Over the past year I have used many different methods of combining Accelerometers, gryos and Magnetometers to get accurate readings of Head angles.
I have also started looking into using a Kalman filter to further improve these readings.
Yet I am still to find a method of removing external magnetic field influences using the other sensors, for example;
If my heading angle was accurate, and suddenly an external magnetic field approaches, my heading angle will be influenced, but to my gyro and accelerometer I haven’t moved.
Is there any algorithms or calculations anyone can think of to override the magnetometer in a way that can determine whether you have moved or not?
Any help would be much appreciated!
One simple solution is to use the gyro/accelerometer as you mentioned, and combine that with delayed filtering, where you wait for a couple of seconds before providing an estimate of the attitude.
Compute the short term attitude from gyro/accel only (start with any arbitrary heading) using gyro integration with accel measurements, and then compute the short term attitude from the magnetometer/accel only using, say TRIAD. Compute the error between these two quantities and decide on a threshold. If the you exceed the threshold, it means there is a magnetic disturbance, and you can thus stop using it in your attitude solution. If they are within threshold, you can continue using the magnetometer.
If you think of more metrics to decide whether you are in a magnetic disturbance or not (such as the magnetometer norm rising to a ridiculous number), then you can add those metric to an HMM, which will combine these metrics and give you an estimate of whether you are in a disturbance or not.
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I am currently working on a mission to fuse GNSS and IMU for a more accurate navigation system for autonomous vehicles. I am very familiar with using GNSS to get the accurate position, however I'm a newbie in using IMU sensor. I've read several kinds of literature but am still confused about which better way should I do to remove bias from the accelerometer and gyroscope measurement.
I have 2 kinds of raw measurement data using MPU-9250, they are acceleration data (m/s2) in the x,y, z-axis and angular velocity data (deg/s) also in the x,y, z-axis. I have tried to input these data into my sensor fusion program. Unfortunately, I got unsatisfied with accuracy.. Hence I think firstly I should correcting (removing bias) of raw data IMU, and then the corrected IMU data can be input to my fusion program.
I couldn't find an answer that my brain could understand or fit my situation. Can someone please share some information about this? Can I use a high-pass filter or a low-pass filter in this situation?
I would really appreciate if there is someone could explain in detail to me without using complex math formulas/symbols, I'm not a mathematician and this is one of my problems when looking for information.
Thank you in advance
Accelerometer and Gyroscope have substantial bias usually. You could break the bias down to factors like,
Constant bias
Bias induced by temperature variation.
Bias instability
The static part of bias is easy to subtract out. If the unit starts from level orientation and without any movement, you could take samples for ~1s, average it and subtract it from your readings. Although, this step removes a big chuck of bias, it cannot still fully remove it (due to level not being perfect).
In case you observe that the temperature of IMU die varies during operation (even 5-10 deg matters), note down the bias and temperature (MPU9250 has an inbuilt temperature sensor). Fit a linear or quadratic curve that captures bias against temperature. Later on, use the temperature reading to estimate bias and subtract it out.
Even after implementing 1 and 2, there will still be some stubborn bias left. If the same is used in a fusion algorithm like Kalman filter (that is not formulated to estimate bias, the resulting position and orientation estimates will be biased too).
Bias can be estimated along with important states (like position) using some external reference/sensor like GNSS, Camera.
Complementary filter (low pass + high pass) or a Kalman filter can be formulated for this purpose.
Kalman filter approach:
Good amount of intuition along with some mathematics is needed to use this approach. Basically the work involves formulating prediction & measurement model and then provide rough noise variances for your measurements and prediction. An important thing to understand is that, Kalman filter assumes that the errors follow normal distribution without any bias. So the formulation should deliberately put bias terms as unknown states that should be estimated too (Do not assume that the sensor is bias free in the formulation)..
You could checkout my other answer to gain a detailed understanding of this approach.
Complementary filter approach
Complementary filter is simpler for simpler problems :P
The idea is that we use low pass filter on noisy measurement and high pass filter on biased measurement. Then add them up and call it a day.
Make sure that both the LPF and HPF are complements of each other (Transfer function of HPF should be 1-LPF). Typically first order filters with same time constants are used. Additionally the filter equations have to be converted from continuous laplace domain to discrete form (Read about ZOH, Tustins approximation...).
The final form is scattered around the internet too.
Personally I would use a Kalman filter for this purpose, but complementary filter can be used with same amount of effort. You could do this,
Assume that the body is not accelerating on average in long term (1-10 s or so). Then you could say that the accelerometer measures the direction of gravity in long term relative to the IMU. Then arctan(accy, accz) can be used to obtain an estimate of pitch and roll. But this pitch and roll readings will suffer from substantial noise. Implement a low pass filter on it with time constant ~5 seconds or so. Additionally add the latest pitch/roll with dt*transformationMatrix*gyroscope to get another pitch and roll. But these suffer from bias. Implement a HPF over gyro based Pitch and Roll. Add them together to get Pitch and Roll. Lets call these IMU_PR.
