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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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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 ...
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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 ...
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“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 ...
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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 ...
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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, ...
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106 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 ...
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32 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 ...
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18 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 ...
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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 ...
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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 ...
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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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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 ...
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136 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 ...
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77 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 ...
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1answer
70 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 ...
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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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56 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. )....
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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 ...
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54 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 ...
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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 ...
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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: ...
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56 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. ...
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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 ...
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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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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 ...
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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 ...
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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?
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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} =...
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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 ...
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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 ...
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258 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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64 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 ...
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59 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 ...
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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 ...
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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 ...
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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 $(x^*,y^*)$ ...
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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}...
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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 ...
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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 ...
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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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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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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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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 ...
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Extended Kalman Filter for state estimation

I am working on a quadrotor (small four rotor drone) and I want to create an Extended KF for which it takes ($x$,$y$,$z$,$\psi$,$\theta$,$\phi$) as an input and give the ($\dot x$,$\dot y$,$\dot z$,$\...
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336 views

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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Problem with state dimensions in IMM algorithm

I'm working on tracking algorithm for radar system. I have 3 motion models with state vector: \begin{align} x_1 &=[x,\ y,\ v_x,\ v_y]\\ x_2&=[x,\ y,\ v_x,\ v_y,\ a_x,\ a_y]\\ x_3&=[x,\ y,\...
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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?
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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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What is the difference between Kalman filter algorithm and stationary Kalman filter algorithm?

I want to compute the stationary Kalman filter algorithm but I haven't found any information about that algorithm ( not even the pseudo code ) so, I wonder what is the difference between the Kalman ...