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Questions tagged [kalman-filters]

The Kalman filter is a mathematical method using noisy measurements observed over time to produce values that tend to be closer to the true values of the measurements and their associated calculated values.

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What Is the Relationship Between a Kalman Filter and Polynomial Regression?

What is the relationship, if any, between Kalman filtering and (repeated, if necessary) least squares polynomial regression?
hotpaw2's user avatar
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How to understand Kalman gain intuitively?

The Kalman filter algorithm works as follows Initialize $ \hat{\textbf{x}}_{0|0}$ and $\textbf{P}_{0|0}$. At each iteration $k=1,\dots,n$ Predict Predicted (a priori) state estimate ...
Tim's user avatar
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1 answer
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Kalman filter for position and velocity: introducing speed estimates

Thanks to everyone who posted comments/answers to my query yesterday (Implementing a Kalman filter for position, velocity, acceleration ). I've been looking at what was recommended, and in particular ...
Stochastically's user avatar
21 votes
3 answers
1k views

Should the input of a Kalman filter always be a signal and its derivative?

I always see the Kalman filter used with such input data. For example, the inputs are commonly a position and the correspondent velocity: $$ (x, \dfrac{dx}{dt}) $$ In my case, I only have 2D ...
Stéphane Péchard's user avatar
19 votes
1 answer
8k views

Kalman filter in practice

I have read the description of the Kalman filter, but I am not clear on how it comes together in practice. It appears to be primarily targeted at mechanical or electrical systems since it wants linear ...
John Robertson's user avatar
17 votes
4 answers
10k views

Intuitive explanation of tracking with Kalman filters

I would much appreciate an intuitive explanation for (visual) tracking with Kalman filters. what I know: Prediction step: Dynamic system state $\mathbf x_t$: target location at time $t$ Measurement $...
matlabit's user avatar
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17 votes
2 answers
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Is a Kalman filter suitable to filter projected points positions, given Euler angles of the capturing device?

My system is the following. I use the camera of a mobile device to track an object. From this tracking, I get four 3D points that I project on the screen, to get four 2D points. These 8 values are ...
Stéphane Péchard's user avatar
15 votes
1 answer
877 views

Will an Unscented Kalman Filter Be "As Good" as Other Optimization Algorithms for This Problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
Benjohn's user avatar
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15 votes
1 answer
1k views

Kalman Filter - Optimal Way to Handle "Derived" Measurements?

Ie, if you have as state variables position (p) and velocity (v), and I make low-frequency measurements of p, this also indirectly gives me information about v (since it's the derivative of p). What ...
Paul Molodowitch's user avatar
14 votes
1 answer
44k views

Kalman filter - understanding the noise covariance matrix

What is the significance of the noise covariance matrices in the Kalman Filter framework? I am referring to: process noise covariance matrix Q, and measurement noise covariance matrix R at any ...
Raaj's user avatar
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14 votes
2 answers
22k views

Given Position Measurements, How to Estimate Velocity and Acceleration

This is simple i thought, but my naive approach led to a very noisy result. I have this sample times and positions in a file named t_angle.txt: ...
lgwest's user avatar
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1 answer
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How to derive the stationary Kalman filter predictor?

In its chapter on Kalman filters, my DSP book states, seemingly out of the blue, that the stationary Kalman filter for a system $$\begin{cases} x(t+1) &= Ax(t) + w(t) \\ y(t) &= Cx(t) + v(t) ...
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13 votes
3 answers
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When to use EKF and when Kalman Filter?

I'm learning Kalman Filter for a week now. I just discovered that EKF (extended Kalman Filter) might be more appropriate for my case. Le't suppose I'm applying KF/EKF for variometer (the device that ...
c0dehunter's user avatar
13 votes
8 answers
9k views

Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
rotating_image's user avatar
13 votes
3 answers
16k views

When Is a Kalman Filter Different from a Moving Average?

this thread asks when a discrete time Kalman filter is better/different from a simple moving average of the observations: Why use a Kalman filter instead of keeping a running average? there's no ...
user24823's user avatar
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12 votes
6 answers
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Kalman Filter - Implementation, Parameters and Tuning

First of all, this is the first time I try to make a Kalman filter. I earlier posted the follwoing question Filter out noise and variations from speed values on StackOverflow which describes the ...
Ole-M's user avatar
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12 votes
1 answer
31k views

Implementing a Kalman filter for position, velocity, acceleration

I've used Kalman filters for various things in the past, but I'm now interested in using one to track position, speed and acceleration in the context of tracking position for smartphone apps. It ...
Stochastically's user avatar
10 votes
2 answers
3k views

Kalman Filter on Sinusoidal Signal

Suppose a system follows this equation: $$ x(t)=A \cos(\omega t + \phi)+\eta$$ where: $\omega = 2\pi f $ and $\eta$ is a random error using Extended Kalman Filter, how does estimated value $\hat{x}$ ...
unwantednoise's user avatar
10 votes
2 answers
3k views

Is the Kalman Filter a Best Linear Unbiased Estimator (BLUE) for Heteroscedastic Noise?

