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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Proving that the uncertainty can not increase during the update step of a Kalman filter - positive semidefiniteness
I am trying to prove mathematically that the update step in a Kalman filter can not result in a increase in uncertainty. I found the following proof which is based on the inversion lemma and the ...
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How to use Kalman filter for altitude prediction based on barometer data?
I have barometer noisy data with known variance.
I studied Kalman filter but I did not find an answer to this problem:
My process model is: altitude is changed because of velocity that is changed ...
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Real-time oscillation-like noise filtering
I am making real-time measurements, which are affected by some noise. This noise has oscillating pattern, i.e. the total signal tends to oscillate around the mean value. The examples of measurements ...
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Covariance matrix, Q, for a Kalman filter given the stochastic differential equation for the state of the system?
Given that I have a stochastic differential equation describing the motion of my system like so:
$$ \ddot{x}(t) + \Omega_0^2x(t) - C\dfrac{dW(t)}{dt} = 0$$
Where $\Omega_0$ and $C$ are constants.
I ...
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Implementing Kalman filter or extended or unscented with only position information
I am new to Kalman filter. Is it possible to use a Kalman filter with just the position information of the target?
I am so confused with states and measurement.
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How to account for multiple signals in the input to a Kalman filter
I am interested in using a Kalman filter to track an oscillating signal due to a physical oscillator in a signal which contains the signal from multiple such oscillators oscillating at different ...
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Kalman filter - question about matrices
In order to familiarize myself with Kalman filter I decided to see how it work step by step. I would gladly use your help.
Let's say I have a falling object with air resistance proportional to its ...
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Update Sub Set of the State Vector in Kalman Filter
I question about Kalman Filter:
If I have system state
$$
\mathbf{X} = [x_1\ x_2\ x_3\ x_4\ x_5]^T,
$$
these state elements are independent. I have measurement from a sensor to correct the ...
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Kalman Filter - Non Linear Measurement Model
I'm new to Kalman filters and estimation in general. I'm running a simple test of an EKF to check my understanding, but I'm getting some odd results with a particular case.
Given a state vector:
$$ \...
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Structuring Kalman filter for tracking problem where only position is known
I'm new to Kalman filters and my extensive web search about them has helped me understand the majority of it (or so I think). However I still need some light shed on my problem formulation.
I have a ...
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Kalman Filter to estimate 3D position of a node
Code given on this link works for 1D:
Kalman filter for position and velocity: introducing speed estimates
In my problem I need to estimate 3D position.What is the criteria ?
How F, G ,H,Q and R ...
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How to represent the nonlinear model as a state space in Unscented Kalman Filter
There is an Autoregressive model of order 1 (AR(1)) that is excited by a non-linear signal as the input:
$$x_t = \rho x_{t-1} + u_t \tag{1}$$
The time series $u_t$ is generated from a nonlinear map,
$$...
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System Identification: smoothing in E-step of EM algorithm
My question is, do the smoothed values affect the estimates obtained from the Maximization Step? If not then we could eliminate the smoothing. Once the estimates are obtained, they do not change apart ...
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Iterative Kalman filters and system parameters estimation
i am working recently on a project in which i want to implement a Kalman filter as being an observer, and i couple this observer with a state feedback controller that produces control actions ...
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Variance of an Implicit Function of Kalman State Vector
Given a state vector, $ x $, given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following:
$$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} =...
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Problem with Kalman filtering accelerometer data
I'm having some trouble implementing a Kalman filter in MATLAB. I have an Android phone connected sending data from accelerometer for 10 seconds. After i have the data I take out the x-axis vector. ...
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Edge following using Hough transform
I am trying to improve an edge following algorithm developed by some students who did a project at my work. The algorithm is supposed to make a robot follow a line with the use of a camera. Their ...
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Kalman filtering in image processing, resources?
I'm looking for a good resource (book, tutorial, lesson etc.) that explains the usage of Kalman filtering in image processing applications.
I'm aware of the fact that Kalman filtering is an optimal ...
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Applying Kalman filter to a data set
I went through the answer Kalman filter in practice and it seems we must know all the first and second order properties of random variables to apply the Kalman filter.
But when I only have a set of ...
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Simulation of the discrete linear Kalman filter
I have been working on a Scilab simulation of the discrete Kalman filter which is used as a state observer of the
linear dynamic system. The Scilab script for the discrete Kalman filter is as follows
<...
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Why does sequential update of Kalman Filter work when you have multiple sensors?
If you are using a kalman filter with multiple sensing sensors there are two ways to fuse them.
One way is doing a single observation step where you include all the sensors in a single vector and a ...
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Kalman Filtering with measurement latency
The timing involved in this problem is a little hard to explain, so I'll start with my specifics:
I'm developing a program that visualizes output (a bounding box) from a computer vision model on top ...
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Estimate smartphone accelerometer bias
I was planning to develop Android / iOS applications that enable users to measure 3D length using their smartphones.
According to this question, you need to know at least the time-varying bias that ...
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Basic questions related to Kalman filter
Since I'm a newbie to Kalman filter, so, I had some confusions that I needed to clarify.
What is the difference between measurement and state?
Can they be of different dimensions?
All the ...
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Line based Extended Kalman Filter for localization : Measurement Jacobian
I have to estimate location w.r.t a given map of the environment. The state is expressed as
$ X = \begin{bmatrix} x \\ y \\ \theta \end{bmatrix}$
Given ,
$ X_{t-1} = \begin{bmatrix} x_{t-1} \\ y_{...
