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.
403
questions
2
votes
1
answer
35
views
Is it possible to force 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 ...
- 21
1
vote
0
answers
16
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
60
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? ...
- 858
0
votes
1
answer
39
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 ...
- 858
0
votes
1
answer
42
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:
$$
X = \...
- 103
3
votes
1
answer
82
views
Kalman Filter Algorithm for Unknown Process and Measurement Noise
I want to be use kalman filter for the state estimation but I don't know about process and measurement noise. How can I estimate process and measurement noise and use this information for kalman ...
- 51
1
vote
0
answers
58
views
Kalman Filter Under Non-Gaussian Noise
I know that Kalman filter is optimal filter under some assumption like process and measurement noise are Gaussian. But if the process and measurement noise is non-Gaussian, the estimation of the ...
- 51
0
votes
1
answer
45
views
What is the intuitive meaning of selecting high or low Q value in Kalman filter?
I am working on experimental data, where I need to choose Q in Kalman filter. How to intuitively understand:
What does selecting low value of Q indicates in Kalman filter?
What does selecting high ...
- 61
1
vote
0
answers
58
views
Non-linear external effect in Kalman filter
Let's say I have a Kalman filter with this simple state model:
$$\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
59
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
51
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 ...
1
vote
1
answer
32
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
5
votes
2
answers
116
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
41
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
15
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?
- 858
1
vote
1
answer
28
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 ...
- 858
4
votes
1
answer
102
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 ...
- 422
1
vote
1
answer
96
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
72
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
<...
- 365
0
votes
1
answer
59
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 ...
- 365
1
vote
1
answer
49
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 ...
- 365
0
votes
1
answer
116
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
75
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
7
votes
1
answer
149
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 ...
- 81
1
vote
1
answer
83
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 ...
- 81
0
votes
0
answers
80
views
Kalman Filter with IMU to estimate position
I'm starting with KF and working with a IMU to estimate position. I'm defining my model and so many questions come to my mind when I have to define the process noise matrix (Q) and the measurement ...
- 1
1
vote
1
answer
56
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
85
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
229
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 ...
- 858
1
vote
1
answer
82
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 ...
- 858
1
vote
0
answers
91
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
85
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
304
views
Unscented Kalman Filter for tracking amplitude, frequency, and phase of a multi-component 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 ...
- 253
0
votes
0
answers
57
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
144
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
85
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
47
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
95
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 ...
- 858
1
vote
0
answers
47
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
2
votes
1
answer
103
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
102
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
37
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
219
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
10
votes
2
answers
862
views
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 ...
- 233
1
vote
0
answers
61
views
How to perform filtering through optimization?
I have an objective function for finding out the signal estimate say $\parallel X_{cap}-X\parallel_2^2 +$ denoising term. Can someone suggest me any techniques on how to incorporate a filter such as ...
5
votes
2
answers
226
views
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 ...
- 51
3
votes
1
answer
147
views
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 "...
- 81
8
votes
2
answers
290
views
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 ...
- 103
1
vote
1
answer
71
views
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 ...
- 115
2
votes
0
answers
74
views
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 ...
- 3,715