I currently work in an experimental rock mechanics lab, and when I conduct an experiment, I record the output signals such as effective torque, normal force and motor velocity. However, the latter quantity causes significant cross-talk over the recorded channels, and I want to filter this out. Let me give an example:
Here the upper plot is the strong signal (motor velocity), and the lower is an idle signal that is affected by the cross-talk (blue is raw signal, red is median filtered). The idle channel is only recording noise. We see three effects here. When the motor voltage changes:
the amplitude of the noise increases
the idle signal's median shifts
there is a spike that lasts approximately 0.1 seconds
If we zoom in on the first spike that occurs at around 115 seconds, we get the following plot. This does not seem to be your typical delta-function type of spike, but rather some kind of electronic "echo".
I have seen much work on blind source separation through independent component analysis (ICA), but that did not prove to be effective in my situation. However, since I know the shape of the signal that is causing the cross-talk, there may be better ways to include this information. My question is this: is there a filter or a combination of filters that can tackle the effects mentioned above?
As I am a geologist and not an electrician or mathematician, I don't have a proper background for this kind of material, so please bear with me. I write Python, MATLAB and C++ quite well, so suggested algorithms written in any of those languages is preferred (but not required).
The crosstalk you encounter, results from a parasitic transmission line. Just think of your typical FM-receiver - where the wires equal the antennae. These effects include parasitic and inductive coupling, and form an oscillator (which is the reason, why you cannot see, the theoretically ideal delta spike)
I recognize two different approaches:
use a hardware filtering circuit
use a software-implemented filter
ad 1:
depending on the needed bandwith (maximum frequency/rate of change) on the idle channel, you can determine the corner frequency, as well as the required filter-order, for a given rate of suppression
ad 2:
you can implement several types of filters (IIF, FIR) which resemble these circuits.
Additionally, if you are measuring the aggressive signal anyways, you can use the measurement on the idle channel to determine system-parameters for a mathematical model of the crosstalk. With this model you'd be able, to exclude the interference by calculation
Related
While trying to implement the Episodic Semi-gradient Sarsa with a Neural Network as the approximator I wondered how I choose the optimal action based on the currently learned weights of the network. If the action space is discrete I can just calculate the estimated value of the different actions in the current state and choose the one which gives the maximimum. But this seems to be not the best way of solving the problem. Furthermore, it does not work if the action space can be continous (like the acceleration of a self-driving car for example).
So, basicly I am wondering how to solve the 10th line Choose A' as a function of q(S', , w) in this pseudo-code of Sutton:
How are these problems typically solved? Can one recommend a good example of this algorithm using Keras?
Edit: Do I need to modify the pseudo-code when using a network as the approximator? So, that I simply minimize the MSE of the prediction of the network and the reward R for example?
I wondered how I choose the optimal action based on the currently learned weights of the network
You have three basic choices:
Run the network multiple times, once for each possible value of A' to go with the S' value that you are considering. Take the maximum value as the predicted optimum action (with probability of 1-ε, otherwise choose randomly for ε-greedy policy typically used in SARSA)
Design the network to estimate all action values at once - i.e. to have |A(s)| outputs (perhaps padded to cover "impossible" actions that you need to filter out). This will alter the gradient calculations slightly, there should be zero gradient applied to last layer inactive outputs (i.e. anything not matching the A of (S,A)). Again, just take the maximum valid output as the estimated optimum action. This can be more efficient than running the network multiple times. This is also the approach used by the recent DQN Atari games playing bot, and AlphaGo's policy networks.
Use a policy-gradient method, which works by using samples to estimate gradient that would improve a policy estimator. You can see chapter 13 of Sutton and Barto's second edition of Reinforcement Learning: An Introduction for more details. Policy-gradient methods become attractive for when there are large numbers of possible actions and can cope with continuous action spaces (by making estimates of the distribution function for optimal policy - e.g. choosing mean and standard deviation of a normal distribution, which you can sample from to take your action). You can also combine policy-gradient with a state-value approach in actor-critic methods, which can be more efficient learners than pure policy-gradient approaches.
Note that if your action space is continuous, you don't have to use a policy-gradient method, you could just quantise the action. Also, in some cases, even when actions are in theory continuous, you may find the optimal policy involves only using extreme values (the classic mountain car example falls into this category, the only useful actions are maximum acceleration and maximum backwards acceleration)
Do I need to modify the pseudo-code when using a network as the approximator? So, that I simply minimize the MSE of the prediction of the network and the reward R for example?
No. There is no separate loss function in the pseudocode, such as the MSE you would see used in supervised learning. The error term (often called the TD error) is given by the part in square brackets, and achieves a similar effect. Literally the term ∇q(S,A,w) (sorry for missing hat, no LaTex on SO) means the gradient of the estimator itself - not the gradient of any loss function.
