# Tag Info

## Hot answers tagged estimation

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 ...
• 106
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 ...

### 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 ...
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 ...
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### 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 ...
• 146
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### 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 ...
• 15.1k
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### 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: ...
• 1,581
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### 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 ...
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### 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 ...
• 306

### 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 ...
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### 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 ...
• 15.1k
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### 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 ...
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 ...
• 434
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### 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 ...
• 6,497
1 vote

### 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 ...
• 3,700
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### 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.
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### 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 ...
• 1,581
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 ...
• 1,364
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 ...
• 6,497
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 ...
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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.
• 1,581
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
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### 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 ...
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.
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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 ...
• 1,823
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 ...
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