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.
409
questions
5
votes
2
answers
372
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
5
votes
2
answers
15k
views
Removing drift from integration of accelerometer data
I am trying to get a positional data from the accelerometer data using the following steps:
Re-zero the accelerometer value
Removing mean from accelerometer value
First integration of accelerometer ...
- 185
5
votes
2
answers
6k
views
How to model the noise in Kalman Filter?
Background:
I am a newbie in DSP. I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope.
My Understanding:
I ...
- 247
5
votes
1
answer
6k
views
Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?
I am attempting to create a Kalman filter to track a sine wave (I am using a linear Kalman filter example assuming I already know the frequency of the sine wave) - the example I am using is derived on ...
5
votes
2
answers
331
views
How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?
I'm trying to understand how I can update a Kalman filter with a state variable for position and velocity when I only measure position. I have a covariance matrix of the position measurements. But ...
- 265
5
votes
2
answers
2k
views
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 ...
- 273
5
votes
2
answers
792
views
Explain the Adaptive Part of Adaptive Algorithms - Kalman Filter and Least Mean Square / Constant Modulus
General questions:
Is the Kalman filter (they have used Unscented Kalman Filter) adaptive or not? Is the Unscented Kalman Filter used in the paper an adaptive algorithm?
Adaptive algorithms such as ...
- 849
5
votes
1
answer
858
views
Frequency tracking with huge noise
I'm working on a frequency tracking problem with noise, where the amplitude of the noise is orders of magnitude higher than the amplitude of my signal (~1000x). Some details:
The signal is roughly ...
- 221
5
votes
3
answers
1k
views
Combining Kalman Filters
Say I want to use Kalman filters for predicting the price of items at a supermarket. I have a Kalman filter for each item (apple/beef/brooms/etc). I notice that some items are sort of related, like ...
5
votes
2
answers
1k
views
Discrete Sinusoidal to State Space
I'm looking to apply an optimal LQR filter to a discrete signal of the form
$x[n]=A\sin[\omega_0n + \phi]+ v[n]$
The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using ...
- 59
5
votes
1
answer
410
views
Is Kalman smoother symmetric in time?
Suppose my model is reversible in time (e.g. GPS + accelerometers for a vehicle), so that I can run Kalman filter forwards or backwards. Kalman filter, of course, cannot be symmetric, because it is ...
- 229
5
votes
3
answers
275
views
How to Improve the Kalman Filter for Tracking the Periodic Motion of a Car?
I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad.
Here is my situation. I have a ...
- 49
5
votes
1
answer
317
views
Model-based Kalman filtering a noisy signal
In a healthcare application, I need to calculate urine flow by differentiating the mass of urine emitted by a person over time. The measuring instrument consists of a load-cell under a fluid container,...
- 1,097
5
votes
1
answer
1k
views
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 ...
- 53
5
votes
1
answer
138
views
Kalman filter restricted by areal constraints
I'm developing a device for tracking pets in a room with several motion detectors. I use a Kalman filter to estimate the position, which is based on the active outputs of the motion detectors. If an ...
5
votes
2
answers
385
views
Particle filter Tracking
I am tracking a car using particle filter by making a rectangle around it, and I am using the state vector $[x, y, u, v, a, h]$, where:
$x$, $y$ is the position of the body
$u$ and $v$ are velocity ...
- 155
5
votes
1
answer
426
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
2
answers
1k
views
Can Kalman Filter be used to track Randomly Moving Target?
i want to track random moving object with a camera using kalman filter...i have the following questions...
Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ is ...
- 601
4
votes
4
answers
457
views
Layman Description of the Kalman Filter
I want to know about Kalman Filter but i tried searching different links including Electrical Engineering StackExchange but the information available there was hardly digestible.
All I am able to ...
- 1,850
4
votes
2
answers
3k
views
Kalman Filter for estimating position with nonconstant velocity & acceleration
I am trying to estimate the position & head direction of a rodent going through a 2D environment (a circular surface of 1m radius). Above his head is an overhead camera which records 4 LEDs ...
- 341
4
votes
1
answer
2k
views
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 $R$.
...
- 41
4
votes
2
answers
224
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
4
votes
2
answers
1k
views
Kalman Filter EM Estimation of Covariances
The question might be very simple, but I get a strange result from Kalman Filter. Let us consider the simplest state-space model, the random walk plus noise:
$$
y_{t} = x_{t} + \varepsilon_{t}\\
x_{t} ...
- 171
4
votes
1
answer
2k
views
Kalman filter for tracking sinusoidal motion
I am wanting to create a Kalman filter that can be used to track an object undergoing sinusoidal (lets assume simple harmonic) motion. I have seen many examples and implemented my own python code for ...
4
votes
1
answer
616
views
How to linearize this state space model and write it in discrete form?
This might not be trivial nor short so in advance thank you all who read this in attempt to help.
I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
- 73
4
votes
2
answers
107
views
Kalman Filter: Why $ Q $ Discrete Is Defined as $\int_0^Te^{\mathbf{A}\tau} Q e^{\mathbf{A}^T \tau} d\tau$?
I would like to ask, why in the transformation to the discretization, $\mathbf{Q}$ is obtained from the expression containing the integral (image attached), what is the theory behind it?
- 41
4
votes
3
answers
1k
views
How do you apply Kalman Filter to track a signal?
The example that I've seen on state estimation involves deriving the ABCD matrix of a physical system (i.e. falling object) and tracking that object.
