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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EM algorithm and Kalman filter

I am new to the subject of Kalman filtering and therefore my question might seem trivial. I see that there is a tight connection between Kalman filter and EM algorithm when one wants to predict the ...
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Kalman Filter for particle tracking

I am new to Kalman and trying to use it for a particle tracking technique for velocity measurments in Multiphase systems. I have particle locations but there are error associated with these locations. ...
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23 views

What is pulse train filter?

I have recently seen some code written in modelling tool like Simulink, ASCET which uses PT1 filter? Why do we use a pulse train filter? What is the difference between FIR, IIR, Chebyschev, ...
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21 views

Improving velocity estimation

I have a sensor reduction model which gives me a velocity estimate of a suspension system(velocity 1) . This suspension system estimate velocity is used to calculate another velocity(velocity 2) via ...
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1answer
26 views

How to form Kalman filtering matrices for a problem with variable acceleration?

Assuming we have time vector $T$ with constant time step $dt$ position vector $X$ velocity vector $V$ acceleration vector $A$ All vectors $X, V, A$ have noise on their measurement ( $n_x$ , $n_v$ ...
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1answer
25 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 ...
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37 views

Kalman filter - understanding the noise covariance matrix

What is the significance of the noise covariance matrices in the Kalman Filter framework? I am referring to: process noise covariance matrix Q, and measurement noise covariance matrix R at any ...
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17 views

Relationship between a Kalman filter and a PLL?

For tracking a single variable frequency signal in noise, what is the relationship, if any, between using a Kalman filter and implementing a generic Phase Locked Loop?
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Hybrid Kalman Filter and State Space Augmentation

I'm having trouble combining state space augmentation and Hybrid Kalman Filter. Let me first clarify what I mean by these two terms: Hybrid Kalman Filter uses a continuous time model. ODEs need to be ...
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16 views

How to filter noise from vibrating particles?

Each particle has its position (x,y,z) tracked in the system over the course of a couple seconds. After analyzing the data, there is quite a bit of noise. I've done some reading and concluded that a ...
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1answer
95 views

Kalman filter, defining the measurement model

I would like to implement a Kalman filter to estimate the velocity and position of an object. I have an accelerometer, therefore the acceleration is known. The approach is same as: More on: Kalman ...
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49 views

Kalman filter - mathematical model for signal strength based tracking

I'm currently trying to wrap my head around Kalman filters. I've read some tutorials/introductions on this subject and am trying to apply it to a problem to get a better understanding of the mechanics ...
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28 views

Estimation of Hit Time Using Kalman

I have the following model for Kalman Filter. The Dynamic Equation: $$ \begin{bmatrix} {r}_{k} \\ {v}_{k} \end{bmatrix} = \begin{bmatrix} 1 & -T \\ 0 & 1 \end{bmatrix} \begin{bmatrix} ...
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1answer
42 views

System Identification: smoothing in E-step of EM algorithm

My question is, do the smoothed values affect the estimates obtained from the Maximization Step? If not then we could eliminate the smoothing. Once the estimates are obtained, they do not change apart ...
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1answer
28 views

can measurements go out of the uncertainty bounds?

In the below picture, the measurements are inside the $\pm 3 \sigma$ bounds. In my experiment, the measurements sometimes go out of the uncertainty bounds. This is a snapshot of my plot where the ...
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39 views

Kalman filter for velocity estimation from acceleration and displacement: constant-acceleration assumption

I have implemented a Kalman filter to estimate the velocity knowing the acceleration and the positon measurements as explained in this Q/A: Estimating velocity from known position and acceleration ...
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3answers
373 views

Question about Q matrix (noise process covariance) in Kalman filter

I am implementing my own discrete Kalman filter to estimate velocity from acceleration and position measurements (using Matlab ). I think I managed to deal with the $R$ matrix (measurements noise ...
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3answers
163 views

when is a kalman filter different from a moving average?

this thread asks when a discrete-time Kalman filter is better/different from a simple moving average of the observations: ...
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1answer
61 views

kalman filter with time-varying noise?

in regular discrete-time (1 dimensional) kalman filter, it is assumed that we have white gaussian noise affecting the transitions and the observations: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
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133 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 ...
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2answers
112 views

Discrete or continuous Kalman filter?

I have position and acceleration measurements and I would like to apply a Kalman filter to estimate the velocity of the system. I am not sure yet about how to procede, but I will check the already ...
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1answer
43 views

Estimating Velocity from Fuzzy Position Data with Known Uncertainty

I was wondering if someone could maybe clarify or direct me to the best answer for this question. I want to estimate velocities from position data. However, the position data is fuzzy but I have an ...
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379 views

How to determine covariance matrix $Q$ and $R$ in Kalman-filter

I am implementing getting orientation from smartphone. I want to use Kalman filter and should determine process noise covariance matrix $Q$ and measurement noise covariance matrix $R$. (newbie to ...
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1answer
132 views

How to get rid of noise and oscillations using Kalman filtering

I have not studied signal processing at all, so please forgive any ignorance in the following discussion. I have some noisy position measurements that I've been trying to smooth. I've been attempting ...
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17 views

Estimating plant parameters from noisy frequecy response data

I have to estimate the parameters of a 1st order transfer function, namely, the coefficients, through experiment. I ran a few experiments and I have a bunch of input-output data vectors. The ...
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35 views

Outlier removal before or after Kalman filtering?

