17 votes
Accepted

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 ...
kamek's user avatar
  • 1,000
9 votes
Accepted

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 ...
user96966's user avatar
  • 126
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 ...
Gouda's user avatar
  • 902
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 ...
Eric Lavigne's user avatar
6 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 ...
Chuck's user avatar
  • 16k
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 \\ ...
Chuck's user avatar
  • 16k
6 votes
Accepted

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 ...
Parker Lusk's user avatar
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 ...
HansPeterLoft's user avatar
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. $H_2$ ...
ryan0270's user avatar
  • 2,804
5 votes

Kalman-Filter: how to solve angles near +/-pi?

Here is a paper on the subject. By doing the proper maths with the SO(2) Lie group to represent the angle, they show that the very simple approach of wrapping the predicted state angle to $[-\pi, \pi)...
Frederik Beaujean's user avatar
5 votes
Accepted

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 ...
abhishek47's user avatar
5 votes
Accepted

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 ...
xperroni's user avatar
  • 1,353
5 votes
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cartesian velocity control loop implementation

The orientation error is not simply subtraction of your current pose and the desired pose. Given $\mathbf{R}_{a}, \ \mathbf{R}_{d} \in \text{SO}(3) $, where $\mathbf{R}_{d}$ is your desired ...
domo_arigato's user avatar
4 votes
Accepted

kalman filter with redundant sensors

Are you sure about your expression for $HH^T$? I get $$ HH^T = \begin{bmatrix} 1 & 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 &...
DXM's user avatar
  • 106
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 ...
trudesagen's user avatar
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 ...
Chuck's user avatar
  • 16k
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 ...
V. Yao's user avatar
  • 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 ...
fibonatic's user avatar
  • 941
4 votes

Process noise and Measurement noise in Kalman filter

Basically, the relative magnitude between process and measurement noise determines how much to trust a new sensor measurement. In one extreme, if the process noise is zero the kalman filter will ...
ryan0270's user avatar
  • 2,804
3 votes

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

Accelerometers measure kinematic acceleration with the addition of gravity. So for an accel to measure 0, the vehicle would need to be accelerating downward at $g$. To get inertial acceleration out of ...
holmeski's user avatar
  • 1,853
3 votes
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What kinematic equations should I use for Kalman filter state propagation in IMU based quadcopter navigation?

The first form, from both the math and the webpage to which you link, is for linear motion only. Tie a string to a rock. Swing the rock around in a circle above your head at a constant speed. If you ...
Chuck's user avatar
  • 16k
3 votes
Accepted

State estimation of mobile robot

My solution is to use the following model with disturbance only at acceleration and curvature. $$ \begin{bmatrix} x_{k+1} \\ y_{k+1} \\ \theta_{k+1} \\ v_{k+1} \\ a_{k+1}...
evolved's user avatar
  • 218
3 votes

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

Adding to the above, my favorite way to debug a misbehaving filter is to isolate each step. Make sure your prediction step works before correcting it. Your bot should drive straight right with 0,0,0 ...
Josh Vander Hook's user avatar
3 votes

Original paper of Kalman filter

The Kalman Gain term is derived in equation 25 (page 7) of the paper. The paper doesn't explicitly use the term "Kalman Gain" as that term was coined after the fact. However, the paper does refer to ...
koverman47's user avatar
3 votes
Accepted

What is the bicycle model for a dynamic robot?

The bicycle model is a simplified model of vehicle dynamics. It's really common so I'm not sure why a web search did not get any results for you. A random paper, first one in my search that had a ...
hauptmech's user avatar
  • 4,435
3 votes
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What is the intuitive explanation of using Jacobian of observation model while calculating Kalman gain in EKF SLAM?

Let's try breaking it down. Projection of uncertainty $H\Sigma H^T$ is projecting the state uncertainty into measurement space. How do we know that? $\Sigma$ denotes the the covariance of our ...
Jacob Panikulam's user avatar
3 votes
Accepted

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

This is really a lot to look at, but the most glaring issue I noticed off the bat is your definition of the control signal $u(t)$. What is the input to your controller? What should be the input to ...
Chuck's user avatar
  • 16k
3 votes
Accepted

I fused a GPS and IMU and I am wondering if my results make sense

Do you have a simulation? I would recommend that you simulate the data first to debug and tune your KF. The simulation should model the true IMU outputs (Grove has some details on that) and true ...
DaveC's user avatar
  • 46
3 votes
Accepted

Industrial Controllers - Why not adaptive control and robust control

In short, adaptive control and robust control (Hinf) are the difficult combination of computationally expensive and complicated to understand. Even if you do an excellent job of implementing one of ...
ryan0270's user avatar
  • 2,804
3 votes

Industrial Controllers - Why not adaptive control and robust control

If I had to guess, I would say that, in an industrial setting, you have a relatively high degree of certainty about the process you're controlling, and/or there isn't much emphasis on transient ...
Chuck's user avatar
  • 16k

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