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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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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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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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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Kalman Filter in Vision - Constant Velocity Model - Units
Let's assume we have series of frames with a known object. I want to track the object using Kalman filter using constant velocity / acceleration models. My questions are:
Which model to use? CV or CA?...
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Which filter is suitable for reducing noise in feature detection?
I have a feature detection algorithm that is called FAST - Feature Accelerated Segmented Test.
It's a very fast algorithm for finding feature points, e.g "corners" inside an image. Here is ...
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How to define Q matrix (covariance matrix for process noise) in EKF
I am implementing an Extended Kalman Filter (EKF). I have developed the model for my system and I know must find the Q matrix. I have searched all over the web and noone explains how to define this ...
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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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Is it possible to reformulate a Kalman Filter as a Gaussian Markov Random Field?
The generic formulation of a KF uses a set of transitition equations, while the GMRF is typically specified through its mean and precision. However, a simple KF involves Gaussianity and Markov ...
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Extended Kalman Filter - Jacobian Computation
I have the following problem. I have the following Kalman filter:
$ \boldsymbol{x}_k=\boldsymbol{x}_{k-1} + \boldsymbol{w}_k$
$ \boldsymbol{y}_k=h(\boldsymbol{x}_{k}, \boldsymbol{v}_k)$
where $\...
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average after Kalman filter and how to deal with drift
This is in the context of mobile device localization. The mobile device does not move.
All I have is the delay estimated from the signal sent by the mobile device ('measure' in blue).
With a simple ...
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Getting position data from 9-axis IMU
I want to track the movement of a person in a 2D plane using a 9-axis IMU. The size of the plane in which the movement is not bigger than 6 by 6 meter.
The IMU is mounted on the head of the person and ...
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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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Initial Process Covariance in 1-D Kalman Filter
Having a bit of confusion about what the initial process covariance (P) should be. Assume a 1-D tracking problem where I am measuring the distance/position of a static object. Would P not just be ...
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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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Time fusion Kalman filter
Suppose I have a set of estimators, $$\{S^1, S^2, S^3, S^4,\ldots,S^n\}$$ that output at each timestep $t$ a measurement representing an estimate of the true signal $y$, however the output of each ...
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How to regularize the latent variables of a kalman filter to be small?
This is perhaps a bit of a weird idea but suppose I want the latent variables of a Kalman filter to be small (like as if the states were being regularized). This is kind of like putting an extra prior ...
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Kalman Filter on Sensor Fusion
Assume I have 2 sensors capable of measuring distance to an object of known distance. If I apply a Kalman filter to these 2 sensors, I would have 2 correction and prediction equations. If I have 2 ...
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Phase rotation compensation in AOA
We are using $4 \times 4$ corehw antenna array with nrf52833 mcu as the receiver and nrf52833 as transmitter. When working on AOA Direction Finding, we found that each element in the antenna array has ...
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Unscented Kalman Filter for Parameter Estimation (Tracking) of Amplitude Frequency and Phase of a Multi Component Harmonic Signal
I'm trying to implement an Unscented Kalman Filter that tracks the amplitude, frequency, and phase of a multi-component oscillatory signal. Below is an attempt using the ...
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Using the Kalman filter given acceleration to estimate position and velocity
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 acceleration to read this data, and as confirmed by ...
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2nd order EKF covariance propagation equation (hessian)
[cross-post on MathExchange]
I am trying to implement a 2nd-order EKF and am having some issues with the propagation equation for covariance.
From the literature (see end of post for references), if $...
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Kalman Filter Algorithm for Unknown Process and Measurement Noise
I want to be use kalman filter for the state estimation but I don't know about process and measurement noise. How can I estimate process and measurement noise and use this information for kalman ...
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Gyroscope Error Propagation: Why not use Euler Angles?
Looking at the EKF formulation for Gyroscopes in more depth I'm wondering, why can't we use Euler Angles in the Error State EKF framework for error and covariance propagation instead of Quaternions? ...
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Confusion on Error State Kalman Filter reset
I have been reading about kalman filters for IMU and I am confused on the error state formulation.
Reading this paper, starting on page 63 and going onto 64 the paper addresses the reset of the error ...
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Deriving equations for IMU Kalman Filter
I am trying to model a Kalman Filter for an IMU (inertial measurement unit) with the method described by Zhou (2004)
and Filippeschi (2017, pp.11-12).
In this method, the state vector is:
$$
X = \...
