15 votes
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Unscented Kalman Filter for Dummies

I'm going to give you a high-level overview without going into much math. The purpose here is to give you a somewhat intuitive understanding of what is going on, and hopefully this will help the more ...
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  • 950
14 votes
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How to rotate covariance?

Covariance is defined as $\begin{align} C &= \mathbb{E}(XX^T) - \mathbb{E}(X)\mathbb{E}(X^T) \end{align}$ where, in your case, $X \in \mathbb{R}^6$ is your state vector and $C$ is the covariance ...
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  • 2,669
8 votes
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What is a good approach for outlier rejection during real time data filtering?

It is both acceptable and standard to use camera observations with a Kalman filter if you are talking about landmark positions in pixel or real-world space. Pixel space observations are usually ...
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  • 872
7 votes

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

Assuming your vehicle is roughly horizontal to the ground, you won't be able get a good estimate of yaw from the accelerometer. Consider the nominal case: when your accelerometer is pointing straight ...
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7 votes
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Measurement model for Kalman filter but non-zero mean

There are actually several issues in this question which I will answer separately. 1) Error is: $$\sqrt{(x_m-x_{gt})^2}$$ No, error is just $$(x_m - x_{gt})$$ This may be part of your problem with ...
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6 votes
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Kalman Filter when states are not observable at the same time?

First, be careful when using the term "observable" with respect to Kalman filters. It has a precise mathematical meaning that basically determines whether or not the filter is even possible. With ...
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6 votes
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Why should I still use EKF instead of UKF?

Here are a few possible points of consideration. Certainly the UKF has many counterpoints where it has an advantage too. The most obvious advantage is computation power. Don't forget that ...
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6 votes

Ambiguous definition of Error-State (Indirect) Kalman Filter

Hi and welcome to the wide, ambiguous, sometimes confusing world of research. But seriously, looking at 20 years of papers will sometimes produce these confusions. Let's look at what's going on. In ...
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6 votes
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Modeling a robot to find its position

Assuming a constant update of 5Hz, your sample time is (1/5) = 0.2s. Get one position of the target, p1. Get a second position of the target, p2. Target speed is the difference in position ...
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  • 14.5k
6 votes

Open source implementations for GPS+IMU sensor fusion?

Yes. The px4 software for the pixhawk autopilot has an extended kalman filter that uses an accelerometer, a gyroscope, gps, and mag. A paper describing the a smaller ekf which only estimates attitude ...
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6 votes

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

If the drone is not falling (holding height in the sky), and it's not accelerating in any particular direction, then the accelerometer should be reading: $$ a = \left[ \begin{array}{} g_x \\ g_y \\ ...
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6 votes
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Extended Kalman Filter in robotics - Worth it?

The Kalman filter is an optimal linear filter in the presence of Gaussian noise. It is optimal in the sense that it minimizes the mean-squared error. This means that the covariance of the estimated ...
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6 votes
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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 ...
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5 votes
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How to estimate yaw angle from tri-axis accelerometer and gyroscope

Gyroscopes will only give you the rate of change of the yaw angle, not the absolute yaw angle. Unless you plan to set the yaw angle initially and have it drift further and further into garbage ...
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5 votes
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How do I go about implementing a Kalman Filter for a pose estimation algorithm?

It sounds like you're using the camera frames to get a PnP solution, or something along those lines. A linear Kalman filter will usually work OK for most purposes if you're using roll/pitch/yaw and ...
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  • 872
5 votes
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Kalman Filter GPS + IMU

This is a complete re-working of the answer I had originally provided. If you're curious, you can check the edit history and see what was posted earlier. In comments to this question, OP stated that ...
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5 votes

Alternatives to Kalmam Filter

A good choice for sensor fusion with the MPU6050 is a second order complementary filter, which I used for the orientation estimation in a project. The complementary filter is computational cheap and ...
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5 votes

What's the diffrence between $H_2$ and $H_\infty$ control?

In short answer: yes Kalman filter is a special case of an $H_2$ observer Yes Yes ... LQG is just Kalman filter + LQR controller, which are both special cases of $H_2$ Depends on the use case. $H_2$ ...
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4 votes
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Multiple position estimates fusion

What you are describing is essentially a textbook case for using a Kalman filter. First you need a prediction step. Let's assume you are predicting the pose of the robot $(x,y,\theta)$, given the ...
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  • 950
4 votes
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How to use a POMDP-based planner on top of a probabilistic filter

I have used POMDP like models on top of a localization algorithm (Adaptive Monte Carlo Localization, from ROS), and a person detector [1][2] to find and follow a person with a humanoid robot. These ...
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  • 260
4 votes

Choosing the state vector for an EKF

In general, I try to obey the following two rules when selecting states: Only use the states necessary for control, and Choose states to be measurable properties, whenever possible. For example, on ...
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4 votes
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Regarding Kalman filter and estimating heading with magnetic compass

I encountered this problem myself when making an extended Kalman filter for a quadrotor. You have to check if the estimate goes above or below +/- pi, and then correct it if it does. You can do this ...
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4 votes
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Paradox: I can't use accelerometer measurements to obtain information about my states in a quadcopter?

I encountered the same puzzle. I had a clue at the beginning that the gravity information is contained within accelerometer measurements due to aerodynamic drag. Then I found a paper The True Role of ...
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  • 56
4 votes

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

Both state space representations are equivalent. For example the eigenvalues of the two closed-loop system matrices should be the same. However when implementing LQG you only have access to the ...
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  • 921
4 votes
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Why is the Kalman filter a filter and not a control system?

A Kalman Filter (estimator is actually more apt than filter) simply estimates states, that's all it does. It, by itself, cannot drive a plant towards a desired output. The estimated states are used to ...
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4 votes

Kalman Filter with multiple inputs

In fact you can update the filter's state using the input from each sensor separately, you just need to use a different covariance matrix $\mathbf{R}$ and observation matrix $\mathbf{H}$ depending on ...
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  • 1,266
3 votes

Kalman filter model values or state space original value? Which values to use?

To apply Kalman filter successfully, you need two requirements namely the system must be linear (i.e. both the motion and observation models) and the noise to be Gaussian with zero mean and some ...
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  • 2,310
3 votes

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

yaw can be measured by rate gyro and magnetometer not with accelerometer because accelerometer values depends on gravity component but on rotation in z axis only there is no change in gravity ...
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  • 31
3 votes

How much should I expect a Kalman filter to converge?

Let's assume a constant Kalman filter $x_n = Gx_{n-1}+\omega$ with $\omega \sim \mathrm{N}(0, W)$ and $y_n = Fx_n+ \nu$ with $ \nu \sim \mathrm{N}(0,V)$, and initial state $x_0 \sim \mathrm{N}(m_0, ...
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  • 131
3 votes

Overcorrecting Kalman Filter

There is an error in your posted equation for the Jacobian $F_J$, so that could be the source of the problem. It should look like this: $F_J = \begin{bmatrix} 1 & 0 & -C \sin \theta \\ C \...
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  • 1,357

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