I am getting radar data points in form of (x,y) coordinate system relative to my position every ms.[around 10-15 data points]. Now, inorder to have better position estimate of the points, I would like ...
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1answer
48 views

Iterative Kalman filters and system parameters estimation

i am working recently on a project in which i want to implement a Kalman filter as being an observer, and i couple this observer with a state feedback controller that produces control actions ...
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Optimal estimation of the static points obtained using kalman filtering?

I have used kalman filtering in the field of image processing. Now I would like to use kalman filtering to have a better estimate of the static points observed by a moving object. Given Data: My ...
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1answer
129 views

Discrete algorithm for low pass filter

I am working on a position controller for a marine vessel. I have an measurement signal containing the y-position of the vessel that consists of both low frequency (<.1 rad/s) and high frequency ...
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2answers
153 views

Picking out a signal that appears to be noise inside a large signal

I have a signal from a photodiode sensor that has two types of noise. One type of noise is ambient light white noise that gets introduced just from the surrounding environemnt. The other type of noise ...
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43 views

Process Noise “Q” covarience matrix in a kalman filter

I am trying to implement a Kalman filter on a Phasor Measurement Unit (PMU) values. I meaured the signal from PMU and give those meaurement as input to Kalman filter to get best estimate. I do not ...
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1answer
137 views

Kalman Filter Estimate vs ACF Least Squares Estimate

I am currently reading Chapter 5, Applications to the Gas Markets, in Stochastic Modelling of Electricity and Related Markets by Benth, Benth and Koekebakker, World Scientific, 2008. In the ...
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41 views

Continuous Time Kalman Filtering

I have a very general question about Kalman Filters. It seems like often the hardest part of a real-world Kalman Filter implementation is discretizing the process noise. I'm curious why it isn't ...
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97 views

Using Fourier Transform on Gyroscope

The original idea is to calculate distance from accelerometer input. However, accelerometer reading also contains the gravitational values, thus to remove gravity, I tried using Gyroscope. The idea ...
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81 views

The role of GPS in INS/GPS navigation systems

Ideally, a gyroscope and an accelerometer would be enough for a complete navigation solution (attitude + position), using dead reckoning. This comprise the Inertial Navigation System, INS. In ...
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110 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 ...
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3answers
268 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 ...
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Is there a standard way for modeling a Kalman filter where the measurements are obtained from differences?

Consider for simplicity a Kalman filter applied to the one-dimensional state space model $x_{n}=f_{n}x_{n-1}+q_{n}$ $y_{n}=h_{n}x_{n}+r_{n}$ with white noise errors. Assume that $r_n=e_n-e_{n-1}$ ...
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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 ...
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1answer
115 views

simulating range-bearing sensor with Matlab with Gaussian noise

I would like to simulate a sensor that provides range and direction of a beacon. This is for EKF localization, so the noise must be Gaussian (i.e. $\mathcal{N}(0, \sigma^{2})$. Also, I would like to ...
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Kalman Filtering with Restrictions

A question on this topic has been asked before: Combining a linear Kalman Filter with additional linear constraints? and I checked out some of the references given: ...
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1answer
46 views

Variance of an Implicit Function of Kalman State Vector

Given a state vector given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...
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Identifiability for Time Invariant State Space Models

Kevin Murphy's Kalman Filter toolbox (for Matlab) contains an example where it's the fact that the state space system in not identifiable causes problems. I include the example in it's entirety but ...
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1answer
117 views

Adding measuruments noises to kalman filter

I'm implementing navigation system for my robot. There are two ways to get data from it: odometry(encoders from motors) and camera. Both of information sources can give me estimate of robot's ...
2
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0answers
67 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 ...
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1answer
451 views

Problem with Kalman filtering accelerometer data

I'm having some trouble implementing a Kalman filter in MATLAB. I have an Android phone connected sending data from accelerometer for 10 seconds. After i have the data I take out the x-axis vector. ...
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1answer
104 views

Edge following using Hough transform

Im trying to improve an edge following algorithm developed by some students who did a projekt at my work. The algorithm is supposed to make an robot follow a line with use of an camera. Their approch ...
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1answer
68 views

Analogous filter to Kalman that maximizes mode (as opposed to minimizing variance)

I may have a potential application where maximizing the mode (as opposed to typically minimizing the variance) would be useful for state estimates. The situation may arise from skewed distributions ...
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65 views

Queries on Kalman Filter

I am trying to apply kalman filter for video processing , i am studying about it from different sources but it take me towards question that if i don't know that where my object come in frame mean i ...
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399 views

Kalman filtering in image processing, resources?

I'm looking for a good resource (book, tutorial, lesson etc.) that explains the usage of Kalman filtering in image processing applications. I'm aware of the fact that Kalman filtering is an optimal ...