I'd like to use an optical flow system to get velocities from surrounding environment. I've read papers about how optical flow works, but they don't treat details about optic sensors.
My question is: How do I determine how much computational power is required to perform optical flow analysis?
I'd like to use a low-power system (like microcontrollers), but I don't know what kind of camera I could use with such a system. I mean, could it be color or does it need to be B/W? Rolling shutter or global shutter? Which frame rate or number of pixels?
I'd like to specify the system myself but, without knowing how those camera attributes impact the processing load, I'm not sure where to start.
As Chuck already said in the comment. You first need to start with something. Opticalflow calculation really depends on what you are using it for and what you are trying to achieve. For realtime applications you might want to consider using faster processors (this is always true though).
Continuing to my answer.
Opticalflow calculation performance depends on few main things:
The optical-flow method you choose (dense or sparse), you can read more about it here and here. Of course that you should take into account not only that sparse is faster than dense, also that sparse might be less accurate in some cases. Again, this depends on what you're trying to achieve.
In addition, you will see that there are different optical-flow algorithms. Some might be faster than others. There are many algorithms such as Lucas-Kanade, Horn-Schunck, TVL1, Farneback, etc.
Most optical-flow methods from libraries such as OpenCV gives you the ability to change some parameters in order to play with the trade-off between accuracy and performance. See this and also check the OpenCV methods such as this and this for example - see the different arguments.
The resolution of your image. Smaller image usually means faster calculation.
Few things you might also want to consider:
If you are using a processor that has multiple cores, make sure that you are using all the cores in the optical-flow calculation. Some libraries may already do this for you, but in some cases you will need to do it by yourself. Take a look at my question and answer in this post, it might give you some idea and help you getting starting with such case.
If you want more accurate optical-flow results you must use global shutter camera. Rolling shutter cameras, such as most of the web-cams, will give you an extra error you don't want.
You don't need color image, if you have a grayscale camera it will be even better. If not, you will need to convert it to grayscale (not B/W) for faster performance as well.
Some libraries such as OpenCV has an option (in some cases) to run these algorithms on a GPU. If using a GPU is an option you might want to consider this as well.
From my own experience, the main thing that gave me a boost in performance was changing my resolution from 640x480 to 320x240 and even 160x120. In my case it didn't really hurt the accuracy.
I used an Odroid U3 mini-pc with OpenCV PyrLK algorithm and input frames of 320x240 resolution. After applying what's described here (splitting the image to 4 for parallel calculation) it worked pretty well (realtime).
The answer given by Sarid has some strong points, and many of them are shared by researchers around the world. My opinions are shared by anyone who has actually worked with these topics in the real-world setting.... with real world, i mean implementing optical flow in drones, on mobile phones and IP cameras that are not sitting in a protected office, and where other systems (such as humans) need to interact and be co-dependent.
First of all, depending on your problem, you may want to invest time in looking for ready-made solutions. Optical flow sensors are readily available, cheap and robust (but usually not strong in accuracy). These are the kind of sensors you find in optical mice. They are low power, and easily interfaced with micro-controllers. Some have staggering sample rates of thousands of fps. They commonly have low spatial resolution however, and (to emphasize) high robustness but low accuracy.
If instead you are looking for the kind of optical flow that can be used for shape from motion, pedestrian detection and video-encoding, for example, then you are probably better off to look for something more advanced, and thats where Sarids answer becomes relevant.
Since your question has been migrated from robotics stack exchange, I am going to assume you are interested applications close to machine control and human machine interaction. In that case, the most important aspects are the ones usually most ignored by people working in the field of optical flow estimation, namely:
Latency. If you have a human interfacing at the front-end... then the common term is "glass-to-glass latency". This is completely different from the fps of your system, which is connected to throughput. If you find that you are in a discussion with someone, and they do not understand the difference between latency and fps, then they are not the expert you are interested in. For example, almost all researchers in computer vision who do GPU implementations of optical flow add massive latency by allowing for frame delays and ineffecient memory handling (inefficient from perspective of latency, but efficient in terms of throughput and hard-ware utilization). Consider the problem of controlling a drone, say make it self-stabilizing, it is better to receive a bad optical flow estimation 10 ms earlier, then a good one with 10 ms extra delay.... especially if the optical system does not give you any upper bounds of the delay for any given time.
Algorithm stability. This is completely different from accuracy. Accuracy is what 99% of all research in optical flow has been obsessing about for the last 30 years. Stability is not at all something evaluated in the Middlebury benchmark for example. Stability deals with how small changes in your data will guarantee small changes in the estimated optical flow. While some good work has been done in the community (on robust statistics most interestingly) in the end the final evaluation of any algortihm disregards stability. Consider the optical mouse as a good example. The first generations of optical mice had higher accuracy (the average error from the true motion was smaller) but they had lower stability (especially when you ran the mice over "bad textures", with rotational motions). Later generations of optical mouse have worse accuracy, but are focusing on the stability, as that is the most important thing. You dont experience the mouse cursor jumping around as much as you did the earlier days of the devices.... but if you move the mouse on your mat, left and right repeatedly, you will see the cursor slowly drifting (i.e. low accuracy).
