise of the wavelength follows Gaussian distribution with zero mean. A good estimate of the wavelength is known, that is not an issue here. The noise of the amplitude may not be Gaussian and may be contaminated with outliers.
How can I compute a single period that approximates 'best' all of the collected 100 periods?
Time-series, ARMA, ARIMA, Kalman Filter, autoregression and autocorrelation seem to be keywords here.
UPDATE 1: I have no idea how time-series models work. Are they prepared for varying wavelengths? Can they handle non-smooth true signals? If a time-series model is fitted, can I compute a 'best estimate' for a single period? How?
UPDATE 2: A related question is this. Speed is not an issue in my case. Processing is done off-line, after all periods have been collected.
Origin of the problem: I am measuring acceleration during human steps at 200 Hz. After that I am trying to double integrate the data to get the vertical displacement of the center of gravity. Of course the noise introduces a HUGE error when you integrate twice. I would like to exploit periodicity to reduce this noise. Here is a crude graph of the actual data (y: acceleration in g, x: time in second) of 6 steps corresponding to 3 periods (1 left and 1 right step is a period):
My interest is now purely theoretical, as http://jap.physiology.org/content/39/1/174.abstract gives a pretty good recipe what to do.
We have used wavelets for noise suppression with similar signal measured from cows during walking.
I'm don't think the noise is so much of a problem here and the biggest peaks represent actual changes in the acceleration during walking.
I suppose that the angle of the leg and thus accelerometer changes during your experiment and you need to account for that in order to calculate the distance i.e you need to know what is the orientation of the accelerometer in each time step. See e.g this technical note for one to account for angle.
If you need get accurate measures of the position the best solution would be to get an accelerometer with a magnetometer, which also measures orientation. Something like this should work: http://www.sparkfun.com/products/10321.
EDIT: I have looked into this a bit more in the last few days because a similar project is in my to do list as well... We have not used gyros in the past, but we are doing so in the next project.
The inaccuracy in the positioning doesn't come from the white noise, but from the inaccuracy and drift of the gyro. And the error then accumulates very quickly due to the double integration. Intersense has a product called Navshoe, that addresses this problem by zeroing the error after each step (see this paper). And this is a good introduction to inertial navigation.
Periodic signal without noise has the following property:
f(a) = f(a+k), where k is the wavelength.
Next bit of information that is needed is that your signal is composed of separate samples. Every bit of information you've collected are based on samples, which are values of f() function. From 100 samples, you can get the mean value:
1/n * sum(s_i), where i is in range [0..n-1] and n = 100.
This needs to be done for every dimension of your data. If you use 3d data, it will be applied 3 times. Result would be (x,y,z) points. You can find value of s_i from the periodic signal equation simply by doing
s_i(a).x = f(a+k*i).x
s_i(a).y = f(a+k*i).y
s_i(a).z = f(a+k*i).z
If the wavelength is not accurate, this will give you additional source of error or you'll need to adjust it to match the real wavelength of each period. Since
k*i = k+k+...+k
if the wavelength varies, you'll need to use
k_1+k_2+k_3+...+k_i
instead of k*i.
Unfortunately with errors in wavelength, there will be big problems keeping this k_1..k_i chain in sync with the actual data. You'd actually need to know how to regognize the starting position of each period from your actual data. Possibly need to mark them by hand.
Now, all the mean values you calculated would be functions like this:
m(a) :: R->(x,y,z)
Now this is a curve in 3d space. More complex error models will be left as an excersize for the reader.
If you have a copy of Curve Fitting Toolbox, localized regression might be a good choice.
Curve Fitting Toolbox supports both lowess and loess localized regression models for curve and curve fitting.
There is an option for robust localized regression
The following blog post shows how to use cross validation to estimate an optimzal spaning parameter for a localized regression model, as well as techniques to estimate confidence intervals using a bootstrap.
http://blogs.mathworks.com/loren/2011/01/13/data-driven-fitting/
First I am going to broadly state what I'm trying to do and ask for advice. Then I will explain my current approach and ask for answers to my current problems.
Problem
I have an MP3 file of a person speaking. I'd like to split it up into segments roughly corresponding to a sentence or phrase. (I'd do it manually, but we are talking hours of data.)
If you have advice on how to do this programatically or for some existing utilities, I'd love to hear it. (I'm aware of voice activity detection and I've looked into it a bit, but I didn't see any freely available utilities.)
Current Approach
I thought the simplest thing would be to scan the MP3 at certain intervals and identify places where the average volume was below some threshold. Then I would use some existing utility to cut up the mp3 at those locations.
I've been playing around with pymad and I believe that I've successfully extracted the PCM (pulse code modulation) data for each frame of the mp3. Now I am stuck because I can't really seem to wrap my head around how the PCM data translates to relative volume. I'm also aware of other complicating factors like multiple channels, big endian vs little, etc.
Advice on how to map a group of pcm samples to relative volume would be key.
Thanks!
PCM is a time frame base encoding of sound. For each time frame, you get a peak level. (If you want a physical reference for this: The peak level corresponds to the distance the microphone membrane was moved out of it's resting position at that given time.)
Let's forget that PCM can uses unsigned values for 8 bit samples, and focus on
signed values. If the value is > 0, the membrane was on one side of it's resting position, if it is < 0 it was on the other side. The bigger the dislocation from rest (no matter to which side), the louder the sound.
Most voice classification methods start with one very simple step: They compare the peak level to a threshold level. If the peak level is below the threshold, the sound is considered background noise.
Looking at the parameters in Audacity's Silence Finder, the silence level should be that threshold. The next parameter, Minimum silence duration, is obviously the length of a silence period that is required to mark a break (or in your case, the end of a sentence).
If you want to code a similar tool yourself, I recommend the following approach:
Divide your sound sample in discrete sets of a specific duration. I would start with 1/10, 1/20 or 1/100 of a second.
For each of these sets, compute the maximum peak level
Compare this maximum peak to a threshold (the silence level in Audacity). The threshold is something you have to determine yourself, based on the specifics of your sound sample (loudnes, background noise etc). If the max peak is below your threshold, this set is silence.
Now analyse the series of classified sets: Calculate the length of silence in your recording. (length = number of silent sets * length of a set). If it is above your Minimum silence duration, assume that you have the end of a sentence here.
The main point in coding this yourself instead of continuing to use Audacity is that you can improve your classification by using advanced analysis methods. One very simple metric you can apply is called zero crossing rate, it just counts how often the sign switches in your given set of peak levels (i.e. your values cross the 0 line). There are many more, all of them more complex, but it may be worth the effort. Have a look at discrete cosine transformations for example...
Just wanted to update this. I'm having moderate success using Audacity's Silence Finder. However, I'm still interested in this problem. Thanks.
PCM is a way of encoding a sinusoidal wave. It will be encoded as a series of bits, where one of the bits (1, I'd guess) indicates an increase in the function, and 0 indicates a decrease. The function can stay roughly constant by alternating 1 and 0.
To estimate amplitude, plot the sin wave, then normalize it over the x axis. Then, you should be able to estimate the amplitude of the sin wave at different points. Once you've done that, you should be able to pick out the spots where amplitude is lower.
You may also try to use a Fourier transform to estimate where the signals are most distinct.