Tagged Questions
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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0answers
18 views
Describing the length of a convolution filter in the time domain
I have a bank of filters that jointly act as bandwidth filters for different frequencies. They are implemented in a Kalman Filter, but the filter is time invariant and far from the boundaries of the ...
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0answers
10 views
Can the Kalman gain matrix contain negative values or absolute values greater than 1?
I have implemented an EKF in a power systems application. When I run a simulation in Matlab, in some iterations of the filter I get a Kalman gain matrix (K) with negative values and/or absolute values ...
0
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0answers
26 views
Likelihood / Error of a Zero Input Sequence
How can I measure how well a known system describes an unknown sequence?
In my work I need to evaluate how likely a particular observation sequence is given any parameterization of an LTI system. The ...
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0answers
20 views
Kalman Filter: Computation of state covariance matrix
A simple system is described with the following state vector with a and b being the states.
$$
x_{k-1|k-1} = \begin{pmatrix} a \\ b\end{pmatrix}
$$
For the sake of discussion, let x be assumed to be a ...
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0answers
27 views
Which Kalman filter do I need to use for my problem?
I'm applying object tracking using Kalman's Filter.
It's working well on when path is linear. But in the following case when path is not linear it doesn't work well.
So my question is :
Is this the ...
0
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1answer
19 views
Should I pass Kalman Filter absolute or offset-from-mean sensor values?
I'm using Kalman filters to segment the loudness of an acoustic signal from surrounding noise. The problem I've encountered is that muffled or faulty microphones measuring 'silence' (-70dB, -69dB, -...
1
vote
1answer
20 views
Filter for denoising a signals using a known (noisy) derivative of that signal
I have a signal and it's 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 ...
1
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0answers
27 views
Rocketry : Combine two accelerometers to reduce noise?
I am designing an IMU for an experimental rocket. I'll be using the BN055 9DOF that has sensor fusion - orientation quaternion - and gravity compensation.
My main goal is speed computation, and I was ...
1
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1answer
53 views
“Bi Directional” Kalman Filter
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 produced decent results. However, lots of ...
2
votes
3answers
76 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 ...
0
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0answers
25 views
Basic Acoustic Tracking with Sensor Fusion for Automatic Gain Control
I'm trying to apply automatic gain control to an audio source emanating from two speakers by measuring the loudness of the signal in the presence of noise at multiple sensors. The sensors can move, ...
2
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2answers
193 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 ...
0
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1answer
56 views
How to find the probability of Kalman filter states? [OpenCV+Python]
I am working on a video object tracking problem. I am using Kalman filter to predict and correct the object position return by an algorithm such as CamShift. I want to adjust the likelihood ...
0
votes
1answer
34 views
How to Realize the Sigma Point Sampling Function in Unscented Kalman Filter?
Recently I'm learning the unscented kalman filter (UKF). When designing the unscented kalman filter, it involves a non-linear function to generate the sigma points and then use the system non-linear ...
1
vote
1answer
54 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 ...
1
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0answers
59 views
Kalman filter equations/code to estimate velocity from known position and acceleration
I was reading this post and I have the same problem: I want to estimate the velocity using displacement and acceleration measures.
But the problem is that I don't know how I have to code/implement an ...
0
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2answers
50 views
Question About Kailath's Paper - An Innovations Approach to Least Squares Estimation Part I: Linear Filtering in Additive White Noise
I'm reading the paper at the link below and I was following it for about 2 pages until I hit a road block on the bottom of page 648 where the author says:
putting together 9-11, we obtain
and ...
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0answers
25 views
How do i estimate the momentary white noise out of three signals sampled at different frequency and phase?
I have three signals sampled at different three frequencies $Fs_1, Fs_2, Fs_3$.
They all suffer from the same white noise source.
I allow my self, if needed, to sample at a higher frequency than ...
0
votes
1answer
272 views
Using the Kalman filter given acceleration to estimate position and velocity
Note : port from this post, until fully merged.
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 ...
2
votes
1answer
92 views
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 ...
2
votes
1answer
97 views
Naive Kalman filter for 3D position
I looked at posts that discusses 3D kalman filter.
Kalman Filter to estimate 3D position of a node
Help with Kalman Filter implementation for estimating 3D position
Both from my understanding, both ...
1
vote
1answer
73 views
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 ...
0
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1answer
97 views
Sample Dataset for Kalman Filter
I'm a newbie to Kalman filter. I have found the code online but I was wondering if there is any sample dataset available online to get hands-on with it (for example: CIFAR-10 for classification etc. )....
0
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1answer
69 views
IMU speed tracking through known path
new to signal processing and KFiltering here. Thanks for your help.
I working with an IMU for a tracking project where the IMU moves throw a known path but at an unknown speed (within limits), the ...
0
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1answer
69 views
A State space model for discrete Sine wave Using kalma filter
I'm looking to apply an optimal LQR filter to a discrete signal of the form
$$
x[n]=A\sin(\omega_0n+\phi)+v[n]
$$
The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using ...
1
vote
0answers
21 views
EKF smoothing for prediction at t=0 when no there is no measurement
I have a simple first-order reaction batch system for which I have some discrete measurements ($0<t_{k}\le t_{endbatchsample}$).