Heat. Any device that will estimate high accuracy optical flow, will require lots of computations. When it comes to computations per watt, GPUs are not that good. In drones, you may be able to get away with this, because it is a setting where you have active cooling as a by-product of the propulsion system. In the real-world, you most often can not assume active cooling nor unlimited power supply.
To conclude, its a fascinating area, and I hope you have a great experience coding solutions.
I have been trying to implement a navigation system for a robot that uses an Inertial Measurement Unit (IMU) and camera observations of known landmarks in order to localise itself in its environment. I have chosen the indirect-feedback Kalman Filter (a.k.a. Error-State Kalman Filter, ESKF) to do this. I have also had some success with an Extended KF.
I have read many texts and the two I am using to implement the ESKF are "Quaternion kinematics for the error-state KF" and "A Kalman Filter-based Algorithm for IMU-Camera Calibration" (pay-walled paper, google-able).
I am using the first text because it better describes the structure of the ESKF, and the second because it includes details about the vision measurement model. In my question I will be using the terminology from the first text: 'nominal state', 'error state' and 'true state'; which refer to the IMU integrator, Kalman Filter, and the composition of the two (nominal minus errors).
The diagram below shows the structure of my ESKF implemented in Matlab/Simulink; in case you are not familiar with Simulink I will briefly explain the diagram. The green section is the Nominal State integrator, the blue section is the ESKF, and the red section is the sum of the nominal and error states. The 'RT' blocks are 'Rate Transitions' which can be ignored.
My first question: Is this structure correct?
My second question: How are the error-state equations for the measurement models derived?
In my case I have tried using the measurement model of the second text, but it did not work.
Kind Regards,
Your block diagram combines two indirect methods for bringing IMU data into a KF:
You have an external IMU integrator (in green, labelled "INS", sometimes called the mechanization, and described by you as the "nominal state", but I've also seen it called the "reference state"). This method freely integrates the IMU externally to the KF and is usually chosen so you can do this integration at a different (much higher) rate than the KF predict/update step (the indirect form). Historically I think this was popular because the KF is generally the computationally expensive part.
You have also fed your IMU into the KF block as u, which I am assuming is the "command" input to the KF. This is an alternative to the external integrator. In a direct KF you would treat your IMU data as measurements. In order to do that, the IMU would have to model (position, velocity, and) acceleration and (orientation and) angular velocity: Otherwise there is no possible H such that Hx can produce estimated IMU output terms). If you instead feed your IMU measurements in as a command, your predict step can simply act as an integrator, so you only have to model as far as velocity and orientation.
You should pick only one of those options. I think the second one is easier to understand, but it is closer to a direct Kalman filter, and requires you to predict/update for every IMU sample, rather than at the (I assume) slower camera framerate.
Regarding measurement equations for version (1), in any KF you can only predict things you can know from your state. The KF state in this case is a vector of error terms, and thus you can only predict things like "position error". As a result you need to pre-condition your measurements in z to be position errors. So make your measurement the difference between your "estimated true state" and your position from "noisy camera observations". This exact idea may be represented by the xHat input to the indirect KF. I don't know anything about the MATLAB/Simulink stuff going on there.
Regarding real-world considerations for the summing block (in red) I refer you to another answer about indirect Kalman filters.
Q1) Your SIMULINK model looks to be appropriate. Let me shed some light on quaternion mechanization based KF's which I've worked on for navigation applications.
Since Kalman Filter is an elegant mathematical technique which borrows from the science of stochastics and measurement, it can help you reduce the noise from the system without the need for elaborately modeling the noise.
All KF systems start with some preliminary understanding of the model that you want to make free of noise. The measurements are fed back to evolve the states better (the measurement equation Y = CX). In your case, the states that you are talking about are errors in quartenions which would be the 4 values, dq1, dq2, dq3, dq4.
KF working well in your application would accurately determine the attitude/orientation of the device by controlling the error around the quaternion. The quaternions are spatial orientation of any body, understood using a scalar and a vector, more specifically an angle and an axis.
The error equations that you are talking about are covariances which contribute to Kalman Gain. The covariances denote spread around the mean and they are useful in understanding how the central/ average behavior of the system is changing with time. Low covariances denote less deviation from the mean behavior for any system. As KF cycles run the covariances keep getting smaller.
The Kalman Gain is finally used to compensate for the error between the estimates of the measurements and the actual measurements that are coming in from the camera.
