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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IMM Kalman Filter for Non Linear State and Measurement Function

Has anyone encountered an article or implementation of IMM Kalman Filter for non linear transformations? Even for the most trivial case, measurements are in Polar Coordinate System ($ R, \Theta $) ...
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Kalman filter for GPS tracking. How to use lat and lon?

Summary - I know how a kalman filter works - I use this as a reference: http://www.mathworks.nl/help/dsp/examples/estimating-position-of-an-aircraft-using-kalman-filter.html - I don't know how to use ...
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67 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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28 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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63 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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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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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 ...
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State variable identification for Ensemble Kalman filter

For those who use the EnKF in a system in which there are a lot of hidden states variable (no observations available for updating because they are not measurable or because they do not have a physical ...
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Kalman Filter Properties with Biased (By Constant) Measurements

Assuming I have a filter with the following form: $$ \begin{bmatrix} {r}_{k} \\ {\dot{r}}_{k} \end{bmatrix} = {F}_{k} \begin{bmatrix} {r}_{k - 1} \\ {\dot{r}}_{k - 1} \end{bmatrix} + {v}_{k} $$ $$ ...
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Incorporating delayed data in Kalman filter

my guide has told me to get familiarized with state estimates and kalman filter ....the problem is that: 1) I am totally new to this topic and finding it really difficult to understand due to lack of ...
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308 views

Re-implementing the “spectrogram” function from matlab

I am trying to make a spectrogram viewer without using the spectrogram command. For this purpose, I used a sin function. I broke up the input signal into 256 segments, multiplied each segment with the ...
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Kalman filter with accelerometer with DC offset

Goal: For a particle moving uniaxially, to estimate position ($d$) and velocity ($v$) from noisy acceleration ($a$) and very noisy position (GPS) measurements using a Kalman filter. Catch: The ...
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2-D Distance for Kalman measurements

I have designed a simple 3-state $[x\ \dot{x}\ \ddot{x}]$ Kalman filter which is updated by measurements for $x$ and $\dot{x}$. The filter is tracking a peak on a surface in the $x/\dot{x}$ plane. At ...
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Estimating Position Based on Range Measurement

I want to present Kalman Filter problem. For simplicity I'd assume the simplest dynamic model - Piece Wise Constant Velocity. The state vector and dynamic model are given by: $$ \begin{bmatrix} ...
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70 views

Applying Kalman filter to a data set

I went through the answer Kalman filter in practice and it seems we must know all the first and second order properties of random variables to apply the Kalman filter. But when I only have a set of ...
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Relation between Kalman filter and Sequential linear MMSE estimation

Are the results of applying Kalman filter and recursive linear MMSE estimation process the same ?
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54 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 ...
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2answers
112 views

Kalman filter covariance

I've recently started playing with the Kalman filter for a simple 2D (x,y,dx,dy) tracking toy problem. But I seem to have some misunderstanding on what I can expect from the filter. I'm interested in ...
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232 views

Kalman Filter - Position/Velocity from Accelerometer and periodic position measurements

I am trying to implement an EKF to estimate my position and velocity states by using accelerometer measurements as well as periodic GPS (position) measurements. Basically I want to use the constantly ...
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188 views

about Kalman gain

Hi everybody. I'm very new in Kalman filter. Today I try to design Kalman filter to get estimated postion, velocity and acceleration from measurement position (by linear encoder). I don't use ...
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103 views

Why is the Kalman gain constant when position and velocity change?

I used the measured position to estimate the velocity using a Kalman filter. But in simulations, the Kalman gain changes quickly and then remains constant when position and velocity continue to ...
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Can a state space model have changing state size over time?

