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7 votes
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the uncertainty of initializing new landmark in EKF-SLAM

You can use the Jacobians of the inverse observation model to initialize the new row/column of the covariance matrix. Suppose your observation model is $g(\mathbf{x})$, which maps your state $\...
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6 votes
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Why should I still use EKF instead of UKF?

Here are a few possible points of consideration. Certainly the UKF has many counterpoints where it has an advantage too. The most obvious advantage is computation power. Don't forget that ...
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  • 2,679
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 \\ ...
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6 votes
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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 ...
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5 votes
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EKF SLAM and Mahalanobis distance?

The value of $\alpha$ is just some threshold Mahalanobis distance. Let's say you have four entries in your map. You take a measurement, then you calculate four predicted measurements (one for each ...
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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 ...
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4 votes
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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 ...
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  • 56
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 ...
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3 votes
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how to plot $\pm 3 \sigma$ of a landmark in EKF-SLAM

What you are referring to is plotting the estimate with the uncertainty bounds - in particular the $3\sigma$ ($\pm3$ standard deviations) bounds which corresponds to 99.7% probability that the true ...
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3 votes

Mahalanobis distance between 2 line features

There are many ways to measure the statistical difference between two distributions. For your case, you might consider the Bhattacharyya distance. From that page, the Bhattacharyya distance $D_B$ is $...
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  • 950
3 votes

Extended Kalman Filter with Laser Scan + Known Map

Using EKF for localisation based on laser scans and a known map is a bad idea and will not work because one of EKF's main assumptions is not valid: The measurement model is not differentiable. I ...
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3 votes
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innovation step ekf localization?

Yes this is correct, given two assumptions: Each measurement is independent (i.e., the (Gaussian) distribution of observation $z_i$ is uncorrelated with $z_j$). Usually this is a fair assumption (e.g....
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  • 950
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 ...
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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 ...
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  • 1,825
3 votes
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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

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 ...
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2 votes

EKF localization known correspondences

The underlying assumption seems to be that if all observed features you measure at the same time are independent, you can apply the EKF correction step several times: Once for each observed feature. (...
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2 votes
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sparse matrix in EKF SLAM

It is certainly your second guess, i.e.: $$ F_{x,j} = \begin{bmatrix} 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 &...
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  • 3,210
2 votes

Maximum likelihood estimator (ML Data Association) EKF

Getting a value larger than 1 in a pdf is normal. Remember that the pdf does not actually evaluate to a probability itself, but to a density. Only the integral over the function has to evaluate to 1. ...
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  • 2,954
2 votes

how to plot $\pm 3 \sigma$ of a landmark in EKF-SLAM

Unless I misunderstood what you're trying to show on this plot, you want to essentially plot your estimate (or, in this case, the estimation error) with its 3 standard deviation bounds. What you have ...
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  • 21
2 votes
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joint compatibility branch and bound (JCBB) data association implementation

Suppose you have three measurements (1, 2, and 3) and four landmarks (a, b, c, d). The joint compatibility is a measure of how well a subset of the measurements associates with a subset of the ...
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  • 950
2 votes
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Open source implementations of EKF for 6D pose esimation

I believe this should tick all your boxes: http://wiki.ros.org/robot_localization It's a ROS node for 6D pose estimation that has the following features: Fusion of an arbitrary number of sensors. ...
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  • 532
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 ...
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  • 950
2 votes
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EKF-SLAM Computing the jacobians for landmark updates

The answer Specifically, the arguments to this jacobian are the state of the robot. The reason It is the jacobian of the measurement function with respect to the landmark state. If you knew the ...
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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 ...
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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 ...
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2 votes
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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 ...
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  • 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 ...
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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 ...
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  • 2,679
2 votes
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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 ...
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