16
votes
Accepted
Unscented Kalman Filter for Dummies
I'm going to give you a high-level overview without going into much math. The purpose here is to give you a somewhat intuitive understanding of what is going on, and hopefully this will help the more ...
- 980
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
8
votes
Accepted
What is a good approach for outlier rejection during real time data filtering?
It is both acceptable and standard to use camera observations with a Kalman filter if you are talking about landmark positions in pixel or real-world space. Pixel space observations are usually ...
- 892
7
votes
Open source implementations for GPS+IMU sensor fusion?
Yes. The px4 software for the pixhawk autopilot has an extended kalman filter that uses an accelerometer, a gyroscope, gps, and mag.
A paper describing the a smaller ekf which only estimates attitude ...
- 1,853
7
votes
Accepted
Measurement model for Kalman filter but non-zero mean
There are actually several issues in this question which I will answer separately.
1) Error is: $$\sqrt{(x_m-x_{gt})^2}$$
No, error is just $$(x_m - x_{gt})$$ This may be part of your problem with ...
- 338
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
6
votes
Accepted
Kalman Filter GPS + IMU
This is a complete re-working of the answer I had originally provided. If you're curious, you can check the edit history and see what was posted earlier.
In comments to this question, OP stated that ...
- 16k
6
votes
Accepted
Extended Kalman Filter in robotics - Worth it?
The Kalman filter is an optimal linear filter in the presence of Gaussian noise. It is optimal in the sense that it minimizes the mean-squared error. This means that the covariance of the estimated ...
- 340
5
votes
Accepted
How do I go about implementing a Kalman Filter for a pose estimation algorithm?
It sounds like you're using the camera frames to get a PnP solution, or something along those lines.
A linear Kalman filter will usually work OK for most purposes if you're using roll/pitch/yaw and ...
- 892
5
votes
Alternatives to Kalmam Filter
A good choice for sensor fusion with the MPU6050 is a second order complementary filter, which I used for the orientation estimation in a project. The complementary filter is computational cheap and ...
- 171
5
votes
What's the diffrence between $H_2$ and $H_\infty$ control?
In short answer:
yes
Kalman filter is a special case of an $H_2$ observer
Yes
Yes ... LQG is just Kalman filter + LQR controller, which are both special cases of $H_2$
Depends on the use case. $H_2$ ...
- 2,794
5
votes
Kalman-Filter: how to solve angles near +/-pi?
Here is a paper on the subject. By doing the proper maths with the SO(2) Lie group to represent the angle, they show that the very simple approach of wrapping the predicted state angle to $[-\pi, \pi)...
5
votes
Accepted
Why is the Kalman filter a filter and not a control system?
A Kalman Filter (estimator is actually more apt than filter) simply estimates states, that's all it does. It, by itself, cannot drive a plant towards a desired output. The estimated states are used to ...
- 323
5
votes
Accepted
Kalman Filter with multiple inputs
In fact you can update the filter's state using the input from each sensor separately, you just need to use a different covariance matrix $\mathbf{R}$ and observation matrix $\mathbf{H}$ depending on ...
- 1,353
5
votes
Accepted
cartesian velocity control loop implementation
The orientation error is not simply subtraction of your current pose and the desired pose. Given $\mathbf{R}_{a}, \ \mathbf{R}_{d} \in \text{SO}(3) $, where $\mathbf{R}_{d}$ is your desired ...
- 884
4
votes
Open source implementations for GPS+IMU sensor fusion?
ROS has a package called robot_localization that can be used to fuse IMU and GPS data. This package implements Extended and Unscented Kalman filter algorithms.
The package can be found here.
- 378
4
votes
Accepted
How to use a POMDP-based planner on top of a probabilistic filter
I have used POMDP like models on top of a localization algorithm (Adaptive Monte Carlo Localization, from ROS), and a person detector [1][2] to find and follow a person with a humanoid robot. These ...
- 260
4
votes
Accepted
kalman filter with redundant sensors
Are you sure about your expression for $HH^T$?
I get
$$
HH^T = \begin{bmatrix}
1 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 1 & 0 \\
0 & 0 & 1 & 0 &...
- 106
4
votes
Accepted
Regarding Kalman filter and estimating heading with magnetic compass
I encountered this problem myself when making an extended Kalman filter for a quadrotor.
You have to check if the estimate goes above or below +/- pi, and then correct it if it does.
You can do this ...
- 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
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
Can I write the seperation principle for LQG controllers in this state space form?
Both state space representations are equivalent. For example the eigenvalues of the two closed-loop system matrices should be the same. However when implementing LQG you only have access to the ...
- 941
4
votes
Process noise and Measurement noise in Kalman filter
Basically, the relative magnitude between process and measurement noise determines how much to trust a new sensor measurement. In one extreme, if the process noise is zero the kalman filter will ...
- 2,794
3
votes
Accepted
State estimation of mobile robot
My solution is to use the following model with disturbance only at acceleration and curvature.
$$
\begin{bmatrix}
x_{k+1} \\
y_{k+1} \\
\theta_{k+1} \\
v_{k+1} \\
a_{k+1}...
- 218
3
votes
Need help regarding development of Extended Kalman Filter for sensor-data fusion of odometry and IMU data
Adding to the above, my favorite way to debug a misbehaving filter is to isolate each step.
Make sure your prediction step works before correcting it. Your bot should drive straight right with 0,0,0 ...
- 5,312
3
votes
Overcorrecting Kalman Filter
There is an error in your posted equation for the Jacobian $F_J$, so that could be the source of the problem. It should look like this:
$F_J = \begin{bmatrix}
1 & 0 & -C \sin \theta \\
C \...
- 1,377
3
votes
How much should I expect a Kalman filter to converge?
Let's assume a constant Kalman filter $x_n = Gx_{n-1}+\omega$ with $\omega \sim \mathrm{N}(0, W)$ and $y_n = Fx_n+ \nu$ with $ \nu \sim \mathrm{N}(0,V)$, and initial state $x_0 \sim \mathrm{N}(m_0, ...
- 131
3
votes
Accepted
What kinematic equations should I use for Kalman filter state propagation in IMU based quadcopter navigation?
The first form, from both the math and the webpage to which you link, is for linear motion only.
Tie a string to a rock. Swing the rock around in a circle above your head at a constant speed. If you ...
- 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 ...
- 1,853
3
votes
Accepted
What is the bicycle model for a dynamic robot?
The bicycle model is a simplified model of vehicle dynamics. It's really common so I'm not sure why a web search did not get any results for you.
A random paper, first one in my search that had a ...
- 4,385
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