Now forget our original acceleration assumption. accelerometer gives specific force (which is net acceleration - gravity). Since we have Pitch and Roll angles (IMU_PR), we know gravities direction. Add gravity to accel readings to get an estimate of acceleration. Apply proper frame conversion to bring this acceleration to same coordinate frame as GPS (you will need an estimate of Yaw to do so. Fuse a magnetometer with gyroscope for this purpose). Then do vel = vel + acc*dt. Integrate it again to get an estimate of position from IMU. But this will drift due to the bias in accelerometer (and pitch, roll). Implement a high pass filter over this position and low pass filter over GPS position to get a final estimate.
I have accelerometer readings of three axis X, Y and z, will be getting data in a frequency of (62 records per second). Could you please suggest me how can I calculate the displacement.
Data in hand:
Accelerometer readings with respect to time.
Do I need to calculate the displacement using time domain data or need to convert into frequency domain. Which one will give a accurate results?
You can double integrate the acceleration vector over time to obtain the displacement. In theory this is a perfectly sensible solution.
But in practice, there will always be a component of g (acceleration due to gravity) acting on at least one of the axes all the time. Let's say you subtract the g component from your xyz vectors. The problem is that any slight error in readings (even off by a small order of magnitude) when double integration will lead to the error adding up over time rendering the displacement wildly inaccurate.
According to the integrated values, you will most likely see even an idle object fly off into space. You'll need an additional sensor to tell you the orientation - like a gyroscope, and have some point of reference (the Wiimote does this with an IR sensor).
This is primarily a time domain problem, but you could have a frequency domain stage where some amount of filtering is done to remove measurement error or process error.
tl;dr Positional tracking with acceleration sensors alone is a hard problem.
I want to calculate the current passing in the wall socket using iphone.I am using CMMotionmanagerFramework and i got X,Y,Z values with that values i can calculate the magnetic field across the surroundings by using those values i want to calculate the voltage level of the wall socket. Please provide me the answer.
The magnetic field strength gives you the electric field strength in volts per meter, related to the velocity of the electrons. The velocity of the electrons is known as the drift velocity, and is related to the current. The electric field strength depends on the charge density in the wire, which should be a constant you can find for the wire you're using, and the distance from the detector to the wire.
So your magnetic field strength depends on a bunch of constants related to the physical arrangement of your problem and the current in the wire. You can derive that using your iPhone's magnetometer, knowledge of its accuracy and some maths. The voltage drop (potential difference) across the outlet is related to the current by the reactance, because you're probably looking at an Alternating Current system so inductances and capacitances play a role, in addition to the resistance.
However you probably don't need to calculate the potential difference, because the electrical utility company will tell you what it is.
I have to find the best approach for tackling a problem for trying to recognize physical movements - with an iPhone in a pocket - like waling, stopping, turning left/right, sitting.
I was thinking on just heuristically find the data corresponding to each action, then to check the incoming values against this data (with a threshold) and see what's happening.
That's a very rough approach, of course, so maybe using something like the Support Vector Machine
methods, but this seems too complicated for the amount of time I have to develop this.
Which approach would you suggest here?
Walking: Do an fft on the gravity direction signal. Measure its frequency response for walking at different speeds and then set a simple threshold.
Stopping: if the average power i.e. total energy in the signal over the last few seconds drops below a certain threshold then you can say the user has stopped.
Turning left,right: Use the gravity vector and the gyroscopes rotation speed vector to determine whether the user is rotating clockwise or counterclockwise
Sitting: This will be very hard to determine but if youre lucky the SVM will find the right pattern.
Each of the above can be given a weighting and then you will have to find a good way to obtain training data to train your SVM. Maybe stream the signals from the phone to a webserver and simultaneously record the users motions by hand.
Your best starting point is Apples Sample code: CoreMotionTeapot
Alternatively you could analyze the GPS signal. This will give you a very good way to determine the users larger scale motion like walking/moving or changing heading etc.
Does anyone know if Core Location in the iPhone OS uses anything but simple vector math to calculate speed? I've read that the GPS system can provide speed measurements that can be accurate when position is not (I believe using the Doppler shifts of the signals).
I've tried and failed to see if the iPhone does this. The question is basically, does this data contain information or is it just convenience functions, using (filtered?) location data?
I suppose my question is if anyone have tried this in reality, or knows beyond what is in the documentation.
The Core Location documentation describes the speed reading thus:
This value reflects the instantaneous speed of the device in the direction of its current heading.
While not absolutely definitive, this strongly suggests that the reading is direct, rather than an interpolation of positions, which cannot be described as "instantaneous" by any reasonable definition.
The GPS system in itself is not able to provide speed measurements. The only way this can practically be done is by comparing to discrete position measurements and the time between those. It's just a matter of applying simple math to get the speed and direction traveled. More samples can be used to get a more accurate measurement.
It is not feasible to measure the speed directly by simple GPS receivers, e.g. by use of Doppler shift. This is due to the fact that each satellite itself is traveling at very high speed around the globe. Each satellite orbits the globe twice every day, resulting at a speed of almost 14000 km/hour. Since the direction of the satellite compared to the GPS unit varies depending on where it is on the sky, the difference in the measure Doppler shift would be huge compared to the Doppler shift resulting from moving of the GPS receiver itself.
I'm however not saying that this couldn't be done by very sophisticated hardware and algorithms, but the cost/benefit would probably not be worth even considering it.