Currently, we are using BNO055 in one of our projects. The IMU is placed next to the dc motor due to space constraints within the hardware setup. Due to motors vibrations, we are applying a low pass filter on quaternion values read from this (https://github.com/adafruit/Adafruit_BN ... awdata.ino) script. We have set 5 Hz as a cut-off frequency of the filter. We have also placed IMU on Sorbothane (damping material) to minimize the vibrations. However, we are still selling the error in the orientation.
What could be done to reduce the impact of motor vibrations on IMU both from a software and hardware point of view? Any inputs are highly appreciated.
Motor vibration may not be the only problem here.
Orientation estimation can go wrong due to multiple factors like,
Bias due to incorrect calibration. Keep the sensor level and idle. Make sure Gyroscope reads close to (0,0,0) on average. Accelerometer should read either (0,0,9.81) or (0 0 -9.81) m/s^2 depending on the convention.
Bias due to temperature changes. Even a 10 deg change in PCB temperature can change the bias in Gyro by 0.3 dps (according to the datasheet)
Motor noise. Seems like you have already tried reducing this one.
If none of them work, you could try implementing your own Kalman or complementary filter based on the raw data from Gyro, Accel and mag. This way you can be sure about calibration process, estimator gains, how the estimator works.
If implementing Kalman filter is difficult, you could try this AHRS filter block/algorithm given here,
https://in.mathworks.com/help/nav/ref/ahrsfilter-system-object.html
Related
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.
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.
My project:
I'm developing a slot car with 3-axis accelerometer and gyroscope, trying to estimate the car pose (x, y, z, yaw, pitch) but I have a big problem with my vibration noise (while the car is running, the gears induce vibration and the track also gets it worse) because the noise takes values between ±4[g] (where g = 9.81 [m/s^2]) for the accelerometers, for example.
I know (because I observe it), the noise is correlated for all of my sensors
In my first attempt, I tried to work it out with a Kalman filter, but it didn't work because values of my state vectors had a really big noise.
EDIT2: In my second attempt I tried a low pass filter before the Kalman filter, but it only slowed down my system and didn't filter the low components of the noise. At this point I realized this noise might be composed of low and high frecuency components.
I was learning about adaptive filters (LMS and RLS) but I realized I don't have a noise signal and if I use one accelerometer signal to filter other axis' accelerometer, I don't get absolute values, so It doesn't work.
EDIT: I'm having problems trying to find some example code for adaptive filters. If anyone knows about something similar, I will be very thankful.
Here is my question:
Does anyone know about a filter or have any idea about how I could fix it and filter my signals correctly?
Thank you so much in advance,
XNor
PD: I apologize for any mistake I could have, english is not my mother tongue
The first thing i would do, would be to run a DFT on the sensor signal and see if there is actually a high and low frequency component of your accelerometer signals.
With a DFT you should be able to determine an optimum cutoff frequency of your lowpass/bandpass filter.
If you have a constant component on the Z axis, there is a chance that you haven't filtered out gravity. Note that if there is a significant pitch or roll this constant can be seen on your X and Y axes as well
Generally pose estimation with an accelerometer is not a good idea as you need to integrate the acceleration signals twice to get a pose. If the signal is noisy you are going to be in trouble already after a couple of seconds if the noise is not 100% evenly distributed between + and -.
If we assume that there is no noise coming from your gears, even the conversion accuracy of the Accelerometer might start to mess up your pose after a couple of minutes.
I would definately use a second sensor, eg a compass/encoder in combination with your mathematical model and combine all your sensor data in a kalmann filter(Sensor fusion).
You might also be able to derive a black box model of your noise by assuming that it is correlated with your motors RPM. (Box-jenkins/Arma/Arima).
I had similar problems with noise with low and high frequencies and I managed to decently remove it without removing good signal too by using an universal microphone shock mount. It does a good job with gyroscope too especially if you find one which fits it (or you can put it in a small case then mount it)
It basically uses elastic strings to remove shocks and vibration.
Have you tried a simple low-pass filter on the data? I'd guess that the vibration frequency is much higher than the frequencies in normal car acceleration data. At least in normal driving. Crashes might be another story...
I'm doing some test with iPhone 4S accelerometer. If I take the raw data in Z-axis (telephone rest over desktop) I get an acceleration 9.65-9.70 m/s2 (after g conversion by 9.8261).
But if i have the telephone resting over edge, the measurement of the accelerometer value in the X-axis is so different, aprox. 9.80-9.85 m/s2 (after the same g conversion).
My question is, if the gravity is the same, why this difference? It is not callibrated?
On the other hand, I check the module value at both situations and the difference is the same.
Thanks.
I don't know what kind of answer you expect, but you should be more precise when you're talking about calibration.
Of course, the g-sensors are calibrated and as always: every calibration comes with an error. In your case the error is under 1%.
So if you want an answer:
Yes, the iPhone accelerometer is calibrated and has an error under 1% in your case. If you collect measurements from other (hundreds of) users, you could calculate the mean error of the device (I guess it's about 1% though).