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How to determine initial values in Kalman Filter
I have EEG signal and exract PSD feature from it, then must apply it a noise reduction algorithm, I used Kalman filter,
but the output signal in the paper is much smoother than my output and
vertical ...
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Active noise cancellation using kalman filter
I am doing signal processing on audio data sampled at 8Ksps in matlab but it is corrupted with random noise. Therefore, I decided to use LMS and RLS ANC algorithms to remove overlapped frequency ...
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Kalman for 3D position and 1D orientation
Is the following state correct for a Constant Acceleration (CA) model KF applied for tracking an object which moves in (x, y, z) and have the freedom of rotation $\phi$ around the $z$ axis?
\begin{...
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Derivation of Transfer Functions for Kalman Filter
Hi All: I'm somewhat familiar with the kalman filter from a statistical point of view. But lately I've been trying to familarize myself with the linear systems-EE way of looking at it. So, I've been ...
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Non-zero mean of Kalman innovation
I am using a Kalman filter to fuse gyro and inclinometer data. The prediction step is given by:
$\hat{\alpha_{i}}^- = \hat{\alpha}^+_{i-1} + \omega_{i}$
Where $\hat{\alpha_{i}}^-$ is the prediction ...
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Estimating Velocity from Fuzzy Position Data with Known Uncertainty
I was wondering if someone could maybe clarify or direct me to the best answer for this question. I want to estimate velocities from position data. However, the position data is fuzzy but I have an ...
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Discrete algorithm for low pass filter
I am working on a position controller for a marine vessel. I have a measurement signal containing the y-position of the vessel that consists of both low frequency (<.1 rad/s) and high frequency (&...
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estimation of the position of the magnetic source
I have a flying robot with magnetic coil as a sensor. An output from the coil is measured every second in different position. I know the position of the coil and its angles. I need to estimate the ...
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How to simulate the synthetic data for 2 pole low pass filter for Kalman application?
I was trying to simulate data for a 2 pole low pass filter inorder to solve with kalman filter to estimate the true states. With the below code I was unable to generate true states that look like sin ...
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Steady-state Kalman filter question
I'm reverse-engineering DSP code and there's a steady-state Kalman filter in it. Because it is a steady-state Kalman filter, the matrix $K$ is fixed. However, I'm a puzzled about the state update ...
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Kalman filter for harmonic oscillator. State variable and Covariance matrix
I've coded a simple damped harmonic oscillator, controlled with a pid. Works fine.
I want to use this model to test a kalman filter. So i added a gaussian noise to the position and want to feed the ...
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How Do Particle Filters Get Velocity When Tracking with Pos Measurements
I am new to particle filtering.
I can see when particle filters are used with Ensemble Kalman's, the velocity of the states are taken care of by the Kalman.
When tracking using particle filters ...
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Estimate standard deviation of random-walk using Kalman filter
I'm new to Kalman filters so this might be a stupid question.
I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
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Why does noise prevent a (kalman) filter from diverging?
I'm using a filter (not exactly kalman) of the following form to estimate angles by fusing gyroscope with accelerometer and gyro with magnetometer:
$(1)\quad \hat{\theta}_k = \hat{\theta}^-_{g,k} + \...
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How to derive an expression for the optimal importance distribution?
I'm trying to answer the exercise 7.6 letter b of this book:
https://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf
page 133 but I'm having some problems in understanding the question ...
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Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori
I am implementing a Kalman filter (for a linear ODE system for now).
My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
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Check if I has right: Is this the Extended Kalman Filter
I have learn the Kalman-Buncy filter for the LQG controllers. I know that this is a signal processing forum and not robotics not math forum. But Extended Kalman Filters are daily discussed here.
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Digital filter for sharp impulse in data
I am looking for an algorithm or a filter to remove sharp peaks from my data. I am collecting raw data after every 1 second from an sensor through an ADC. The ADC has an internal FIR filter. I use ...
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Filtering for Wright-Fisher HMM
I am trying to understand what filter may be suitable for the following HMM:
The signal is a Wright-Fisher one-dimensional diffusion characterised by the SDE
$$dX_{t}=\frac{1}{2}\left(\alpha(1-x)-\...
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Kalman Filter - Gaussian representation
I'm trying to understand well the kalman filter, as a result i'm having this question :
Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
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Kalman filter without model versus RLS
As I found out in my previous question Where to get transtion matrix for Kalman filter?, I need a model for correct usage of Kalman filter.
In paper On the Intrinsic Relationship Between the Least ...
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Kalman filter to filter noise from acceleration data
I would like to apply a Kalman filter to remove noise from my measured acceleration data. The idea is then to compare the results obtained in this way whit the results obtained by applying a low-pass ...
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Open source GPS+IMU sensor fusion?
Are there any Open source implementations of GPS+IMU sensor fusion (loosely coupled; i.e. using GPS module output and 9 degree of freedom IMU sensors)? -- kalman filtering based or otherwise
I see a ...
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Can I model process noise as a known "error" in my dynamics while designing a Kalman Filter?
Consider I am modelling the dynamics of a robot and using a Kalman filter to obtain estimates of some state. I have certain terms in my equation which correspond to data not accessible to this robot ( ...
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Purple Noise Modeling / Differentiated White Noise (Kalman Filtering)
I am designing a Kalman Filter for a signal which features a certain kind of noise and I do not know how to model it properly in the filter.
The noise is constructed from a white noise source, called $...
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