Signal Processing

Questions tagged [kalman-filters]

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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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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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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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Kalman Filter implementation is too slow

I have implemented with a simple code a Kalman Filter for time domain, based on these: KG = error_est / (error_est+error_measurment) estimate = estimate_prev + KG ( measurment - estimate_prev) ...
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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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Does Kalman Consensus Filter have any public implementations?

I am trying to solve a problem using the KCF described here: https://ieeexplore.ieee.org/document/5399678 Does there exist an implementation of this (preferably in python) which is available openly? I ...
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Can we combine the application of SIFT with Kalman filter for 3D reconstruction of structural buildings?

This is just a novice question from somebody who just got into this topic. Can the application of Scale-Invariant Feature Transform be combined with extended Kalman Filter?
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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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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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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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Alternatives to offline Kalman filtering

Recently I got into vehicle models and filtering in general and immediately faced with the following question. I have the recorded GPS data from car driving on a highway. However, there is a ...
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UKF with nonlinear noise effect

I was recently experimenting with UKF that compensates nonlinear effects of noises by forming appended state vector. The general way of dealing with such case in the literature is the following: Form ...
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Parameter tracking using Augmented state vector approach and unscented Kalman filter

I'm trying to reproduce and extend figure 9 results in Nonlinear dynamical system identification from uncertain and indirect measurements"HU Voss, J Timmer, J Kurths - International Journal of ...
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How to find parameters of Kalman filter using matrix information?

I'm trying to understand concepts on Kalman Filters. Consider the overdetermined system $Ax=y$; $$\begin{bmatrix}1 \\ 1 \\ 1 \\1 \end{bmatrix} x = \begin{bmatrix} 3 \\ 5 \\ 4 \\ 8 \end{bmatrix}$$ Let $...
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1answer
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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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Using a Kalman filter to clean acceleration data

I am collecting acceleration, gyroscope and magnetometer data in all 3 directions. I would like to filter noise from the accelerometer using a Kalman filter. I am not trying to esimate orientatoin or ...
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1answer
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Deriving a Kalman Filter Equation for a Linear Gaussian Filtering Model with Non Zero Mean Noise

I am trying to answer an exercise question from the book Simo Sarkka - Bayesian Filtering and Smoothing. The question is: Does anyone know if there is a resource that has the solutions for this book?
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Colored noise and adjusting covariance matrix with change of frequency

Assume a signal sampled at 2Hz. Assume it is a colored noise with known PSD. The measurement equation to be used in a Kalman filter requires a covariance matrix. If I want to sample at 9Hz (for ...
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Kalman Filter: Difference between sensor input and control input

I recently saw a matlab sensor fusion example which combined IMU and GPS data for drone localization. What was surprising about it was that the IMU was used to predict future behavior of the system as ...
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1answer
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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 ...
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The optimization problem of pulse signal filtering using Kalman filter

I'm trying to use a Kalman filter to process a pulse signal. My model is: x= [x1,x2]$^T$ System model: X$_k$ = x$_{k-1}$ + W$_{k-1}$ , so A = I$_{2×2}$, the identity matrix. and Q= $$ \begin{matrix} ...
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1answer
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Purpose of Extended Kalman Filter with Constant Minimum MSE Matrices

I work with a client that wants me to implement in real-time system an extended Kalman filter they have designed in Matlab. I reverse engineered their code to find out that the Minimum Prediction MSE ...
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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 ...
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What could be the optimal filter given this situation?

I am using a camera and a Deep Neural Network to predict one angle. This network received as input the frame, and calculates the mean and the variance associated to the prediction (which is basically ...
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Interpret and adjust Kalman Filter velocity prediction

This is a copy of question I posted in StackOverflow, now I realize that this is better place to find help. I use MATH.NET implementation of Kalman Filter My example is similar to the example ...
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1answer
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What is the name for a constant-heading Kalman filter model for vehicle tracking?

When applying Kalman filtering to estimate the position of a car, there are several different vehicle dynamics models that you could use. One of the simplest is "constant velocity" or CV, ...
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Remove noise from distance calculated from accelerometer data

I got distance calculated from accelerometer raw datas using double integral accelerometer.I attached the image below.But it shows noise with it.Please help me to remove this noise.
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How to Improve the Kalman Filter for Tracking the Periodic Motion of a Car?

I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a ...

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