The problem is that it's not possible to determine gravity 100% exactly when all of the sensors (gyro and compass as well) show an intrinsic error. The lack of a precise external reference system leads to this error. Accelerometer and gyroscope are corrected mutually and if there is a slight drift it does affect the direction where the sensor fusion algorithm (Kalman-Filter or others) calculates gravity should be.
While gyroscope is very fast in detecting the direction it tends to drifting effects. Accelerometers are slower in reaction but provide a way to detect gravity. Magnetometers are even slower but can contribute to stabilising the overall result. Combine Gyroscope and Accelerometer Data shows some graphs of the raw and the processed sensor data.
I continued working with accelerometers. The results are not bad. About iPhone accelerometers calibrating, I can say that STMicroelectronics does calibration over his own sensor. Later, iPhone factory assemblies accelerometer onto circuit board. The soldering affects to accelerometer accuracy (thermal effects) and probably, the accelerometer requires a new calibration, but for consumer requirements, the accuracy is already good, but if you need high requirements, you need a new calibration.
Before I reinvent the wheel I wanted to see if anyone can share code or tips for the following:
In order to get relative position of the iPhone, one needs to
Set the accelerometer read rate
Noise filter the accelerometer response
Convert it to a vector
Low pass filter the vector to find gravity
Subtract gravity from the raw reading to find the user caused acceleration
Filter the user caused acceleration to get the frequencies you are interested in ( probably bandpass depending on the application)
Integrate to find relative speed
Integrate to find position
So what I'm hoping is that people have already written some or all of the above and can provide tips, or better yet code.
A few questions I haven't found the answer to:
What is the frequency response of the iPhone accelerometer? What hardware filters exist between the accelerometer and the analog to digital converter?
What is the fastest reading rate the accelerometer delegate can be called without duplicating reading values?
Differences in the above for the various phones?
Any good tips for designing the filters, such as cutoff frequency for separating gravity and user motion?
Any code or tips for the integration steps? Any reason to integrate in the cartesion coordinate system rather than as vector, or vise versa?
Any other experiences, tips, or information that one should know prior to implementing this?
As I find information out, I'll be collecting it in this answer.
Hardware
The 3GS uses an ST LIS331DL 3-axis ±2g/±8g digital accelerometer.
The iPhone 4 and iPad use an ST LIS331DLH 3-axis ±2g/±4g/±8g digital accelerometer.
They are both capable of being read at 100Hz and 400Hz, although on the iPhone 3G (under iOS 4.1) the accelerometer delegate is not called more frequently than 100Hz even if setUpdateInterval is set for faster updates. I do not know if the API permits faster updates on the iPhone 4, and Apple's documentation merely states that the maximum is determined by the hardware of the iPhone. (TBD)
The A/D converter is on the same silicon as the MEM sensor, which is good for noise immunity.
The DL version is 8 bits (3GS) while the DLH version is 12 bits (iPhone 4). The maximum bias (offset) in the DL version is twice the bias of the DLH (0.04g vs 0.02g) version.
The data sheet for the DLH reports acceleration noise density, but that value is not reported on the DL datasheet. Noise density is reasonably low at 218 μg/√Hz for the DLH.
Both sensors give either 100Hz sampling or 400Hz sampling speeds, with no custom rate. The sensor discards values if the iPhone doesn't read the output register at the set sampling rate.
The "typical" full scale value for the DL sensor is ±2.3g, but ST only guarantees that it's at least ±2g.
Temperature effects on the sensor are present and measurable, but not very significant.
TBD:
Is the hardware filter turned on, and what are the filtering characteristics?
How noisy is the power supply to the accelerometer? (Anybody just happen to have the iPhone schematic laying around?)
The accelerometer uses an internal clock to provide timing for the sample rate and A/D conversion. The datasheet does not indicate the accuracy, precision, or temperature sensitivity of this clock. For accurate time analysis the iPhone must use an interrupt to sense when a sample is done and record the time in the interrupt. (whether this is done or not is unknown, but it's the only way to get accurate timing information)
API
Requesting lower than 100Hz sampling rates results in getting selected samples, while discarding the rest. If a sampling rate that is not a factor of 100Hz is requested in software, the time intervals between real sensor readings cannot be even. Apple does not guarantee even sampling rates even if a factor of 100 is used.
It appears that the API provides no software filtering.
The API does scale the raw accelerometer value into a double representing Gs. The scaling factor used is unknown, and whether this is different for each phone (ie, calibrated) and whether the calibration occurs on an ongoing basis to account fo sensor drift is unknown. Online reports seem to suggest that the iPhone does re-calibrate itself on occasion when it's lying flat on a surface.
Results from simple testing suggest that the API sets the sensor to ±2g for the 3GS, which is generally fine for handheld movements.
TBD:
Does Apple calibrate each unit so that the UIAccelerometer reports 1G as 1G? Apple's documentation specifically warns against using the device for sensitive measurement applications.
Does the reported NSTimeInterval represent when the values were read from the accelerometer, or when the accelerometer interrupt indicated that new values were ready?
I'm just dealing with the same problem. The only difference to your approach is that I don't want to rely on the low pass filter to find gravity. (TBH I don't see how I can reliably tell the gravity vector from the accelerometer readings)
Am trying it with the gyros right now.