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
4
votes
Accepted
Visual Odometry terminology: Scale, Relative scale, absolute scale
What does the absolute scale mean? In this context, scale refers to
what property related to an image?
Essentially scale refers to the size of the object/scene that the camera sees.
As a projective ...
- 1,831
3
votes
Accepted
Why Does an Exponential Make ANYTHING a Probability Distribution
I believe it's because you're essentially constructing an exponential distribution which has the form
Because your loss function will always be >= 0, you form a valid PDF (valid in that it ...
- 191
2
votes
Advantage of Kalman filter in differential drive planar robot
It seem that your are missing some intuition about the function of a Kalman filter type filtering method. To a large degree the working principle of the Kalman filter is combining information from ...
- 208
2
votes
Accepted
How to properly initialize every new pose in a Visual SLAM algorithm (namely DSO)?
DSO initializes the scene and camera poses with a specific scale factor such that the average inverse depth of the pointHessians is one. After the initialization the first two frameHessians are led ...
- 36
2
votes
How do I get competent in using c++ for my projects?
I would say that in order to learn C++ up to an acceptable level there is no shortcut: you learn it by using it. And more often than not you learn it by using it together with others that know more ...
- 156
2
votes
Accepted
Kalman Filter Design
The measurements don't get inserted into $H$. The $H$ matrix is the "measurement matrix" or "output matrix" such that you get an estimate of the output when you multiply $H$ by ...
- 16k
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
Accepted
Synthesis gradient observer
As you pointed out, $y=f\left(u\right)$ is a static map, hence it does not represent in any way the temporal evolution of a dynamical system.
With this in mind, resorting to an observer is ...
- 3,995
2
votes
Obtaining Heading vector from IMU
Probably the easiest way to do this would be to convert from Quaternion to Roll-Pitch-Yaw rotations, and then your heading is the Yaw angle.
I'll note that the Yaw angle is not fixed/correct unless ...
- 16k
2
votes
Accepted
How to compute the Hessian matrix in the robustified Gauss-Newton method for optimization
I was reading the same paper today. If you look at equation (3), the objective function is actually
$$\frac{1}{2}\rho(\mathbf{z}(\mathbf{x})^T \mathbf{z}(\mathbf{x})),$$
not what you stated at first
$$...
- 36
2
votes
Accepted
wheeled vehicle forward velocity from RPM brushless data
This project does exactly that on an RC car. The author is a top competitor in the DIYRobocars community; it's the blue car in this video. He uses tachometry from the brushless motor, an IMU and ...
- 356
2
votes
Why Does an Exponential Make ANYTHING a Probability Distribution
To complement what Octopuscabbage correctly reported, there exists a strong theoretical foundation for using normal probability distributions in many different contexts, which builds on the Central ...
- 3,995
2
votes
Rotation of a point in 3D space
1st Rotation of 45 degrees about what axis?
$$x_{new} = R_x(45)R_y(45)R_z(45) x_{old}$$
describes 3 rotations of 45 degrees in all the fixed axis. In that order ($R_x(45)R_y(45)R_z(45)$), you first ...
2
votes
Is Luenberger observer applicable in practical systems?
I don't understand the question here. It seems like the question boils down to "Kalman filters can be adapted to nonlinear systems, so why use Luenberger observers?" There are plenty of ...
- 16k
1
vote
Accepted
UKF for a serie of observations with covariance
It seems that since your "measurements" are just deltas in the state, they should really be considered your control inputs. Intuitively, measurements are supposed to reduce the variance in ...
- 449
1
vote
Unstable principal point estimation in zoom camera calibration
It is very natural to have unstable principal estimation with low distortion.
I don't see any other option rather than just defining spline-based continuous time parameter for your zoom lens and give ...
- 1,527
1
vote
Is this encoder error expected?
This might be "normal", depending on how the signal is acquired. Whenever a signal is derived, timing of the signal acquisition is crucial.
Counting ticks is not time sensitive, as it does ...
- 6,652
1
vote
Estimate noise covariance matrix of measurements using a ros-bag
You can estimate the noise in the kf by adding a covariance state to your state vector. I don't know how practice this is but it can be done.
- 1,853
1
vote
Applying Rotation & Translation Matrix Obtained from Iterative Closest Point
I don't know if your confusion is with applying the transform to the points or applying it to the pose. So I'll just show you both.
The easiest way is to store your points and transform in the ...
- 1,831
1
vote
How do you handle angle discontinuities in estimation problems?
As mentioned by @long-smith the standard solution is to use quaternions.
However if you specifically are asking how to deal with errors using angles that are modulo $2\pi$ you are going to want to add ...
- 24.7k
1
vote
Reset coordinate system of robot while maintaining relationship to the previous
Instead of just considering it a reset, you should consider it a coordinate system transformation:
You set the position to zero, that means that you create a transformation matrix which brings your ...
- 6,652
1
vote
Accepted
How can I compute the covariance of a camera-based relative pose measurement?
Typically, when doing this type of pose estimation, the essential matrix would be wrapped inside of RANSAC. i.e., you would have a lot of candidate point correspondences and would randomly sample 5 of ...
- 324
1
vote
Accepted
Fusing IMU sensor with odometry
Yes.
Example of this can be found here.
Depending on how good your modeling is you could also use the IMU to help detect wheel slippage.
- 1,831
1
vote
The biases in the state vector of Extended Kalman Filter(EKF)
Indeed position, velocity and acceleration (but also the unit quaternion and the angular velocity of the gyroscope) are related to each other. But the word "biases" refers to the measurement of these ...
- 941
1
vote
Orientation from magnetometer data
Usually the magnetometer is used to find the yaw. It acts as a digital compass in this case. To calculate roll and pitch you need an accelerometer. But there are some techniques that can be used to ...
- 354
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
Methods for state estimation and real-time path planning of a mobile robot
I am assuming that by real time path planning, you mean starting off in a partially known environment and updating your 'plan' as you gain more knowledge through your SLAM algorithm. For a real world ...
- 1,096
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