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Why is the prediction step in my Kalman Filter failing?
I am trying to become familiar with state estimation, specifically with the use of an accelerometer.
I am simulating the following experiment: a 1D spring-mass system (mass $m = 1$, spring constant $k ...
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Forward problem of Kalman filter causing NaN values during recursion?
\begin{eqnarray}
X_k &=& F X_{k-1}+ \omega_k \nonumber \\
Z_k &=& H X_k + \nu_k
\end{eqnarray}
The first equation is state exploration equation and second one measurement ...
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Kalman Filter Under Non-Gaussian Noise
I know that Kalman filter is optimal filter under some assumption like process and measurement noise are Gaussian. But if the process and measurement noise is non-Gaussian, the estimation of the ...
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What is the intuitive meaning of selecting high or low Q value in Kalman filter?
I am working on experimental data, where I need to choose Q in Kalman filter. How to intuitively understand:
What does selecting low value of Q indicates in Kalman filter?
What does selecting high ...
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Non-linear external effect in Kalman filter
Let's say I have a Kalman filter with this simple state model:
$$\begin{pmatrix} x^0_{k+1}\\ x^1_{k+1}\\ \end{pmatrix} = \begin{pmatrix} 1 & \Delta t\\ 0 & 1\\ \end{pmatrix} \begin{pmatrix} x^...
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How to generate ground truth in constant velocity Kalman simulation?
I'm trying to simulate a particle going from (-3,0) to (3,0) with a constant velocity and some noise (e.g. the particle is a quadcopter trying to fly at constant velocity, but may be pushed by gusts ...
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Unscented Kalman Filter Equations for Constant Turn Rate and Velocity Process Model
I am learning about Unscented Kalman Filters in Udacity's Self-Driving Car Nanodegree. The UKF is designed to track an object moving under the assumptions of constant turn rate $\ddot\psi$ and ...
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Kalman filter in data fusion
I am very new to Kalman filter. I am doing a project using one sensor the track the sensor's position. I developed 2 methods to solve the position, one in better accuracy and one is less accurate.
I ...
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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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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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Advice for Kalman filter for position with velocity input
I am currently building a Kalman filter to add positions derived from high-sample rate velocity data (from an IMU) to lower-sample rate GNSS data. Normally, I understand you would use acceleration ...
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UKF vs random sampling/monte carlo error propagation
What are the pros/cons of propagating uncertainty of a system via random sampling the distribution of the current state and refitting a gaussian on the prediction vs using UKF?
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Understanding an adaptative single neuron PID controller
I only know the "vanilla" use of a Kalman filter and I am currently trying to understand an article available here (the algorithm is presented in the 6 first pages) :
Adaptive Single Neuron ...
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Kalman Filter - Comparing the Static Kalman gain and the Dynamic/Recursively updating Kalman Gain
I studied Kalman filters some time ago, and recently came to realize I do not understand some parts on them. Specifically related to the difference between
using a static Kalman-gain, found by ...
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Finite Difference Estimation for error propagation
For a complex system where symbolic computation of the jacobian is challenging, is estimating the jacobian via finite difference a viable option?
To be explicit I'm mostly interested in playing around ...
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Kalman filter - understanding the noise covariance matrix
What is the significance of the noise covariance matrices in the Kalman Filter framework?
I am referring to:
process noise covariance matrix Q, and
measurement noise covariance matrix R
at any ...
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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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How to set initial values of the elements in the covariance matrices in the Kalman filter?
Let's say I would like to use the discrete version of the Kalman filter in a role of a state observer of a linear dynamic system. The observed continuous time domain dynamic system can be described ...
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What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?
I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system.
In the time being I have been using a discrete ...
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Sensor Fusion of Two Same Type of Data
I have an object moving with sinusoidal motion. I estimate the position of the object using lidar and camera separately. Then I want to fuse these two estimation data in the optimal way. For example I ...
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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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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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What's the best way of modeling 3d target motion with only 2d angle observations?
A maneuvering target is flying in 3d cartesian space, but a sensor (passive infrared or mic array, etc.) can only observe it in polar coordinate with 2d orientations
(azimuth, elevation). For ...
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Approaches to work around differing signal lengths when using Kalman filter
I have a set of vector valued signals $\boldsymbol{y}_{1:T}$ where each $\boldsymbol{y}_k \in \mathbb{R}^{v_k}$. Each signal is potentially of different dimensionality. I'd like to apply filtering and ...
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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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