Again, this elegant technique first ensures that the error in the quaternion values converge around zero.
Q2) EKF is a great technique to use as long as you have a non-linear measurement construction technique. Be very careful in using EKF if their are too many transformations in your system, i.e don't try to reconstruct measurements using transformation on your states, this seriously affects the model sanctity and since noise covariances would not undergo similar transformations, there would be a chance of hitting singularity as soon as matrices are non-invertible.
You could look at constant gain KF schemes, which would save you from covariance propagation and save substantial computation effort and time. These techniques are quite new and look very promising. They actively absorb P(error covariance), Q(model noise covariance) and R(measurement noise covariance) and work well with EKF schemes.
Is this because it's a complex problem ? I mean to wide and therefore it does not exist a simple / generic solution ?
Because every (almost) software making signal processing (Avisoft, GoldWave, Audacity…) have this function that reduce background noise of a signal. Usually it uses FFT. But I can't find a function (already implemented) in Matlab that allows us to do the same ? Is the right way to make it manually then ?
Thanks.
The common audio noise reduction approaches built-in to things like Audacity are based around spectral subtraction, which estimates the level of steady background noise in the Fourier transform magnitude domain, then removes that much energy from every frame, leaving energy only where the signal "pokes above" this noise floor.
You can find many implementations of spectral subtraction for Matlab; this one is highly rated on Matlab File Exchange:
http://www.mathworks.com/matlabcentral/fileexchange/7675-boll-spectral-subtraction
The question is, what kind of noise reduction are you looking for? There is no one solution that fits all needs. Here are a few approaches:
Low-pass filtering the signal reduces noise but also removes the high-frequency components of the signal. For some applications this is perfectly acceptable. There are lots of low-pass filter functions and Matlab helps you apply plenty of them. Some knowledge of how digital filters work is required. I'm not going into it here; if you want more details consider asking a more focused question.
An approach suitable for many situations is using a noise gate: simply attenuate the signal whenever its RMS level goes below a certain threshold, for instance. In other words, this kills quiet parts of the audio dead. You'll retain the noise in the more active parts of the signal, though, and if you have a lot of dynamics in the actual signal you'll get rid of some signal, too. This tends to work well for, say, slightly noisy speech samples, but not so well for very noisy recordings of classical music. I don't know whether Matlab has a function for this.
Some approaches involve making a "fingerprint" of the noise and then removing that throughout the signal. It tends to make the result sound strange, though, and in any case this is probably sufficiently complex and domain-specific that it belongs in an audio-specific tool and not in a rather general math/DSP system.
Reducing noise requires making some assumptions about the type of noise and the type of signal, and how they are different. Audio processors typically assume (correctly or incorrectly) something like that the audio is speech or music, and that the noise is typical recording session background hiss, A/C power hum, or vinyl record pops.
Matlab is for general use (microwave radio, data comm, subsonic earthquakes, heartbeats, etc.), and thus can make no such assumptions.
matlab is no exactly an audio processor. you have to implement your own filter. you will have to design your filter correctly, according to what you want.
I'm hoping someone will be able to tell me why no filtering is helping in my application.
I have a MEMS microphone monitoring the pressure of a small chamber, which has a membrane stretched over the far end. This device is placed on a human muscle and when I flex said muscle the membrane is disturbed, producing a pressure difference in the chamber, which the microphone picks up. Therefore, by flexing a muscle I can see nice spikes of activity. However, this method is very susceptible to noise, both motion artefacts and other undesirable artefacts.
The muscle activity I'm interested in is above 10Hz and below 100Hz, so I'm trying to bandpass (or at the very least, highpass) the noise. If I tap the device, or if I have the device on my upper forearm and tap my wrist, I'm to understand that this is a very low frequency noise, somewhere in the region of 1Hz/2Hz, but I can't get rid of this noise!
I'm using MATLAB to process. Generally I sample this microphone at 1KHz, but I currently have it hooked up to a DAQ at 5KHz sampling rate. I desperately want to get rid of this low frequency noise but nothing I try seems to make any difference, it's very hard to see what the filter is doing at all. It's definitely attenuating the signal, but not getting rid of the noise I want. I don't expect perfect results, but certainly better than what I'm seeing.
I've used lots of methods to create filters in MATLAB (manually and fdatool), along with different types of filters (Butterworth, Chebyshev, Elliptic) all not helping. I'm worried that my desired frequency of 10Hz is perhaps too close to the noise I'm trying to filter out, and it's not able to attenuate the noise enough.
Any ideas, code samples, or recommendations would be very helpful.
Tapping or percussive sounds are broad spectrum, producing frequency content well above the repeat rate of 1 Hz or so. So any linear band pass or high pass filter will not be able to completely remove this broad spectrum noise.