Questions tagged [kalman-filter]

A Kalman filter is an optimal estimator for linear dynamical systems with Gaussian noise. Extensions to non-linear systems are included through the Extended KF and Unscented KF.

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11
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3answers
14k views

How to rotate covariance?

I am working on an EKF and have a question regarding coordinate frame conversion for covariance matrices. Let's say I get some measurement $(x, y, z, roll, pitch, yaw)$ with corresponding 6x6 ...
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1answer
188 views

Slam and Vision (good resources)? [closed]

I would like to know if there is a good source that combines Slam problem with vision. From mathematical perspective, there are numerous resources that handle SLAM ,however, I didn't find a good ...
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1answer
126 views

Can motion model noise be zero?

Can I assume the noise of motion model to be zero? If so, what are the consequences of doing so?
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2answers
3k views

covariance matrix in EKF?

I'm struggling with the concept of covariance matrix. $$ \Sigma = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{x \theta} \\ \sigma_{yx} & \sigma_{yy} & \sigma_{y \theta} \\ \...
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1answer
193 views

Explanation of the Kalman Filter [closed]

I am a beginner in robotics, and I am learning about the Kalman filter. I do not seem to get it, though. I am a mathematician, and so it would be helpful if the Kalman filter could be explained in a ...
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2answers
91 views

What is the Kalman Filter in the basics of its aspects? [closed]

My question is very broad. However I would like a complete description to the very last detail in a way that a foreign exchange student would understand. I want to try my best to master the way the ...
5
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1answer
418 views

Overcorrecting Kalman Filter

I'm trying to get an extended Kalman Filter to work. My System Model is: $ x = \begin{bmatrix} lat \\ long \\ \theta \end{bmatrix}$ where lat and long are latitude and longitude (in degree) and $\...
6
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2answers
361 views

Kalman Filter and the state noise vector?

I'm reading Probabilistic Robotics by Thrun. In the Kalman filter section, they state that $$ x_{t} =A_{t}x_{t-1} + B_{t}u_{t} + \epsilon_{t} $$ where $\epsilon_{t}$ is the state noise vector. And ...
10
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2answers
1k views

Extended Kalman Filter with Laser Scan + Known Map

I am currently working on a project for school where I need to implement an extended Kalman Filter for a point robot with a laser scanner. The Robot can rotate with 0 degree turn radius and drive ...
3
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2answers
231 views

Do I need an accurate flight model for a UAV?

As I understand it, a Kalman filter uses a mathematical model of the robot to predict the robot's state at t+1. It then combines that prediction with information from sensors to get a better sense of ...
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1answer
630 views

EKF partial state update question

This is a follow up to Maintaining positive-definite property for covariance in an unscented Kalman filter update ...but it's deserving of its own question, I think. I am processing measurements ...
7
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1answer
5k views

Maintaining positive-definite property for covariance in an unscented Kalman filter update

I have an unscented Kalman filter (UKF) that tracks the state of a robot. The state vector has 12 variables. Each time I carry out a prediction step, my transfer function (naturally) acts on the ...
4
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2answers
1k views

Jacobian of the observation model? [closed]

The state vector is $$ \textbf{X} = \begin{bmatrix} x \\ y \\ v_{x} \\ v_{y} \end{bmatrix}$$ transition function is $$ \textbf{X}_{k} = f(\textbf{X}_{k-1}, \Delta t) = \begin{cases} x_{k-1} + v_{...
6
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1answer
907 views

What to do when the control input of the Kalman filter is unknown?

I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope. Say at time $t-dt$, the compass reports a reading $\...
9
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2answers
1k views

How to model unpredictable noise in Kalman Filter?

Background: I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope. My Understanding: I am thinking about ...
0
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1answer
156 views

existence probability of an object in fusion

I want to compute an existence probability of an object in a sensor fusion on the high level (having from each sensor list of objects already filtered with e.g. Kalman Filter). There are these ...
3
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1answer
484 views

Is there a benefit to using 2 IMU units on a UAV set at different sensitivities?

I noticed that some IMU units are tuned to be sensitive to small changes, other to large changes and some that can be adjusted between different sensitivities. I am familiar with the use of a Kalman ...
7
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2answers
509 views

object level sensor fusion for multiobject tracking

I want to fuse objects coming from several sensors, with different (sometimes overlapping!) fields of view. Having object lists, how can I determine whether some objects observed by different sensors ...
7
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3answers
2k views

information filter instead of kalman filter approach

I read many sources about kalman filter, yet no about the other approach to filtering, where canonical parametrization instead of moments parametrization is used. What is the difference? Other ...
8
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2answers
278 views

At which stage should filtering be applied to the sensors data?

Shall I filter (kalman/lowpass) after getting the raw values from a sensor or after converting the raw values to a usable data? Does it matter? If so, why? Example: Filter after getting raw values ...
5
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7answers
1k views

Source to learn Kalman Fusion, explanatory code snippets

Currently I am reading a book of Mr. Thrun: Probabilistic Robotics. I find it really helpfull to understand concept of filters, however I would like to see some code in eg. Matlab. Is the book "Kalman ...
6
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2answers
1k views

Taylor Series expansion for EKF

In Probablistic Robotics by S. Thrun, in the first section on the Extended Kalman Filter, it talks about linearizing the process and observation models using first order Taylor expansion. Equation ...
9
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1answer
490 views

Chaining Kalman filters

My team is building a robot to navigate autonomously in an outdoor environment. We recently got a new integrated IMU/GPS sensor which apparently does some extended Kalman filtering on-chip. It gives ...
14
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3answers
4k views

Extended Kalman Filter using odometry motion model

In the prediction step of EKF localization, linearization must be performed and (as mentioned in Probabilistic Robotics [THRUN,BURGARD,FOX] page 206) the Jacobian matrix when using velocity motion ...
7
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1answer
218 views

Can you seed a Kalman filter with a particle filter?

Is there a way of initializing a Kalman filter using a population of particles that belong to the same "cluster"? How can you determine a good estimate for the mean value (compute weighted average ?) ...
7
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1answer
765 views

Noise in motion and measurement models

When using an EKF for SLAM, I often see the motion and measurement models being described as having some noise term. This makes sense to me if you're doing a simulation, where you need to add noise ...
16
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2answers
2k views

EKF-SLAM Update step, Kalman Gain becomes singular

I'm using an EKF for SLAM and I'm having some problem with the update step. I'm getting a warning that K is singular, rcond evaluates to ...
28
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2answers
24k views

How to fuse linear and angular data from sensors?

My team and I are setting up an outdoor robot that has encoders, a commercial-grade IMU, and GPS sensor. The robot has a basic tank drive, so the encoders sufficiently supply ticks from the left and ...
8
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1answer
197 views

What kind of performance can I expect when using an Extended Kalman Filter for calibration and localization?

Currently I have a tricycle style robot that uses an extended kalman filter in order to track 6 state variables. The inputs to the system are a steer encoder, a distance encoder, and a rotating laser ...
64
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5answers
10k views

Why do I need a Kalman filter?

I am designing an unmanned aerial vehicle, which will include several types of sensors: 3-axis accelerometer 3-axis gyroscope 3-axis magnetometer horizon sensor GPS downward facing ultrasound. A ...
17
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3answers
4k views

What are good methods for tuning the process noise on Kalman filters?

Most often tuning the Kalman filter noise matrices is done by trial and error or domain knowledge. Are there more principled ways for tuning all the Kalman filter parameters?

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