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.
411
questions
1
vote
0
answers
16
views
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-...
- 121
1
vote
0
answers
10
views
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. ...
- 121
1
vote
0
answers
63
views
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 ...
- 403
3
votes
1
answer
61
views
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 ...
- 33
1
vote
0
answers
34
views
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 ...
- 11
0
votes
0
answers
33
views
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 $\...
1
vote
0
answers
70
views
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 ...
- 63
1
vote
0
answers
54
views
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 ...
- 11
4
votes
1
answer
105
views
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 ...
- 41
1
vote
0
answers
32
views
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 $...
- 111
1
vote
1
answer
74
views
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? ...
- 818
0
votes
1
answer
100
views
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 ...
- 818
0
votes
1
answer
101
views
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:
$$
X = \...
- 103
3
votes
1
answer
163
views
Kalman Filter Algorithm for Unknown Process and Measurement Noise
I want to be use kalman filter for the state estimation but I don't know about process and measurement noise. How can I estimate process and measurement noise and use this information for kalman ...
- 51
1
vote
0
answers
222
views
Kalman Filter Under Non-Gaussian Noise
I know that Kalman filter is optimal filter under some assumption like process and measurement noise are Gaussian. But if the process and measurement noise is non-Gaussian, the estimation of the ...
- 51
0
votes
1
answer
104
views
What is the intuitive meaning of selecting high or low Q value in Kalman filter?
I am working on experimental data, where I need to choose Q in Kalman filter. How to intuitively understand:
What does selecting low value of Q indicates in Kalman filter?
What does selecting high ...
- 61
1
vote
0
answers
59
views
Non-linear external effect in Kalman filter
Let's say I have a Kalman filter with this simple state model:
$$\begin{pmatrix} x^0_{k+1}\\ x^1_{k+1}\\ \end{pmatrix} = \begin{pmatrix} 1 & \Delta t\\ 0 & 1\\ \end{pmatrix} \begin{pmatrix} x^...
- 111
1
vote
2
answers
90
views
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 ...
- 11
0
votes
1
answer
100
views
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 ...
2
votes
1
answer
52
views
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 ...
- 61
4
votes
2
answers
228
views
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 ...
- 61
0
votes
0
answers
55
views
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 ...
0
votes
0
answers
19
views
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?
- 818
1
vote
1
answer
34
views
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 ...
- 818
4
votes
1
answer
124
views
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 ...
- 487
1
vote
1
answer
254
views
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 ...
- 111
2
votes
1
answer
78
views
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
<...
- 375
0
votes
1
answer
175
views
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 ...
- 375
1
vote
1
answer
62
views
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 ...
- 375
0
votes
1
answer
374
views
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 ...
- 1
1
vote
0
answers
139
views
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 ...
- 51
5
votes
1
answer
459
views
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 ...
- 61
1
vote
1
answer
130
views
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 ...
- 61
1
vote
1
answer
72
views
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 ...
- 11
2
votes
1
answer
120
views
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 ...
- 23
2
votes
1
answer
622
views
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 ...
- 818
1
vote
1
answer
115
views
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 ...
- 818
1
vote
0
answers
144
views
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 ...
- 53
0
votes
0
answers
108
views
Using kalman filter in R for sine wave frequency estimation
I'm pretty new to Kalman filtering techniques, and have a problem that I'm trying to solve.
Imagine in a lake I have a splash generator that sends out sine waves across the lake. At various places ...
- 1
3
votes
0
answers
469
views
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 ...
- 243
0
votes
0
answers
70
views
Wiener filter for vector-valued signal
I'm trying to understand the derivation of a Wiener filter for a vector-valued signal, found in the paper "Kalman filtering in non-Gaussian model errors: a new perspective," IEEE Signal ...
- 131
1
vote
1
answer
229
views
Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)
Consider the following discrete-time system:
\begin{equation}
\mathbf{x}(k+1) =
\mathbf{A}_d
\mathbf{x}(k)
+
\mathbf{B}_d
\mathbf{u}(k)
\end{equation}
\begin{equation}
y(k) =
\mathbf{C}_d
\mathbf{x}(k)...
- 75
1
vote
1
answer
96
views
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 ...
0
votes
1
answer
75
views
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 ...
- 9
1
vote
1
answer
181
views
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 ...
- 818
1
vote
0
answers
51
views
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 ...
- 41
3
votes
1
answer
124
views
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 ...
0
votes
0
answers
164
views
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 ...
- 41
1
vote
0
answers
41
views
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\...
- 11
3
votes
1
answer
534
views
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 ...
- 41