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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 with sensitivity to the parameters

We all know the most crucial part of Kalman Filter is the calibration of process noise and observation noise covariance matrices. ($R$ and $Q$ in Wikipedia convention ) Frequently we don't really know ...
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Signal Detection in Noise

I have known pulses, e.g. $A\exp(-\frac{t}{\tau})\cos(\omega t)$, but they are "hidden" in additive (let's say Gaussian) noise and it is not possible to predict when such events will occur. ...
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Kalman filters which only update a subset of variables?

What is the general approach to updating a subset of variables with a kalman filter? IE sensor X only updates variable Y. What I'm a little bit confused on is how the covariance would be propagated.
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PLL Phase Error Detectors for non-bandpass-communication type signals

I'm quite familiar with PLLs for bandpass signals (e.g., GPS) which operate on IF or complex baseband signals. However, I now have a phase tracking problem where the signal is not necessarily ...
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Gyroscope sensor drift problem at speed

I have an iPhone mounted on a bike to measure the slope of the road in real-time. This works pretty well at first but as soon as I speed up, the reported pitch starts to drift. I'm using CoreMotion ...
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SAR and ISAR sampling time

This is a repost of a question that I've previously asked in the EE section of SE. Unfortunately, I've not solved my problem. I'm seeking insight into the typical values of sampling times or refresh ...
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Fusing multiple IMUs in EKF framework

What is the approach to fuse multiple IMUs in EKF framework? Normally you take the IMU as the motion model and the sense step to consist of other sensors but when have multiple IMUs operating, what is ...
FourierFlux's user avatar
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Implementing signal processing techniques for consistent RSSI signal reception

I've tried to optimize the LoRa setup using Arduino IDE libraries to ensure accurate or acceptable RSSI measurements and for distance estimation between multiple nodes and a master in an outdoor ...
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Temperature estimation via Kalman filter

Based on the recommendation I would like to ask you for your opinion regarding my question I have asked on different forum.
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Does it make sense to have diverging Kalman gain and covariance when system accuracy worsens over time?

I've developed an UKF for a system, whose dynamics change slowly over time. The state & measurement equations are quadratic and linear equations fitted to experimental data in the following form: $...
square potato's user avatar
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Wiener Filter for Noise Reduction in GPS Sensor Measurement

I am getting position and velocity measurements out of a GPS sensor and I want to filter these data, so I can have a better, less noisy, estimation of the true measurements. I thought of doing this ...
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Kalman filter for multiple data sources, measurements from which have different characteristics of Gaussian noise

I am trying to use the Kalman filter for my task: During the time, I receive data from different sensors. The state of the model may change over time according to the Const Velocity model, or the ...
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What happens when Kalman filter is applied on a memoryless system?

I'm trying to set up a Kalman filter for my system $$ x_{k+1} = f(u_k) $$ $$ z_{k+1} = g(x_{k+1}) $$ and found that while the filter "works" (able to reduce rmse from 1.5% in the open loop ...
square potato's user avatar
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Can the Kalman Filter process covariance be estimated from measurements?

I'm looking for the simplest possible method for estimating the process noise covariance $\mathbf{Q}$ and measurement noise covariance $\mathbf{R}$ for a Kalman Filter. This is assuming a time-...
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When is the Kalman Filter state (un)observable?

In Rudolf Kalman's seminal paper, the problem of filtering is defined as below (p. 2): We are given signal $x_1(t)$ and noise $x_2(t)$. Only the sum $y(t) = > x_1(t) + x_2(t)$ can be observed. ...
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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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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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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 ...
user68463's user avatar
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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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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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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? ...
FourierFlux's user avatar
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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 ...
FourierFlux's user avatar
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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 = \...
Jacob Sánchez's user avatar
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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 ...
guidolard's user avatar
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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 ...
guidolard's user avatar
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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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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 ...
Ko Chunwai's user avatar
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1 answer
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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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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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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 ...
SquirrelKing's user avatar
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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 ...
FourierFlux's user avatar
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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 ...
Chris_abc's user avatar
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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 <...
Steve's user avatar
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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 ...
Steve's user avatar
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1 answer
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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 ...
Steve's user avatar
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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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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 ...
guidolard's user avatar
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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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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 ...
6900HS's user avatar
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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 ...
Steven Ding's user avatar
2 votes
1 answer
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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 ...
FourierFlux's user avatar
1 vote
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IMU state estimation Covariance updating

EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps? In essence I want to evolve the state of an object using an IMU ...
FourierFlux's user avatar
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Derivation of the process noise covariance matrix for non linear system in UKF

I have a continuous (in time) non-linear system in the form $\dot{x}=f(x(t)) + Bu(t) + w(t)$ which I would like to track with a UKF. $w(t)$ represent white noise (in particular, the acceleration and ...
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