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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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61
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5answers
9k 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 ...
26
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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 ...
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?
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 ...
15
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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} \\ \...
13
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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 ...
11
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1answer
3k views

Ambiguous definition of Error-State (Indirect) Kalman Filter

I am confused by what precisely the term "Indirect Kalman Filter" or "Error-State Kalman Filter" means. The most plausible definition I found is in Maybeck's book [1]: As the name indicates, in ...
10
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1answer
2k views

Why should I still use EKF instead of UKF?

The Unscented Kalman Filter is a variant of the Extended Kalman Filter which uses a different linearization relying on transforming a set of "Sigma Points" instead of first-order Taylor series ...
9
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2answers
881 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 ...
9
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3answers
11k 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 ...
9
votes
1answer
451 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 ...
9
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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 ...
8
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1answer
1k views

Multiple position estimates fusion

I have a system in which I have two separate subsystems for estimating robot positions. First subsystem is composed of 3 cameras which are used for detecting markers the robot is carrying and which ...
8
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1answer
2k views

What is the best way to fuse measurements from IMU, LIDAR, and Encoder information in some recursive bayesian filter?

I am doing SLAM with a four wheeled (2-wheel drive) differential drive robot driving through some hall way. The hallway is not flat everywhere. And the robot turns by spinning in place, then traveling ...
8
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2answers
258 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 ...
8
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1answer
182 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 ...
7
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3answers
1k 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 ...
7
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1answer
705 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 ...
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 ...
7
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2answers
486 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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1answer
603 views

kalman filter with redundant sensors

Suppose I have one robot with two 3D position sensors based on different physical principles and I want to run them through a Kalman filter. I construct an observation matrix two represent my two ...
6
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1answer
2k views

Uncented Kalman Filter for Dummies

I need some help here because I can't figure how the Unscented Kalman Filter works. I've searched for examples but all of them are too hard to understand. Please someone can explain how it works step ...
6
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2answers
16k views

Open source implementations for GPS+IMU sensor fusion?

Are there any Open source implementations of GPS+IMU sensor fusion (loosely coupled; i.e. using GPS module output and 9 degree of freedom IMU sensors)? -- kalman filtering based or otherwise. I did ...
6
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2answers
927 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 ...
6
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2answers
341 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 ...
6
votes
1answer
211 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 ?) ...
6
votes
1answer
877 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 $\...
6
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2answers
268 views

Ensemble Kalman Filter SLAM

I know that there is an extended kalman filter approach to simultaneous localization and mapping. I'm curious if there is a SLAM algorithm that exploits the ensemble kalman filter. A citation would ...
5
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7answers
994 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 ...
5
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3answers
33k views

How to estimate yaw angle from tri-axis accelerometer and gyroscope

I would like to estimate the yaw angle from accelerometer and gyroscope data. For roll and pitch estimate I've used the following trigonometric equations: ...
5
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2answers
1k views

What is a good approach for outlier rejection during real time data filtering?

I'm trying to finish up a localization pipeline, and the last module I need is a filtering framework for my pose estimates. While a Kalman filter is probably the most popular option, I'm using cameras ...
5
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2answers
496 views

Need help regarding development of Extended Kalman Filter for sensor-data fusion of odometry and IMU data

I'm trying to develop an Extended Kalman Filter (EKF) for the positioning of a wheeled vehicle. I have a 'Baron' robot frame with 4 static wheels, all driven by a motor. On the 2 rear wheels I have an ...
5
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1answer
779 views

Regarding Kalman filter and estimating heading with magnetic compass

I have trouble estimating the heading when close to the "pivot" point of the compass, and could use some input on how to solve it. I have set up my angles to be from 0-360 degrees during the testing ...
5
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1answer
628 views

Solution for INS and GPS integration

I have a GPS module and an IMU (gyro, accelerometer and magnetometer) and I need to build an autonomous navigation system for a quadcopter. It must know its position at any time so that it can track a ...
5
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1answer
1k views

Simple Sensor Fusion for pose estimation

I am currently working on a balancing robot project, which features fairly low-cost sensors such as an 9-Dof IMU with the measurement states $\textbf{x}_\text{IMU} = \left[a_x, a_y, a_z, g_x, g_y, ...
5
votes
1answer
588 views

How to choose the state space model for 1 axis gyroscope to implemnt a good kalman filter

I am using this gyroscope in order to measure the rotation of my robot around the z axis. I want to implement a kalman filter in order to improve the values. What i came with since now is this space ...
5
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3answers
1k views

How exactly does sensor fusion work in Kalman filters?

I've been looking into implementations of Extended Kalman filters over the past few days and I'm struggling with the concept of "sensor fusion". Take the fusion of a GPS/IMU combination for example, ...
4
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2answers
283 views

Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?

I'm currently developing an EKF to estimate the position and orientation of a quadcopter. My state vector is comprised of 3D position, 3D velocity, 3 euler angles and the angular velocity vector. ...
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_{...
4
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1answer
169 views

Modeling a robot to find its position

The task of the robot is as follows. My robot should catch another robot in the arena, which is trying to escape. The exact position of that robot is sent to my robot at 5Hz. Other than that I can use ...
4
votes
2answers
6k views

Kalman Filter GPS + IMU

I know this probably has been asked a thousand times but I'm trying to integrate a GPS + Imu (which has a gyro, acc, and magnetometer) with an Extended kalman filter to get a better localization in my ...
4
votes
2answers
852 views

What is the bicycle model for a dynamic robot?

I was asked this in a phone interview for a robotics job. Googling has not really helped. I assume it is some sort of state prediction model that can be used in a Kalman filter. Can anyone give me a ...
4
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1answer
260 views

How to use a POMDP-based planner on top of a probabilistic filter

POMDPs extend MDPs by conceiling state and adding an observation model. A POMDP controller processes either action/observation histories or a bayesian belief state, computed from the observations (...
4
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3answers
6k views

How much should I expect a Kalman filter to converge?

I am learning about Kalman filters, and implementing the examples from the paper Kalman Filter Applications - Cornell University. I have implemented example 2, which models a simple water tank, ...
4
votes
1answer
405 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 $\...
4
votes
1answer
2k views

Kalman filter GPS + IMU fusion get accurate velocity with low cost sensors

I'm new to all this robotics stuff. Especially to Kalman filter. My initial goal is to have velocity as accurate as possible Here is my case: I have a phone which is mounted, for example in the ...
4
votes
2answers
714 views

Structuring EKF to estimate pose and velocity with odometry inputs

I have a differential drive robot for which I'm building an EKF localization system. I would like to be able to estimate the state of the robot $\left[ x, y, \theta, v, \omega \right]$ where $x, y, \...
4
votes
1answer
831 views

Kalman filter Issue - GPS Odometry Fusion

I am working on estimating a robots pose using Odometry and GPS. My first problem is that all kinematic model i have seen for a differential drive robot proposes using the displacement of the left ...
4
votes
2answers
95 views

Delayed Kalman navigation based on two way ranges

I am interested to know the basic principle of the "Delayed KF" when considering an underwater robot aiming to localize it self using a LBL system. More practically, in order to calculate the ...
4
votes
1answer
170 views

Why doesn't this kalmanfilter filter anything? Reduce disturbances and noises with LQG controller

I have a state space model which look like this: $$ \ \begin{bmatrix} \dot{x} \\ \\\dot{\tilde{x}} \end{bmatrix} =\begin{bmatrix} A - BL& BL \\ 0 & A-KC \end{bmatrix} \begin{bmatrix} x\\ \...