# 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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### What would be a way to estimate IMU noise covariance matrix?

Weirdly enough, my robot platform which has an official ROS package supported by a manufacturer doesn't provide any covariance matrices of its sensors. So, I'm basically trying to estimate these ...
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### UKF for a serie of observations with covariance

I have some doubts about how to implement a UKF-like algorithm when I only have motion observations and no control inputs. Assume I have a robot with state $s_t = (x_t, y_t, \theta_t)$ and the ...
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### How do you convert the covariance matrix of a 3D rotation error-state to the covariance matrix of the corresponding quaternion?

I'd like to convert the covariance matrix of an error-state Kalman Filter that uses Euler angles to the corresponding covariance matrix of a quaternion state. I basically use this for standard INS-...
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### Nonlinear Sensor Fusion with Space-Time Finite Element and Static Condensation?

I have recently implemented an algorithm for the nonlinear fusion of GNSS, barometer, magnetometer, accelerometer and gyroscope data. The algorithm is based on a space-time finite element where the ...
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### What is a general definition for pseudo-measurement (e.g., zero-velocity update as often used in robotics)?

I understand what a pseudo-measurement, but I am curious if there is a formal definition of the pseudo-measurement. A pseudo-measurement is sort of a constraint on the states of a system, which can be ...
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### How to actually fuse sensor using Extended Kalman Filter

Background I'm working on 4-omniwheel mobile robot. It have encoder on each wheel and MPU 6050 IMU. The robot positioning suffer a great error because slip, so i try to increase the accuracy of ...
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### Drone lost traj recovery

So I am using slam algorithm to localize the drone which is gps denied . The input to the slam algo is imu data and a video . Now after the first run of the slam algorithm it creates the trajectory ...
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### No difference between UKF and EKF for SLAM

I built EKF and UKF SLAM algorithms. The problem is that I expected to see a difference because of the more precise approximation of the system in the UKF. Here's a screenshot from the estimated path ...
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### UKF - sigma point creation - Mirroring the chol matrices

maybe this is a stupid question but i came across a problem with my ukf implementation. I use chol() in matlab for my sigma point creation instead of the normal square root of my covariance matrix. Do ...
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### UKF - Correction Step [SLAM] - Only compute the sigma point of the vehicle pose and the specific landmark that got spotted?

i want to implement an UKF Filter for SLAM but i cant seem to wrap around the update step. When computing the innovation matrices and everything, do i need to compute the sigma points in respect to ...
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### How is IMU noise dealt with between steps?

Direct integration of IMU will result in massive error incredibly quickly. What I am wondering is, how do you use an IMU over a small time intervals to aid in pose estimation? In particular, suppose ...
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### Kalman filter for visual tracking of a ball sliding on a gutter

I'm working on a project where a robot needs to keep a ball at a desired position on a gutter. The gutter is fixed at one end and held at the other end by the robot’s ...
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### Fusing cross-correlated measurements for mobile robot's localization using unscented kalman filter (ukf)

I'm currently working on a mobile robot's indoor localization. On the perception side, I can only rely on a 2D lidar and wheel odometry. I have used these sources as input of different localization's ...
234 views

### GPS Course vs IMU Course

Im currently working with Kalman Filter for position and velocity, one of the important parameters that im using is the heading that the sensor fusion of the imu gives me, but i have seen that the GPS ...
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### Kalman Filter with multiple inputs

Let's say I have one laser scanner and a radar device, which I should use to measure a distance to a wall (Fig. 1). Both devices are place on the same support, so... they should measure the same ...
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### Particle Filter for IMU tilt angle and bias estimation from Kalman Filter models

I understand the functioning of Particle Filters from the book Probabilistic Robotics and the robotics course provided by Cyrill Stachniss. I want to implement, from scratch, a particle filter to ...
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### IMU + GPS fusion and change of reference frame

I started working with GPS + IMU fusion using Kalman Filter. For this, I'm using Python, with Madgwick filter from a library (https://github.com/morgil/madgwick_py) and Kalman filter also from an ...
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### IMU-Camera Senor Fusion

I am working on fusing IMU and Camera Sensor Fusion for the Drone to precisely land on the target location. With the Camera, I am tracking the April Tag which is on the ground. This gives me the x,y,z ...
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### Kalman Filter Design

I'm new to Kalman filter design and I'm struggling to understand how to apply the Kalman filter methodology to my problem. I've read a research paper which seems to describe what I'm trying to do ...
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### How do Particle Filters give estimates of uncertainty?

In the Kalman Filter the final covariance matrix is the estimate of the filter's uncertainty. How does one do so in Particle filters? Is it just the variance among the particles for each state? If so, ...
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### Is Kalman filter really desired here?

I am trying to use Kalman Filter in my project to eliminate outliers that go beyond certain limit. I am use 1D lidar to get the distance between the robot and an object. I get pretty accurate values ...
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### Is the covariance matrix in the extended Kalman filter guaranteed to be positive definite (ignoring numerical errors)?

