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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Example for implementing the unscented kalman filter

Currently, I'm learning about the UKF and in order to understand it in a good way, I programmed it, however in order to see it working I need a problem to solve which I can't now find. Can you please ...
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EKF: IMU vs State Transition Model

Suppose you have an object you're interested in estimating the state of, ex position. Suppose you don't have a state transition model but you do have an IMU. Can the IMU be used to simulate a state ...
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Single Kalman Filter: Resistance based on measurment of current and Voltage [closed]

Given measurement of voltage and current, which contain gaussian noise with known variance and a constant unknown offset $a_0$, I have attempted to estimate the resistance $R=\frac{V}{I}$. The ...
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Interpreting sensor noise data

Introduction :I am trying to create an EKF for an autonomous vehicle, and i need to model the error of the sensors. (I am a mechanical engineer so my knowledge on electric signals is limited). The ...
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Extended Kalman Filter: Error Covariance

I am trying to implement an EKF for orbit determination of a spacecraft(SC). The state which i am interested to estimate is the following $x = [r_{SC}\,v_{SC}\,\Delta Cd\, \Delta Cs\, b\,d]$ where $r_{...
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Simulink delay block doesn't recognize vectors as intial conditions

I am trying to implement the kalman filter on simulink, for which I need the delay block to compute the new estimate based on the previous one. My state vector is three dimensional, and for some ...
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In particle filter: what is the meaning of $\pi_n(x_n|x_{1:n-1})$?

In the survey article of particle filter A Tutorial on Particle Filtering and Smoothing: Fifteen years later, the equation (39) are $$ \begin{aligned} \pi_{n}\left(x_{n} \mid x_{1: n-1}\right) &=p\...
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When is it necessary to use a Kalman Filter, and not a simple estimation method?

I know its a stupid question, but I got understand this very fundemental point. Say we have a sinousodial signal, which we want to extract from a noisy (known variance and mean) measurement. It is ...
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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 ...
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How to perform filtering through optimization?

I have an objective function for finding out the signal estimate say ||X_cap-X||_2^2 + denoising term. Can someone suggest me any techniques on how to incorporate a filter such as Kalman filter as an ...
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Kalman Filter Motion model with moving sensors

Suppose I have an object that I am tracking with moving sensors using a basic Kalman Filter (for example, think of a ship being tracked by satellites). In the simplest case where the sensors are ...
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What do I measure in a Sound Sample Buffer to remove noise from an audio file using the Kalman Filter?

I am developing a computer program that removes or reduces the background noise from an audio file using the Simple Kalman Filter. I have implemented the Kalman Filter and a way of obtaining the "...
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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 ...
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How does sampling jitter affect state estimation?

Suppose I have some process which is governed by: $$ \vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$ where $u_k$ is the input, and $w_k$ is process disturbance. This process is continuous time in ...
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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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State estimation in HyperSonic Missiles

I'm curious, what would be the correct approach for state estimation for hypersonic Missiles? Would it be exclusively GPS and IMU? Historically these are what was used, but I have also seen ground ...
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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 ...
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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 $\hat{x}$ ...
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Too low measurement error Q (much lower than real measurement noise) in Kalman Filters

What do we expect by setting a too low measurement error in a Kalman Filter model, much lower than the noise existing in the measurements? And why? Let's say we simulate some measurements and we add ...
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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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Kalman filtering with dynamic covariance/variance

What is the appropriate way to implement KF if your sensor confidence is time and observation dependent? Ex, you asses the quality of camera tracking by the percentage of features correctly matched by ...
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How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
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In what sense is the Kalman filter optimal?

The Kalman filter is a minimum mean-square error estimator. The MSE is defined as $E\left(||\hat{x}_k-x_k||^2\right)$ where $x$ is the state and $\hat{x}$ is the estimate. When $x$ is a vector, for ...
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Kalman filter for heading estimation with magnetometerv + gyroscope only considers magnetometer

I implemented a Kalman filter to estimate the heading of a robot that is moving in 2D, given the measurements coming from a magnetometer (X, Y) and a gyroscope (Z). The code is the following: ...
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Mixing Constrained Properties in an Interacting Multiple Model Filter

While implementing an Interacting Multiple Model tracking filter with one model being a constant turn rate model, I began questioning how the mix should behave while taking into account that some ...
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Does a gyroscope get impacted by gravity?

