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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Active noise cancellation using kalman filter

I am doing signal processing on audio data sampled at 8Ksps in matlab but it is corrupted with random noise. Therefore, I decided to use LMS and RLS ANC algorithms to remove overlapped frequency ...
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24 views

Are the RLS filter and Kalman filter gradient methods?

I would like to extend my previous question What is difference between LMS and gradient-descent adaptation? with this other question. I found out, that RLS and Kalman filter learning seems to be ...
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Good Reference Problem to Test Filtering/Estimation Algorithms

I am looking to figure out if a current filter algorithm I have built could be useful for some problems I am looking into at work. It isn't a Kalman filter, but is instead making estimations using a ...
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43 views

Kalman for 3D position and 1D orientation

Is the following state correct for a Constant Acceleration (CA) model KF applied for tracking an object which moves in (x, y, z) and have the freedom of rotation $\phi$ around the $z$ axis? ...
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51 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 ...
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27 views

Derivation of transfer functions for Kalman filter

Hi All: I'm somewhat familiar with the kalman filter from a statistical point of view. But lately I've been trying to familarize myself with the linear systems-EE way of looking at it. So, I've been ...
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22 views

Observability for Kalman Filtering?

I wanted to know how observability of a stochastic state space system affects the performance of a Kalman Filter. Do we check for the usual observability matrix involving $\mathbf{C}$ (observation ...
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32 views

Extended kalman filter for linear system

I studied about Kalman filter(KF) for about a week. And I understand that Kalman filter(KF) is suitable for linear system and extended Kalman filter(EKF) can be used for nonlinear system. However, I ...
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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 ...
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11 views

Kalman Filtering and space parametrization

I am familiar with Kalman filtering given a linear (time-invariant) state space model. However, the state space parametrization is not unique. Given a controllable and observable state space model ...
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35 views

100 samples ahead signal prediction [duplicate]

I have a signal sampled at 100 sample per second. After low pass filtering of 200 order and some calculation such as zero crossing detection, I am getting around 1 second delayed signal. I want it in ...
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RLS Algorithm Convergence

I am looking for some help to understand the concept how RLS converges? If possible to present it graphically that would be best. It is very easy to understand the understanding of convergence in case ...
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28 views

Apply Kalman filter to remove process noise, given zero measurement error

I have a recording, corrupted by environment noise. The measurement noise is zero. How can I use Kalman filter to remove environment noise? I tried this Matlab code here but if the measurement error ...
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22 views

EKF covariance prediction - different methods

I am currently working on a Extended Kalman Filter and found two different versions to predict the covariance matrix $P$. First approach: The time derivative of $P$ is defined as $\dot{P} = FP_k + ...
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34 views

fetal ecg and maternal ecg using kalman filter

i would like to extract the fetal ecg from maternal ecg using kalman filters.. but i dont know much about matlab.i have the datas from physiont. i want to know how to find or get the A,B,C,D in ...
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79 views

Estimate $s$ from $y=s+n$

Thank you in advance. My question is: Now I receive $y=s+n$, $s$ is the signal and $n$ is the white guassion noise. Everytime $s$ will be change irregularly, have some methods to get a estimation ...
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46 views

Extended Kalman filter (EKF)

I am working on the localization problem of an underwater vehicle. However the problem is still in very simple and it does not matter that it is about underwater. How can I use the EKF when I have ...
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77 views

Structuring Kalman filter for tracking problem where only position is known

I'm new to Kalman filters and my extensive web search about them has helped me understand the majority of it (or so I think). However I still need some light shed on my problem formulation. I have a ...
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21 views

Non-zero mean of Kalman innovation

I am using a Kalman filter to fuse gyro and inclinometer data. The prediction step is given by: $\hat{\alpha_{i}}^- = \hat{\alpha}^+_{i-1} + \omega_{i}$ Where $\hat{\alpha_{i}}^-$ is the prediction ...
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Will an unscented Kalman filter be “as good” as other optimisation algorithms for this problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
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30 views

Can a (vanilla) Kalman Filter's Observation Matrix $H_k$ depend on the state vector $x_k$?

A vanilla Kalman Filter allows for a time varying observation matrix $H_k$. Is it allowable for $H_k$ to be a function of the system state $x_k$ in a vanilla Kalman filter? First, am I correct that ...
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162 views

Why Runge-Kutta for Quaternion integration in Kalman filter?

