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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 ...
user96966's user avatar
  • 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 \\ ...
Chuck's user avatar
  • 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 ...
V. Yao's user avatar
  • 56
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 ...
Chuck's user avatar
  • 16k
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 ...
holmeski's user avatar
  • 1,853
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 ...
Jacob Panikulam's user avatar
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 ...
Chuck's user avatar
  • 16k
2 votes

Direct vs semi-direct methods for visual inertial odometry

The answer to your question is explained clearly and well classified in the introduction of this paper Direct Sparse Odometry. Also, I would recommend you to read another representative semi direct ...
Chanoh Park's user avatar
  • 1,577
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 ...
holmeski's user avatar
  • 1,853
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 ...
Vignesh's user avatar
  • 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 ...
Chuck's user avatar
  • 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 ...
ryan0270's user avatar
  • 2,814
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 ...
Josh Vander Hook's user avatar
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 ...
Vishnu Prem's user avatar
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: ...
edwinem's user avatar
  • 1,871
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 ...
Ralff's user avatar
  • 345
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 ...
edwinem's user avatar
  • 1,871
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 ...
Chuck's user avatar
  • 16k
1 vote

Doubt with linearization and discretization process - Ekf

concerning the first symbol, it represents the identity matrix of the appropriate size. then equation (20) is used for (14)-(19) and the matrix is $\Omega(\omega)$, it applies for continuous space, ...
N. Staub's user avatar
  • 1,412
1 vote

provide world map for ekf global localization problem

In EKF slam generally we include landmarks which can be marked as points: Corners, columns, trees etc. The uncertainties for landmarks are calculated by assuming that those are point landmarks. (1) ...
Tharindu Suraj's user avatar
1 vote
Accepted

EKF localization data association

It should be processed features. Extracting features from raw data is usually called as front-end in SLAM. The easiest forms of features in cased of 2D LiDAR are corners, edges, and lines. You can run ...
Chanoh Park's user avatar
  • 1,577
1 vote
Accepted

GraphSLAM equation doubt

1) I believe the previous replies/comments already directed you to good online resources. I will just add some comments about the intuition behind the equations. Putting aside SLAM, in general ...
al-dev's user avatar
  • 331
1 vote

GraphSLAM equation doubt

As I mentioned previously, this isn't my topic of expertise, but I'll again point out the passage on page 417 of the Thrun paper: The algorithm GraphSLAM_solve in Table 4 calculates the mean and ...
Chuck's user avatar
  • 16k
1 vote

How to detect loop in robot movement observing odometer data

I haven't heard of residual uncertainty in the context of robotics, but I would imagine what you're getting at is the fact that odometry data has an inherent amount of uncertainty because of minor ...
Chuck's user avatar
  • 16k
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 ...
SteveO's user avatar
  • 4,396
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 ...
koverman47's user avatar
1 vote

EKF implementation on odometry/IMU

Try this dataset, Localization and Mapping Dataset. It will be helpful for your problem.
Saswati Bhattacharjee's user avatar
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.
dikay97's user avatar
  • 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 ...
holmeski's user avatar
  • 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 >...
ryan0270's user avatar
  • 2,814

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