According to the Gauss-Markov Theorem, a ordinary least squares estimator is BLUE if the noise entering a system is uncorrelated with zero mean and is homoscedastic (has a constant finite variance). I ...
sid's user avatar
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0 answers
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Estimating the input to a system from a system state using EKF [closed]

[ Cross-posted from: https://math.stackexchange.com/questions/164169/estimating-the-input-to-a-system-from-a-system-state ] I have a system for which I have obtained a non-linear time-varying state-...
IainCunningham's user avatar
9 votes
3 answers
13k views

Estimating velocity from known position and acceleration

I am stuck at modeling a system model, i.e. getting my state vector and input vector. My guess is that position and velocity are state vector and acceleration is input vector. My 2nd guess is that all ...
c0dehunter's user avatar
9 votes
2 answers
6k views

Different state-space representations for Auto-Regression and Kalman filter

I see that there are different ways to write an AR model into a state-space representation, so that we can apply Kalman filter to estimate the signal. See Example 1, 2 and 3 here. I wonder what ...
Tim's user avatar
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9 votes
2 answers
288 views

Statistical properties of the Kalman estimates under Gaussian noise

For a linear state-space model with independent Gaussian state and output noises and perfect guess for initial state, do Kalman estimates have the following properties: $$ E(\hat{x}_{k|k} - x_k) = 0 $$...
Tim's user avatar
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8 votes
2 answers
1k views

What sensors can be fused using the Kalman Filter framework

I was recently introduced to the concept of Kalman filtering in the context of projectile tracking. A classmate recommended this to me, and what intrigued me most was its ability to fuse different ...
batlike's user avatar
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8 votes
2 answers
4k views

How to Reduce Phase Lag Caused by Kalman Filter

Background I have been developing a system using a moving robot with a distance sensor against another robot. I want to control these robots by estimating relative velocity and acceleration derived ...
mhirano's user avatar
  • 93
8 votes
1 answer
13k views

How do I choose the parameters of a Kalman filter?

Suppose I want to track the position of a car in 2D. What I get as sensor data is my current position. So my state is $$\mathbf{x} = \begin{pmatrix}x\\y\\\dot{x}\\\dot{y}\end{pmatrix}$$ where $x \in \...
Martin Thoma's user avatar
8 votes
2 answers
6k views

Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

I'm new to Kalman filtering and state estimation and I'd like some guidance on EKFs. Currently, I'm trying to use a linear prediction model coupled with nonlinear measurements to estimate the state ...
bparikh's user avatar
  • 83
8 votes
1 answer
22k views

How to Determine Covariance Matrix $Q$ and $R$ in Kalman Filter

I am implementing getting orientation from smartphone. I want to use Kalman filter and should determine process noise covariance matrix $Q$ and measurement noise covariance matrix $R$. (newbie to ...
jakeoung's user avatar
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7 votes
5 answers
5k views

Why Does the Kalman Filter Remove Only Gaussian Noise?

What and where in the derivation of the Kalman filter is the assumption of Gaussian noise? Why and how does this assumption help?
IG123's user avatar
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7 votes
4 answers
11k views

Observation Matrix in Kalman Filter

I've been trying to understand the concept of the Kalman Filter. I came across this great article which makes the concept sufficiently clear. However I could not understand the concept of the matrix $...
Jose Kurian's user avatar
7 votes
2 answers
5k views

What are the advantages and disadvantages of Kalman filter compared with FIR, IIR and low pass filter to filter data with noise?

It is known that the Kalman filter can filter the data with noise. I also find it works well after using it compared with FIR, low pass filter,etc. Now, I have a couple of questions about the ...
marcus zhang's user avatar
7 votes
1 answer
2k views

Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter

There is sinusoidally controlled signal, which other than being noisy, can change values for amplitude, frequency, phase and offset. At every new sample a new sine is fitted for the last N samples. ...
user3761419's user avatar
7 votes
2 answers
3k views

Why Runge-Kutta for Quaternion integration in Kalman filter?

