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.
125
questions with no upvoted or accepted answers
5
votes
1
answer
462
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
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
4
votes
1
answer
452
views
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?
- 41
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
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
3
votes
0
answers
76
views
State estimation in HyperSonic Missiles
I'm curious, what would be the correct approach for state estimation for hypersonic Missiles?
Would it be exclusively GPS and IMU? Historically these are what was used, but I have also seen ground ...
- 818
3
votes
0
answers
244
views
How to compute (in non adaptative way based on MMSE FIR) the feedback and feedword filter for DFE equalization?
System Model
Consider the single-input single-output (SISO) communication system in the figure below:
where the information bit stream is encoded and mapped such that the output of the encoder is a ...
user47976
3
votes
0
answers
276
views
Kalman Filter for position : introducing acceleration estimates
I want to estimate the position on a 3D environment by introducing only acceleration estimates. Is that possible? If I use the extended Kalman Filter and introduce these estimates will I have the ...
- 31
3
votes
0
answers
493
views
Converting an FIR Filter Model to a State Space Model for Kalman Filtering
I want to try and determine the true value of a quantity $\alpha[k]$ from observations of a related quantity $\vartheta[k]$ using a Kalman filter. The observations are of the following FIR filter form:...
- 29
3
votes
0
answers
43
views
Inconsistant Variation in BLE Beacon RSSI Values for Distance Measurement
I am developing an application to estimate the distance to a BLE Beacon using its RSSi values measured from a Mobile Phone. But when I started to collect data I could see that they varied so much that ...
- 31
3
votes
0
answers
336
views
Role of Riccati Equations in Kalman Filter Design
I am working on a Kalman Filter (KF) design problem and I am struggling to understand the role of the Riccati equations in the design process of a KF.
Some sources discuss the importance of Riccati ...
- 131
3
votes
0
answers
173
views
(Unscented) Kalman Filter with variable state dimensions
i have to estimate a process which changes over time, not with respect to the system-evolution or the measurement-function, but regarding the number of objects that have to be estimated. So every ...
- 171
3
votes
0
answers
113
views
Optimal inference for nonlinear state space models
When considering a linear-Gaussian state space model, it is often referred that, optimal inference is tractable which is very rare in state space models. When considering a nonlinear state space model,...
- 638
3
votes
0
answers
885
views
Optimal measurement model for Kalman in Augmented Reality
I am developing an augmented reality SDK that uses Kalman for tracking a planar marker. My state is composed of 3D position, a quaternion, velocity and angular velocity.
\begin{bmatrix}{\vec{p}}\\{\...
- 1,213
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
2
votes
0
answers
87
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 ...
- 3,735
2
votes
0
answers
352
views
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 ...
- 21
2
votes
0
answers
213
views
How Do Particle Filters Get Velocity When Tracking with Pos Measurements
I am new to particle filtering.
I can see when particle filters are used with Ensemble Kalman's, the velocity of the states are taken care of by the Kalman.
When tracking using particle filters ...
- 21
2
votes
0
answers
568
views
Estimate standard deviation of random-walk using Kalman filter
I'm new to Kalman filters so this might be a stupid question.
I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
- 121
2
votes
0
answers
444
views
Why does noise prevent a (kalman) filter from diverging?
I'm using a filter (not exactly kalman) of the following form to estimate angles by fusing gyroscope with accelerometer and gyro with magnetometer:
$(1)\quad \hat{\theta}_k = \hat{\theta}^-_{g,k} + \...
2
votes
0
answers
248
views
Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori
I am implementing a Kalman filter (for a linear ODE system for now).
My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
2
votes
0
answers
153
views
Check if I has right: Is this the Extended Kalman Filter
I have learn the Kalman-Buncy filter for the LQG controllers. I know that this is a signal processing forum and not robotics not math forum. But Extended Kalman Filters are daily discussed here.
...
- 403
2
votes
0
answers
228
views
Digital filter for sharp impulse in data
I am looking for an algorithm or a filter to remove sharp peaks from my data. I am collecting raw data after every 1 second from an sensor through an ADC. The ADC has an internal FIR filter. I use ...
- 21
2
votes
0
answers
47
views
Filtering for Wright-Fisher HMM
I am trying to understand what filter may be suitable for the following HMM:
The signal is a Wright-Fisher one-dimensional diffusion characterised by the SDE
$$dX_{t}=\frac{1}{2}\left(\alpha(1-x)-\...
- 21
2
votes
1
answer
65
views
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 ?
2
votes
0
answers
447
views
Kalman filter without model versus RLS
As I found out in my previous question Where to get transtion matrix for Kalman filter?, I need a model for correct usage of Kalman filter.
In paper On the Intrinsic Relationship Between the Least ...
- 657
2
votes
0
answers
896
views
Kalman filter to filter noise from acceleration data
I would like to apply a Kalman filter to remove noise from my measured acceleration data. The idea is then to compare the results obtained in this way whit the results obtained by applying a low-pass ...
- 413
2
votes
0
answers
185
views
Open source GPS+IMU sensor fusion?
Are there any Open source implementations of GPS+IMU sensor fusion (loosely coupled; i.e. using GPS module output and 9 degree of freedom IMU sensors)? -- kalman filtering based or otherwise
I see a ...
- 121
2
votes
0
answers
244
views
Purple Noise Modeling / Differentiated White Noise (Kalman Filtering)
I am designing a Kalman Filter for a signal which features a certain kind of noise and I do not know how to model it properly in the filter.
The noise is constructed from a white noise source, called $...
- 21
2
votes
0
answers
235
views
Identifiability of a state space model (Dynamic Linear Model)
Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM):
\begin{align}
X_{t+1}&=FX_t + V_t\\
Y&=HX_t+W_t\\
V_t &\sim \mathcal N(0,Q)\\
W_t &\sim \...
- 179
2
votes
0
answers
996
views
Velocity estimation knowing acceleration and displacement from measurements using Kalman filter
I am having a hard time in trying to use a Kalman filter to obtain velocity
from acceleration and position measurements. I think the main reason is that
I am not familiar with Kalman filters (I had ...
- 413
2
votes
0
answers
140
views
Correct Kalman Filter for Gaussian State Space Model
I am trying to follow a paper where they say they apply the Kalman filter, but don't give the forumulation for the Kalman filter! Moreover I have looked at two references Wikipeadia and Durbin and ...
- 179
2
votes
0
answers
419
views
Extended kalman filter for accelerometer data on shaking table
I am using an accelerometer to record the motion of a shake table (a rocking table) which moves forward and backward in one direction. The signal is very noisy and decided to use Extended Kalman ...
- 21
2
votes
0
answers
404
views
Kalman Filter: continuous state space, discrete observations
This is just an idea. How can we model the kalman filter to get the state representation in continuous space when the observations to the system are actually from the discrete space. The discrete ...
- 21
2
votes
0
answers
557
views
Extended Kalman Filter - how do I get transition functions
I am measuring position and velocity, both have some noise in them. Velocity is defined as derivative of position. The system is apparently non-linear so I need to use EKF.
Model:
\begin{align}
X&...
- 375
2
votes
0
answers
300
views
Estimate process error for Kalman filter on financial data
I'd like to apply a Kalman filter, using Octave, to financial data but due to the nature of the data it will be difficult to impossible to specific the process error in advance of applying the filter. ...
- 487
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
11
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
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
1
vote
0
answers
71
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
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
0
answers
227
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
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
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
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
0
answers
147
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
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 ...
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