When processing IMU data, does the gyroscope get impacted by gravity? Linear accelerometers need to have gravity compensation but nothing is said of IMU.
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I have read multiple sources on the IMM filter but I cannot understand how to implement it

I am working on an image detection and tracking problem and have correctly implemented the Kalman filter. I have two Kalman filters and want to track a maneuvering target. After all the books I have ...
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Can the Kalman filter estimate a factor of the model? Product of two state variables

I've written down a discrete state-space model for a simple pendulum, with the state variables angle, angular velocity and angular acceleration. This can be easily plugged into a simple Kalman filter ...
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Is the discrete or continuous-time state-space model most appropriate for implementing an embedded Kalman filter? [duplicate]

I'm writing down a state-space model of a mathematical pendulum, in order to estimate the system parameters in an embedded simple Kalman filter. So far I'm just modeling the system in Matlab and haven'...
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Why is the prediction step in my Kalman Filter failing?

I am trying to become familiar with state estimation, specifically with the use of an accelerometer. I am simulating the following experiment: a 1D spring-mass system (mass $m = 1$, spring constant $k ...
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If there are state variables in the Kalman filter that aren't being measured, is their output just rubbish?

I've been learning about the Kalman filter on this website: https://www.kalmanfilter.net/multiExamples.html As you can see there is a numerical example regarding a car that is traveling in a 2 ...
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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 ...
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8 votes
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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. ...
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Space-Time Finite Element and Static Condensation for Sensor Fusion

My recent pastime interest deals with the nonlinear sensor fusion of GNSS, barometer, magnetometer, accelerometer and gyroscope data. I had a look at the EKF, UKF and Particle Filters but gave up as ...
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How to determine covariance matrices $\mathbf P$, $\mathbf Q$, and $\mathbf R$ in Extended Kalman Filter

I am implementing an Extended Kalman-Filter and an Unscented Kalman-Filter for state and parameter estimation of a conveyer belt system. The problem is that I don't really know how to determine the ...
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Mixing Kalman filter and least-squares

I'm not sure it is the right department. I try my chance I am wondering if there is a way to make a hybrid formulation of a least-square problem and a Kalman filter. Let me explain what I mean: The (...
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Kalman Filter: Why do we decrease the state uncertainty regardless of the current measurement?

I'm struggling with fully understanding the concept behind a Kalman filter. For the sake of simplicity, let's ingore the input variable $u$ and assume constant process $Q$ and measurement noise $R$. ...
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Kalman filter continues to update position even though speed is zero

Background I set up a conventional Kalman filter that makes use of smartphone GPS only (no inertial sensors). That is, it uses the position, doppler speed, and course, in order to create positions ...
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Are there any general heuristics for Kalman filter noise parameters

Are there any generally applicable heuristics for Kalman filter noise parameters? I am working with a non-linear unscented filter and getting an initial guess for the noise covariances $Q_k$ and $R_k$ ...
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Accelerometer Bias estimation with kalman filter

I have to estimate biases of a 3-axes accelerometer by modyfying an existent kalman filter mounted on a drone. The biases are assumed constant. The filter has 9 states: position (xyz), velocity (xyz) ...
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Recommendation for courses / studies on digital signal processing

I hold a master's degree in mechanical engineering. However at my job I am more and more diving into topics of signal processing and data science. I find it great to discover about new topics and to ...
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Extended Kalman Filter measurment vs input vector

What is difference between measurement and input vector in Extended Kalman Filter? Isn't always input also measurement? If so how to update input vector if I have acceleration or yawrate as input ...
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2 votes
1 answer
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Kalman Filter - Deriving state transition function

I am relatively new to using Kalman Filtering. Currently I am trying to understand it and how to implement it in Matlab. I found a website with some nice examples that I would like to rewrite in ...
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1 vote
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How to initialize observation Matrix in Kalman Filter when there is no clear relationship between measurement and state?

I am try to use Linear Kalman to do time series prediction. I understand that I have to define a model process matrix which indicate how system state evolve, and a measurement matrix H which convert ...
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How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?

I'm trying to understand how I can update a Kalman filter with a state variable for position and velocity when I only measure position. I have a covariance matrix of the position measurements. But ...
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How to handle a logarithmic term in Kalman filter?

I am trying to implement a Kalman filter for an echo pulse detection application as similar to this paper. (an open source version is here (pg 16)) The measurement variable is $h(x,t)=A_0 (\dfrac{t-\...
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Kalman filter with multiple sensors

I have been reading more about EKF and I am a bit confused on how you handle predictions with multiple sensors. Ex, I have IMU, GPS, Odom and Stereo Camera. Each can be used to predict location, how ...
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2 votes
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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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Kalman Filter from 2D LookUp Table

I have two sets of inputs, A (10 values) and B (20 values), and for each point (A,B) I have a measurement to make a (10x20) table of measurements C. Is there a way to use a Kalman Filter to improve ...
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Is Kalman Filter for LTV systems applicable on Hybrid systems?

As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But nobody in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of ...
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