I understand that due to numerical errors (e.g., round off error and machine precision) that the covariance matrix may not be positive definite, but if computers had infinite precision, is the ...
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### Not getting expected performance from kalman filter+mahalanobis distance

I am using a 1D lidar in one of my projects and it returns the distance it measures, in millimeters (mm). At some point in time, it gives garbage values that go as high as 10,000 or higher, when the ...
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### Sensor fusion of GNSS and IMU using UKF

I do have a land-based robot with an IMU and a GNSS receiver. From the IMU, I get the velocity and acceleration in both $x$ and $y$ directions. From the GNSS receiver, I get the latitude and ...
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### IMU Vision Fusion using EKF

I am trying to track an object indoors using an IMU (only accel and gyroscope) and a visual marker. This is similar to IMU+GPS fusion, where GPS is effectively replaced by the position that my vision ...
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I'm struggling to implement Unscented Kalman Filter for tracking objects using radar. My state vector contains [x y z vx vy vz] and I can measure [rho phi theta velocity]. So everything looks trivial ...
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### State propagation from uncertain control input

Consider a nonlinear system $x(k+1)=f(x(k),u(k))$, where $x(k)\in\mathbb{R}^{n}$ is the state, $u(k)\in\mathbb{R}^m$ is the control input. Here $u(k)$ is normally distributed RV with mean $\mu_u(k)$ ...
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### Kalman Filter for 2d pose

I'm really sorry if this is a dumb question, but I don't have a clue on how to do this. I'm trying to write a kalman filter with a State vector of : {x, y, ẋ, ẏ, ẍ, ÿ } To estimate the 2 dimensional ...
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### 2D Visual-Inertial Extended Kalman Filter

I am trying to implement an Extended Kalman filtering for combining IMU data and visual odometry in a simple 2D case where I have a robot that that can only accelerate in its local forward direction ...
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### Kalman filter with missing dimension on measurement input

I am exploring the option of using a EKF with my differential drive robot. I do not have any prior experience with kalman filters. The robot that is under consideration has two wheel encoders for ...
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### How do you handle angle discontinuities in estimation problems?

When one is implementing a state estimator in a system that involves kinematics, will inevitably face the problem of angle discontinuities, i.e., the fact that the angles have to be wrapped between ...
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### Custom implementation of robot_localization package

I plan to implement a sensor fusion of IMU + Visual odometry using an EKF. I came across the excellent robot_localization package which does pretty much all that I want. However, I need to use perform ...
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### Bias correction for multiple sensor fusion through Kalman Filtering

I am learning Kalman Filters and was working on a simple example: Temperature measurement of a room by using 4 thermometers(different biases and noises) if i consider that there is no bias in the ...
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### Where do matrix A and A transpose come from in calculating the predicted covariance matrix?

I don't understand where the matrices A and A transpose come from in the equation in this series. I have done a one-dimensional ...
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### EKF sensor fusion

What is the standard way to fuse multiple sensor measurements in an EKF framework? Say you have Odometry, IMU and some form of Lidar which can produce landmarks. EKF is normally presented as a ...
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### EKF-SLAM what should the observation model be?

I am implementing an EKF algorithm for a drone localization, and while I was defining the observation model I got a bit confused. This is my situation: I have a drone which is able to give me the ...
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### Kalman filter with a known motion model

I have a robot whose pose $(x, y)$ is defined relative to the global frame. I have a sensor which estimates the robot's current pose in the global frame, and the sensor is known to have Gaussian error....
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### Can someone help me understanding reference frames in OxTS data in KITTI Vision Benchmark dataset?

If anyone has worked with KITTI dataset, can you explain the reference frame used in roll pitch yaw values? I downloaded the raw data from this link: http://www.cvlibs.net/datasets/kitti/raw_data.php ...
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### what kind of processing is required on raw IMU data before it is fed into a filter?

Im working on quadcopter. At this stage im coding a reference system for quadcopter using 10DOF board.At this stage im at the point of only getting raw data values from accelerometer, gyroscope, & ...
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### How can i fusion gyroscope and accelerometer when accelerometer has only roll,pitch val?

I'm currently studying IMU Sensor with 6dof(gyro and accelerometer). My goal is to get Orientation of robot, and i found out that only 6dof imu sensor wouldn't be possible to get a correct Orientation ...
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### EKF landmark-based help needed

I am new in localization algorithms and EKF is new for me as well. I think that I implemented EKF (the whole code of class is here. I have problems in updating bearing angle of the robot. Basically I ...
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### Uncertainty in grid based fastslam

Given I am building a grid map, and poses are represented using particles, how can I calculate the uncertainty of a pose In a grid based fastslam 2.0?
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### Advantage of Kalman filter in differential drive planar robot

We need to estimate the position and orientation of differential drive robot by using encoders and imu sensor. For this specific case, is there any advantage of using Kalman filter than taking the ...
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### Transforming between a local and global frame for a Kalman filter

I want to track an object in a global Cartesian frame, denoted $G$. The object has a local frame, denoted $L$. The object is controlled by a velocity command $v$, defined in its local frame. This "...
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### Where to include velocity in a Kalman filter

I am trying to understand some of the basics of the Kalman filter. The problem I am working on is quite complex, but I have spent some time trying to simplify the problem with an example. So, let's ...
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### Some Kalman filter implementation queries

Just to clear some doubts: Qn 1. Does kalman filter require constant time step? From my own study, it does not seem necessary to have a constant time step. You just need to take into account time ...
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### In a Kalman filter, what should be included in the state, and what should be included in the control?

Let's say I am controlling a robot using a velocity controller. This involves specifying a target velocity for the motors, which is achieved using a PID controller (the low-level details of this PID ...
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### State-dependent Covariance in the Kalman Filter

When using a Kalman filter, one of the variables that must be defined is a matrix representing the covariance of the observation noise. In the implementations I have seen, this matrix is defined once, ...
If we consider the first-order Taylor expansion of a general nonlinear function at the operating point $x=x_0$, then we have the following, f(x) \approx f(x_0) + \frac{\partial{f}}{\partial{x}}|_{x=...