I would like to use Kalman Filter for signal ...
- 601
4
votes
2
answers
203
views
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 ...
4
votes
1
answer
872
views
Kalman Filter | Difference Between Minimizing the Mean Square Error (MMSE) & Maximizing Likelihood Value in Bayesian Estimation
I am going through data assimilation slides on Multi Sensor Data Fusion by Hugh Durrant Whyte and it mentions:
The Kalman Filter, and indeed any mean-squared-error estimator, computes an estimate ...
- 169
4
votes
1
answer
226
views
Likelihood of Unscented Kalman filter
Short version:
How to calculate a likelihood of Unscented Kalman filter?
Long version:
Likelihood for linear Kalman filter (KF) is:
$$\mathcal{L} = \frac{1}{\sqrt{2\pi S}}\exp \left[-\frac{1}{2}\...
- 388
4
votes
1
answer
1k
views
How to include phase in a sinusoidal Kalman Filter
I start with the equation for sinusoidal motion with an offset and differentiate to get the 2nd order ODE describing the motion of the object.
\begin{align}
x &= A\sin(\omega t + \phi) + O\\
\dot{...
4
votes
1
answer
142
views
Kalman Filter - Updating the Covariance Matrix Step
I am trying to simulate the Kalman Filter. I have the covariance matrix P_{0|0}. Tell me please, how can I get the predicted (a priori) estimate covariance matrix ...
- 43
4
votes
1
answer
136
views
Estimation of accelerating target using position measurements only
I am currently thinking about approaches to estimating the position and velocity of an accelerating target.
At this time, I have tried a few approaches that work alright. I have tried two variations ...
- 263
4
votes
2
answers
10k
views
Smoothing data by using Kalman filter
I would like to ask about smoothing data by using Kalman filter. Due to quantization, I have data that is not smooth. How can I smooth this data by using Kalman Filter. For your information, the data ...
- 133
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
4
votes
1
answer
245
views
Application of UKF on quaternions
I'm trying to perform a state estimation on quaternions to predict the future orientation of a human head. The only sensor data I can obtain (from the AR headset) is the current orientation of the ...
- 429
4
votes
1
answer
167
views
IMU Speed Tracking Through Known Path
I am new to signal processing and Kalman Filtering here. Thanks for your help.
I working with an IMU for a tracking project where the IMU moves throw a known path but at an unknown speed (within ...
- 41
4
votes
1
answer
269
views
Evaluation of Jacobian for Extended Kalman Filter
For the non-additive noise case,
\begin{equation} x_k = f(x_{k-1}, u_{k-1}, \xi_{k-1}) \\
y_k = h(x_k, \nu_k)
\end{equation}
the EKF takes into account the jacobian wrt to the noise terms $ L_{k-1} =...
- 41
4
votes
1
answer
97
views
When Kalman's assumptions are relaxed
From Kalman's seminal paper "A New Approach to Linear Filtering and Prediction Problem", it is clear that Kalman's exposition is based on the following fundamental assumptions:
Measurements that are ...
- 141
4
votes
1
answer
666
views
Is acceleration noise modelled differently in EKF and UKF Kalman Filters?
In a lecture on basic Kalman filter, I came across the following assumption about acceleration noise.
Every component of the noise vector $\nu$ is itself a product of time and acceleration values. ...
- 273
4
votes
2
answers
2k
views
State Estimation by steady state Kalman Filter
I am working with a discret Kalman filter on a System
$x_{k+1}=A_k x_k+B_k u_k+\omega_k$
$y_k=C_k x_k+\upsilon_k$
$E[\omega_k\omega_k^T]=Q$
$E[\upsilon_k \upsilon_k^T]=R$
I have estimated the ...
- 41
4
votes
2
answers
728
views
Intertial navigation on android phone with Kalman filter
Ok, so suppose I've got a phone with gyroscope, compass and 3-d accelerometer.
I wanted to track position of the moving phone for about 1 minute with let's say 50 mm accuracy. Actually let's say that ...
- 151
4
votes
1
answer
298
views
Kalman filter for random observation matrix $G_t$
I have a problem that is similar to the state space model in Kalman filter but the observation matrix $G_t$ of $$y_t=G_tx_t +w_t,$$ is random. The elements of $G_t$ are i.i.d. random variables with a ...
- 195
4
votes
1
answer
149
views
Filtering difference of correlated measurements
I have an application with two separated GPS receivers giving live positions and I'm deriving a heading/displacement from the vector between them. Each set of position measurements is noisy and has ...
- 824
4
votes
1
answer
100
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
4
votes
1
answer
576
views
How to Find the Probability of Kalman Filter States?
I am working on a video object tracking problem. I am using Kalman filter to predict and correct the object position return by an algorithm such as CamShift. I want to adjust the likelihood ...
- 43
4
votes
1
answer
1k
views
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. )....
- 41
3
votes
3
answers
361
views
Kalman Filter Sensor Processing
Kalman filter achieves convergence of state vector by using sensor observations.
Assuming a sensor such like velocity sensor, giving two axis velocity information in X-axis as well as Y-axis(see edit ...
- 131
3
votes
1
answer
4k
views
What are the advantages and disadvantages of Kalman filter compared with FIR, IIR and low pass filter to filter data with noise?
It is known that the Kalman filter can filter the data with noise. I also find it works well after using it compared with FIR, low pass filter,etc. Now, I have a couple of questions about the ...
- 55