I have an initial guess for $x_0$ and $P_0$ and from here I ...
1
vote
0answers
149 views
Help with Kalman Filter implementation for estimating 3D position
I wrote a kalman Filter implementation using the Eigen Library in C++ and also using the implementation at this link to test my filter: My prediction step looks like this:
...
4
votes
1answer
67 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.
...
0
votes
1answer
24 views
Handling a number of simultaneous measurements in Extended Kalman Filter?
If I have a number of sensors whose measurements arrive at the same time - how can I handle them properly in the Kalman filter?
P.S.
The measurements are not necessarily taken at the same time but I ...
0
votes
2answers
245 views
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 ...
1
vote
2answers
69 views
What is the value of $0.01\log_{10}$?
I have posted this question in math.stackexchange.com, [can be found here], which I originally thought it is a math question. I now believe this would fit more to the Signal Processing community. For ...
1
vote
3answers
154 views
Kalman Filter Sensor Processing
Kalman filter achieves convergence of state vector by using sensor observations.
Assuming a sensor such like velocity sensor, giving two axis velocity information in X-axis as well as Y-axis(see edit ...
0
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2answers
57 views
In kalman Filter why Q discrete is defined as $\int_0^Te^{\mathbf{A}\tau} Q e^{\mathbf{A}^T \tau} d\tau$?
I would like to ask, why in the transformation to the discretization, $\mathbf{Q}$ is obtained from the expression containing the integral (image attached), what is the theory behind it?
2
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0answers
18 views
Evaluation of Jacobian for Extended Kalman Filter
For the non-additive noise case,
\begin{equation} x_k = f(x_{k-1}, u_{k-1}, \xi_{k-1}) \\
y_k = h(x_k, \nu_k)
\end{equation}
the EKF takes into account the jacobian wrt to the noise terms $ L_{k-1} =...
2
votes
2answers
341 views
Image Restoration using kalman filter
I have been trying to restore an image that was blurred with a known Point Spreading Function and corrupted with noise using a kalman filter. I have looked at theory and have a basic understanding of ...
0
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0answers
110 views
Kalman gain and filter bandwidth
For Kalman filter is it possible to relate analitically (or through numerical simulation) the steady-state gain and the Kalman filter bandwidth?
I wasn't able to find a reference where this topic is ...
0
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2answers
404 views
[Python ]How can I improve my 1D Kalman Filter estimate?
I have written the following code to smooth an (almost) linear function:
...
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0answers
98 views
Unscented Kalman Filter - estimation of two parameters
I am working with Unscented Kalman Filter (UKF) in thermal modelling of a box.
I have 3 state variables ($T$ temperature, heating $h_h$ and cooling rates $h_c$) in my model and I am observing just ...
0
votes
1answer
70 views
Frequent update of the Kalman Filter covariance matrices
I have inherited some code that does vehicle localisation based on two main inputs: sensor input from the vehicle odometry and map localisation based on matching camera images to road features. Both ...
0
votes
2answers
66 views
How to estimate ALL time-delays across MULTIPLE signals?
Imagine there are 100 recordings of the same signal or pattern, but those recordings are not properly aligned with each other in time. In other words, each sample has some unknown time delay in ...
0
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0answers
71 views
Using Kalman filter to estimate ARR (p) model's parameters
Recently I came across the fact that Kalman filtering can be used to estimate time-varying series parameters. Since I'm totally new to the time series type of data it wasn't a surprise I couldn't ...
0
votes
0answers
18 views
How to fit a constant acceleration model given a set of x,y,t point with nonuniform timestamp?
I have a bunch a point $(x,y,t)$ in 2D $(x,y)$ with their sampled timestamp t.
assuming acceleration do not change.
How can I estimate a model $(x^*, y^*, vx^*, vy^*, ax^*, ay^*)$
where $(x^*,y^*)$ ...
0
votes
2answers
120 views
Alternative to Extended Kalman Filter when prediction function is not differentiable
I am looking at a tracking problem. It can be modelled similarly to the Extended Kalman Filter:
$$
\begin{array}{rcl}
\mathbf{x}_k &=& \mathbf{f}(\mathbf{x}_{k-1}, \mathbf{u}_k) + \mathbf{w}...
1
vote
0answers
39 views
Sensor fusion under unknown correlations: can covariance intersection account for delays?
Of late, there has been some interest in cooperative estimation algorithms in robotics, where the information sources are usually sensors such as cameras. When multiple robots observe surrounding ...
0
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0answers
107 views
Online Frequency and Amplitude Estimation with an Extended Kalman Filter
I'm trying to reproduce some results from a research paper that uses an Extended Kalman filter to estimate the instantaneous frequency and amplitude from accelerometry data. However, I don't ...
1
vote
0answers
83 views
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 ...
1
vote
0answers
79 views
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} + \...
1
vote
0answers
99 views
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 ...
2
votes
1answer
52 views
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_{...
4
votes
1answer
63 views
When Kalman's assumptions are relaxed
From Kalman's seminal paper "A New Approach to Linear Filtering and Prediction Problem", it is clear that Kalman's exposition is based on the following fundamental assumptions:
Measurements that are ...