I'm reading up on Kalman filtering at the moment. In particular, I'm interested in using the "extended" and "unscented" variants for IMU sensor fusion and calibration. In A comparison of unscented ...
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135 views

Kalman filter : simple code example

I read lots of things about Kalman filtering, but in order to fully understand it, I would probably need to see it working on some data. Would you have a minimal example (Python code or any other ...
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58 views

Implementing a 1-D Kalman Filter Regression, Missing the smoothing action (getting the opposite)

I am implementing the 1D Kalman Filter in Python on a fundamentally noisy set of measurement data, and I should be observing a large amount of smoothing...but, instead, my Kalman Filter is doing the ...
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53 views

Tracking position and velocity using a kalman filter

I am using a kalman filter (constant velocity model) to track postion and velocity of an object. I measure x,y of the object and track x,y,vx,vy . Which works but if a add gausian noise of +- 20 mm to ...
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63 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 ...
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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 ...
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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 ...
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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 ...
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91 views

Observation Matrix in Kalman Filter

I've been trying to understand the concept of the Kalman Filter. I came across this great article which makes the concept sufficiently clear. However I could not understand the concept of the matrix ...
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46 views

What f() for unscented kalman filter for stock trading?

I am trying to estimate to "next" price of a stock, based on a group of 5 other correlated stocks. I believe this is a 6 state unscented Kalman problem. However, I do not know how to describe ...
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51 views

Why does my GAIN remain constant after a few cycles? [closed]

I am assuming that GAIN is the matrix P? From this example: ...
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Kalman Filter initial Q values

I have a 6 state Kalman Filter (Unscented). When I use a diagonal matrix only for Q (i.e only the diagonal has covariances), I get a "smooth" plot of estimate against actual. If I use the entire Q ...
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Is the Kalman Filter a Best Linear Unbiased Estimator (BLUE) for Heteroscedastic Noise?

According to the Gauss-Markov Theorem, a ordinary least squares estimator is BLUE if the noise entering a system is uncorrelated with zero mean and is homoscedastic (has a constant finite variance). I ...
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Can I model process noise as a known “error” in my dynamics while designing a Kalman Filter?

Consider I am modelling the dynamics of a robot and using a Kalman filter to obtain estimates of some state. I have certain terms in my equation which correspond to data not accessible to this robot ( ...
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Optimality of Kalman Filter for Process Noise dependent on magnitude of state

Consider I have a dynamical system $\dot{x} = Ax + w(t)$, $x \in \mathbb{R^2}$ where $w(t)$ is a Gaussian random variable with mean $E(w(t)) = C\|x\|^2$ where $C \in R^2$ is a constant and covariance ...
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Kalman Filter - Velocity [Matlab]

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 ...
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21 views

Convergence analysis and Kalman Gain

I have a general question in regard to stability and convergence analysis of filtering algorithm like Kalman filter and its non-linear version - Extended and Unscented for parameter estimation. In ...
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173 views

Kalman Filter to estimate 3D position of a node

Code given on this link works for 1D: More on: Kalman filter for position and velocity In my problem I need to estimate 3D position.What is the criteria ? How F, G ,H,Q and R change in 3D case. ...
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81 views

Q matrix and updating times in a Kalman filter

The context of the problem is that I have several robots located remotely which give their position (x,y coordinates) every x seconds and send it to a centralized remote server. The value of the ...
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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 ...
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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 ...
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Correct form for State Space Equation for Kalman Filter

In this paper: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf in eqns 3,5 the state eqn has the mean removed. $(z_t-\mu)=A(z_{t-1}-\mu) + \epsilon_t$ $y_t=C z_t + \delta_t$ ...
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Fusing data from multi rate accelerometers

I am working on a project that requires combining multiple accelerometers with different frequencies. What is the best way of combining signals from these accelerometers to obtain dynamic behavior? ...
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22 views

reverse engineering - RT frequency estimation

I need to maintain code I inherited. The code is for RT frequency estimation. There is not a single line of comment in the code. I was hoping someone here will recognize which technique is being used ...
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Smoothing process of Kalman filter

I have a question about the smoothing (backward) process of Kalman filter. Is it correct to say $E[x_{t|T}] = x_{t|t}$ where $x_{t|t}$ is the estimated result from forward process? I am struggling ...
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How to represent the nonlinear model as a state space in Unscented Kalman Filter

There is an Autoregressive model of order 1 (AR(1)) that is excited by a non-linear signal as the input: $$x_t = \rho x_{t-1} + u_t \tag{1}$$ The time series $u_t$ is generated from a nonlinear map, ...
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Wrong estimation of derivatives with an extended Kalman filter

I am trying to implement an extended Kalman filter (EKF) in MATLAB for the estimation of joint trajectories (angular position, angular velocity and angular acceleration) from noisy motion capture ...
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Sensor Data Fusion with Orientation Sensors in 3D Euclidian Space

Preconditions For measuring the position of a mobile device in 3D space, I utilize two sensors with different characteristics that measure device orientation. Sensor A (a combined sensor of ...
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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 ...