I have worked with state space models in relation to Kalman estimation. Here I have always seen state space models with fixed state size over time, i.e. the state transition matrix is square. Let us ...
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374 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 ...
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102 views

Situations where complexity is too big to exceed linearity and gaussianity

I'm studing about Kalman Filter and Particle Filter in multiple target tracking in computer vision (tracking pedestrians). Reading sientific papers I'm colliding with a lot of sentences like: The ...
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94 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 ...
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have position, want to calculate velocity and acceleration

This is simple i thought, but my naive approach led to a very noisy result. I have this sample times and positions in a file named t_angle.txt: ...
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Extended Kalman Filter linearization of non-linear functions

I have more general question about the extended Kalman filter usage. What is not clear to me is why the EKF uses non-linear functions $f$ and $h$ for state prediction and estimate, while in other ...
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Association of multiple measurements to multiple objects

In every cycle I obtain measurements from which I initiate and later on update objects. I want to match properly measurements to objects. For this purpose I create a matrix of M measurements by N ...
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(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 ...
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851 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 ...
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More on: Kalman filter for position and velocity

Thanks to everyone who posted comments/answers to my query yesterday (Implementing a Kalman filter for position, velocity, acceleration ). I've been looking at what was recommended, and in particular ...
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Implementing a Kalman filter for position, velocity, acceleration

I've used Kalman filters for various things in the past, but I'm now interested in using one to track position, speed and acceleration in the context of tracking position for smartphone apps. It ...
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96 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 ...
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263 views

information filter instead of kalman filter approach

I read many sources about kalman filter, yet no about the other approach to filtering, where canonical parametrization instead of moments parametrization is used. So I would like to learn on examples ...
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123 views

Sequential processing of uncorrelated measurements in Kalman Filter

I'm starting to brush up on the Kalman Filtering I learned a couple decades ago. From what I remember, if you have a measurement vector $$ z=H x + v $$ and the $n$ components of the measurement ...
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174 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 ...
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109 views

How to combine a perfect signal with a limited dynamic range with a poor one with high dynamic range?

I have two sensors that measure speed $v(t)$ of a moving vehicle. The first sensor produces a signal $f(t)$ which is a very accurate estimation of speed. However, it only works for slow to moderate ...
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278 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 $x(T)$ ...
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87 views

estimation of the position of the magnetic source

I have a flying robot with magnetic coil as a sensor. An output from the coil is measured every second in different position. I know the position of the coil and its angles. I need to estimate the ...
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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 ...
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113 views

Doubt on Weighted Least Square Estimation

This is a page from the book linear algebra,geodesy and gps by Gilbert Strang.... the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ ...
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Least Square Error Estimation doubt when can we write $(A^TA)^{ -1} = A^{-1}(A^T)^{-1}$?

I am new to linear algebra and have this simple question... in least sqaure estimation...the best estimation of the equation $Ax = b$ is $x_{Estimated} = A (A^t A )^{-1} A^t b$...the projection of $b$ ...
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Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
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2answers
2k views

Estimating velocity from known position and acceleration

I am stuck at modeling a system model, i.e. getting my state vector and input vector. My guess is that position and velocity are state vector and acceleration is input vector. My 2nd guess is that all ...
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Kalman filter in practice

I have read the description of the Kalman filter, but I am not clear on how it comes together in practice. It appears to be primarily targeted at mechanical or electrical systems since it wants linear ...
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693 views

When to use EKF and when Kalman Filter?

I'm learning Kalman Filter for a week now. I just discovered that EKF (extended Kalman Filter) might be more appropriate for my case. Le't suppose I'm applying KF/EKF for variometer (the device that ...
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Estimating the input to a system from a system state using EKF

[ Cross-posted from: http://math.stackexchange.com/questions/164169/estimating-the-input-to-a-system-from-a-system-state ] I have a system for which I have obtained a non-linear time-varying ...
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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: Questions: ...
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112 views

Role of Kalman filter in nonlinear dynamics

I am quite interested to know the significance of using kalman filter,unscented kalman filter and extended kalman filter in chaos synchronization when infact the very basics of chaos ...
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Kalman filter - implementation and deciding parameters

First of all, this is the first time I try to make a Kalman filter. I earlier posted this thread on stackoverflow which describes the background for this post. This is a typical sample of values I'm ...