9
votes
Accepted
How exactly does sensor fusion work in Kalman filters?
I realize this question already has an accepted answer, but I'd like to provide some additional input. The question of sensor fusion is a good one, but, depending on the application, you don't ...
- 126
6
votes
Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?
If the drone is not falling (holding height in the sky), and it's not accelerating in any particular direction, then the accelerometer should be reading:
$$
a = \left[ \begin{array}{}
g_x \\
g_y \\
...
- 16k
4
votes
Accepted
Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?
I encountered the same puzzle. I had a clue at the beginning that the gravity information is contained within accelerometer measurements due to aerodynamic drag. Then I found a paper The True Role of ...
- 56
4
votes
Choosing the state vector for an EKF
In general, I try to obey the following two rules when selecting states:
Only use the states necessary for control, and
Choose states to be measurable properties, whenever possible.
For example, on ...
- 16k
3
votes
Accepted
What is the intuitive explanation of using Jacobian of observation model while calculating Kalman gain in EKF SLAM?
Let's try breaking it down.
Projection of uncertainty
$H\Sigma H^T$ is projecting the state uncertainty into measurement space. How do we know that?
$\Sigma$ denotes the the covariance of our ...
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3
votes
Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?
Accelerometers measure kinematic acceleration with the addition of gravity. So for an accel to measure 0, the vehicle would need to be accelerating downward at $g$. To get inertial acceleration out of ...
- 1,853
3
votes
Plotting location using wheel encoder data
A few things:
I took a look at your data set. Did you make sure you used the time column correctly? The first entry is "1429481388546050050" without the decimal. To make it in seconds, it should be ...
- 980
3
votes
Multi-Rate Sensor Fusion using EKF
Part 1. Use one or the other. Often odometery is used instead of kinematics or dynamics for prediction, at least in my work.
Part 2.
This is handled by the construction of the measurement equation ...
- 5,312
3
votes
Why innovation equation in Extended Kalman filter is called innovation?
From the Wikipedia entry:
In time series analysis (or forecasting) — as conducted in statistics, signal processing, and many other fields — the innovation is the difference between the observed ...
- 16k
3
votes
what exactly is 'observation model' for a robot
An observation model is what relates your measurement to your states. For example, you might have a state that is vehicle speed, but the only thing you can measure is tire RPM. Tire RPM is not vehicle ...
- 16k
2
votes
Multi-Rate Sensor Fusion using EKF
I've performed 2D localization with just odometry and a gyroscope before, and to be honest, depending on (i) how good your encoders are; (ii) what type of environment you're in (is there a chance your ...
- 980
2
votes
Should I use or not EKF for Baro-Acc altitude estimation?
EKFs are appropriate when you have nonlinear equations describing the system, either in the system dynamics or the measurement dynamics. In this case, I think a plain KF should be sufficient assuming ...
- 1,853
2
votes
Plotting location using wheel encoder data
Thanks for the update. Now it looks like $x_c$ and $y_c$ denote the origin/starting position, and $\theta$ is positive, measured CCW from the positive x-axis. Now I am even more concerned about the ...
- 16k
2
votes
Accepted
Unscented Kalman Filter VS Extended Kalman Filter on stability
You mentioned that EKF wasn't very robust for your application. This means that the continuous time model is considerably non-linear. In this setting, the UKF is better than the EKF and handles the ...
- 146
2
votes
How is gyroscope bias exposed and tracked?
I think you're confused. The method you're talking about would only really work if you know the magnitude and orientation of the accelerations you're trying to measure. If that's the case, then why ...
- 16k
2
votes
EKF singularity problem when measurement noise R is zero
I think you need to step back a bit and think beyond the math. An (E)KF is used to estimate the true value of a signal in the presence of noise; it's only because of this noise that we even need the ...
- 2,794
2
votes
Accepted
extended kalman filters, linearization of output
Hi and welcome to stack exchange: robotics edition.
Yes. Your derivation for the landmark update Jacobian is correct. If you are doing SLAM with respect to the landmarks, don't forget to form the ...
- 5,312
2
votes
Accepted
EKF sensor fusion
An EKF or any of the variants of the Kalman filter, as you said mainly works in two steps: prediction and correction. The prediction steps gives you a state estimate based on your process model and ...
- 124
2
votes
Accepted
Is the covariance matrix in the extended Kalman filter guaranteed to be positive definite (ignoring numerical errors)?
It is always guaranteed to be positive semi definite.
That being said you have to somewhat deliberately set up your system to be that way. So essentially yes it is always positive definite.
Reasoning:
...
- 1,831
2
votes
No difference between UKF and EKF for SLAM
The EKF is a first-order approximation, which is achieved by linearizing the system about the current state estimate (i.e., the mean). In some cases, the EKF is not stable due to nonlinearities. For ...
- 335
2
votes
Accepted
EKF slam vs global bundle adjustment
I am assuming your pipeline is that you are running an EKF SLAM algorithm over some data to estimate a set of initial poses and landmarks, and then you feed all of these states into a global bundle ...
- 1,831
2
votes
Extended Kalman Filter and PID controller
You always act on the estimated state, because if you knew the actual state then you wouldn't need an estimator!
Since you're in simulation, you could run the same test several times, running the PID ...
- 16k
1
vote
GPS/ 1GYRO - 2D + ACCEL+GPSEKF
Low cost accelerometers have a bias that varies with temperature and from startup to startup. Your model does not appear to have a state to simulate these accelerometer bias offsets. Note that in ...
- 146
1
vote
How to avoid matrix singularity in GraphSLAM
If $\Omega$ is singular, you cannot avoid a matrix singularity. This is like saying you want to solve the system of equations $$x = 1$$ $$x = 7$$
There are many techniques to avoid robotic ...
- 4,386
1
vote
Accepted
Confusion of EKF equations
For your first question, $F(x, j)$ is a $6 * 3N + 3$ dimensional matrix. Why? $F(x, j)$ is a factor of $H_t^i$. The reason $H_t^i$ is a $3 * 3N + 3$ matrix is because of the problem set up. We are ...
- 493
1
vote
EKF implementation on odometry/IMU
Try this dataset, Localization and Mapping Dataset. It will be helpful for your problem.
1
vote
Tracking vehicle 6 states extended kalman filter required?
there is some error in your matrix I think. P(k+1)=V(k) And
V(k+1)=A(k) so I don't kwon what is the A(k+1) maybe the jerk(jolt) of the vehicle.
- 11
1
vote
Accepted
Tracking vehicle 6 states extended kalman filter required?
If you can write the dynamics with a matrix, which you have, then a normal kalman filter will be best.
However, your measurements will probably be nonlinear. You will find that you won't be able to ...
- 1,853
1
vote
Accepted
Robot heading uncertainty values
No, the uncertainty should not be wrapped.
Remember, uncertainty is fundamentally different than angle. At the most trivial level, uncertainty cannot be negative or even zero (i.e. $\sigma_\theta >...
- 2,794
1
vote
Extended Kalman Filter for IMU
There are a couple of potential traps with the scenario you seem to be outlining. Many of them have already been addressed in literature on inertial navigation. You can find many good references on ...
- 11
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