I'm reading up on Kalman filtering at the moment. In particular, I'm interested in using the "extended" and "unscented" variants for IMU sensor fusion and calibration. In A comparison of unscented ...
Benjohn's user avatar
  • 347
7 votes
2 answers
3k views

Kalman Filter Covariance

I've recently started playing with the Kalman filter for a simple 2D (x,y,dx,dy) tracking toy problem. But I seem to have some misunderstanding on what I can expect from the filter. I'm interested in ...
Nghia's user avatar
  • 73
7 votes
1 answer
698 views

Kalman Filter: How to Define Inputs and Outputs of a Model

I'm a software engineer with a CS degree working in machine learning. I'm trying to learn about Kalman Filters. In this short YouTube video from Mathworks, there's a discussion on a Kalman Filter with ...
stackoverflowuser2010's user avatar
7 votes
2 answers
1k views

Deriving the Matrix Inversion Lemma for RLS Equations vs the Woodbury Derivation

Can any one help me in deriving the matrix inversion lemma rule for RLS algorithm? I don't know how to start with. Many books have just stated but they haven't derived it.
Abhi's user avatar
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7 votes
1 answer
279 views

Can a state space model have changing state size over time?

I have worked with state space models in relation to Kalman estimation. Here I have always seen state space models with fixed state size over time, i.e. the state transition matrix is square. Let us ...
Thomas Arildsen's user avatar
7 votes
1 answer
986 views

Fundamental questions about state-space and Kalman filters

I am a dsp guy, I only did a minimum of control theory back in university. While trying to grok state space analysis and (discrete time) regular Kalman filters, I am hitting a few questions that ...
Knut Inge's user avatar
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7 votes
1 answer
716 views

"Bi Directional" Kalman Filter - Kalman Filter for Smoothing

I am working on a project in Object Tracking, i.e. need to predict the location of next bounding box. I used a Hungarian algorithm with a Kalman Filter (which is a common method in this domain) which ...
Anuar Y's user avatar
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6 votes
4 answers
34k views

Question About $ Q $ Matrix (Model Process Covariance) in Kalman Filter

I am implementing my own discrete Kalman filter to estimate velocity from acceleration and position measurements (using Matlab ). I think I managed to deal with the $R$ matrix (measurements noise ...
Rhei's user avatar
  • 413
6 votes
3 answers
865 views

How to Deal with Outliers in Measurement of a Simple Model of Kalman Filter

I am trying to find the one-dimensional velocity of a car based on position measurements, similar to the Wikipedia article. The car moves at almost constant speed and I am mostly interested in ...
Crenguta's user avatar
6 votes
3 answers
7k views

EM algorithm and Kalman filter

I am new to the subject of Kalman filtering and therefore my question might seem trivial. I see that there is a tight connection between Kalman filter and EM algorithm when one wants to predict the ...
polaq's user avatar
  • 61
6 votes
3 answers
1k views

Unscented Kalman Filter - Multiple Consecutive Measurement Updates

In trying to implement an Unscented Kalman Filter (UKF), I have come across the issue of what to do when my measurement signals come in at a different rate than my control inputs, which I use in the ...
theo1010's user avatar
6 votes
1 answer
893 views

Kalman Filter State Covariance Matrix for Non Constant Process Noise Matrix in PyKalman

I'm experimenting with the pykalman Python library to learn about Kalman Filters. In the code below, I'm generating a random walk where each step is the last step ...
SuperCodeBrah's user avatar
6 votes
2 answers
9k views

Using the Kalman filter given acceleration to estimate position and velocity

I am reading data from an accelerometer. I want to use this data to estimate velocity and position. Originally, I performed a double integration of acceleration to read this data, and as confirmed by ...
angryip's user avatar
  • 283
6 votes
1 answer
682 views

Extended Kalman Filter for Linear Systems with Non Linear Measurements

I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates. ...
c-a's user avatar
  • 95
6 votes
2 answers
1k views

Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

I am learning estimation theory through Steven M. Kay - Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. In the ...
McZhang's user avatar
  • 73
6 votes
2 answers
487 views

Estimating a Signal Given a Noisy Measurement of the Signal and Its Derivative (Denoising)

I have a signal and its derivative simultaneously measured, both including additive noise. The measurement is completed before the analysis, so it can be looked ahead. Now I want to reconstruct a less ...
Mav's user avatar
  • 63
6 votes
3 answers
909 views

Question on Wiener Filtering

I have read that a Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process. Now, my doubt ...
Curiosity's user avatar
  • 367
6 votes
1 answer
817 views

How do I model a system to use with a Kalman Filter?

So I have an accelerometer, gyroscope, magnetometer and GPS. I would like to use a Kalman filter to optimally measure speed, position, acceleration and orientation. I have done research and I need to ...
Adam's user avatar
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