# 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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### Orientation estimation using gyro and accelerometer when sensor platform has high acceleration

I am trying to estimate the orientation of a sensor platform using gyroscope and accelerometer. I am using a Kalman filter based approach. I integrate the readings ...
1answer
125 views

### The final step in kalman filter to correct/update the covariance matrix

I see that, in the correction step of Kalman filter, there is an equation to update the covariance matrix. I have been using it in the form: P = (I - KH)P' Here ...
0answers
148 views

### Kalman filter for slow ground vehicle with RTK

I have been using dual RTK receivers for my tractor projects. This gives me reliable position, heading, and tilt at low rates (10 Hz). I recently began working with an INS (an Advanced Navigation ...
1answer
38 views

### Transforming an inverse covariance matrix

I have a linear map, $J$, from one space to another. I can transform a covariance matrix, $P$, from one space to another by using: $P' = JPJ^{T}$ However, in my situation I have an inverse ...
1answer
313 views

### Rotation composition When using Kalman Filter

I am implementing a Kalman Filter for the following situation. I have a camera set in a room that can detect the position and orientation of a marker (ARUCO) in the room. Therefore I have the ...
2answers
105 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 ...
1answer
72 views

### Why does a Bayesian Filter require random controls?

As stated in Probabalistic Robotics, the proof for correctness of a Bayesian Filter relies on the fact that $$p(x_{t-1}|z_{1:t-1},\ u_{1:t}) = p(x_{t-1}|z_{1:t-1},\ u_{1:t-1})$$ In order to justify ...
2answers
145 views

### Robot heading uncertainty values

I'm tracking the state of a robot using an EKF defined by: $$(x,y,\theta)$$ where $x$ and $y$ are the coordinates in the ground-plane and $\theta$ the heading angle. I initialized the covariance ...
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### 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\\ \...
2answers
598 views

### Can I write the seperation principle for LQG controllers in this state space form?

Look at this picture. This is the seperation principle diagram. It is an LQG controller which going to control the real life process. What I want to do, is to create a state space model for this ...
1answer
714 views

### Guessing the K matrix gain for the Optimal Control LQR?

I'm are going to create a LQR to control a system. The problem is to choose the Q and R weighting matrices for the cost function. The Q and R matrices are going to minimize the cost function so the ...
2answers
252 views

### Kalman filter prediction questions [closed]

I have a dataset where measurements were taken at 1 Hz, and I am trying to use a Kalman filter to add predicted samples in between the measurements, so that my output is at 10 Hz. I have it ...
1answer
269 views

### What is the intuitive explanation of using Jacobian of observation model while calculating Kalman gain in EKF SLAM?

The idea of using Kalman gain in EKF SLAM is to figure out how much we trust our motion model and sensor/observation model. As explained in The Extended Kalman Filter: An Interactive Tutorial for Non-...
1answer
126 views

### Why EKF-SLAM uses EKF instead of linear Kalman Filter?

I am writing a bachelor's diploma on vSLAM. I learned and programmed EKF-SLAM like it's written in MonoSLAM paper, and I was going to write, that I can't use KF and have to use EKF because of non-...
2answers
308 views

### Is it possible that a quadcopter hold height for long time stable only using IMU (without GPS) and barometer?

As we know, we can calculate altitude from barometer readings, and a UAV can hold height by referring to these data. However the real air pressure is varying with many conditions. These variance will ...
2answers
363 views

### Can i use a predictive kalman filter to 'increase' my sample rate?

I have a slam algorithm that outputs at around 30Hz, an implementation of ORBSLAM2. https://github.com/raulmur/ORB_SLAM2 I am reading this into a renderer that expects 60+ Hz. Because my sample ...
1answer
319 views

### How to model transition matrix in indirect kalman filter with external orientation estimate

I am trying to implement an indirect/error state kalman filter following Quaternion kinematics for the error-state Kalman filter. However, instead of modelling the orientation and error in orientation ...
0answers
121 views

### Help with fusing multiple measurements with known covariances

I am working on an estimation application for multiple robots, each of which uses measurements from various sources to calculate position and orientation data. For now, I am looking at about three ...
1answer
186 views

### Why does one IMU axis influence another?

For a home robotics project I just bought a BerryIMU to connect it to my Raspberry Pi. After hooking it up I ran the provided Python code to read out some values while moving it around. If I keep the ...
0answers
122 views

### What's the mathematical definition of quaternion 3x3 covariance matrices, and how does it relate to euler angles?

I'm adapting a KF orientation filter that represents the orientation as quaternion, and uses a 3x3 covariance matrix. Would someone know what 3x3 covariance represents in the case of a quaternion, and ...
4answers
1k views

### Alternatives to Kalmam Filter

I am currently working on a self balancing robot project. I am going to use a MPU6050 to get data from both the accelerometer and the gyroscope. Since I need to get accurate data in a very small ...
0answers
130 views

### How does a measurement model for camera based PNP work?

I am trying to write an EKF that can estimate the covariance of a pose estimate, where the estimation is being done by a PNP algorithm and 3D-2D correspondences in images. Although EKF based camera ...
1answer
218 views

### Question about EKF covariance equations

I am trying to perform uncertainty aware planning, where my planner tries to connect start and goal in such a way that the resultant path provides the least covariance at the end. This is inspired by ...
2answers
982 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 ...
2answers
7k 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 ...
3answers
362 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. ...
1answer
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### EKF state propagation model using variables that are not part of state vector

I am trying to understand the EKF theory. Can the state transition function depend on variables that are not part of the state space? For example, the state propagation below depends on the ...
1answer
819 views

### How to implement a particle filter when sensors can't identify landmarks?

I'm attempting to build a robot that leverages a particle filter to identify where it is relative to a map that is known. The robot only has IR sensors, so while it is able to determine its distance ...
1answer
884 views

### What kinematic equations should I use for Kalman filter state propagation in IMU based quadcopter navigation?

I am working on implementing a Kalman filter for position and velocity estimation of a quadcopter using IMU and vision. First I am trying to use the IMU to get position and velocity. In a tutorial [1] ...
1answer
659 views

### Adding magnetic field vector to a Kalman filter

I currently have an error state Kalman filter with the state vector $(p, v, q, \omega, a, g)$ where $q$ is the quaternion orientation. I would like to add the information coming from a magnetometer to ...