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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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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21 views

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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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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1answer
44 views

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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1answer
71 views

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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13 views

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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21 views

Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): $X_{t+1}=FX_t + V_t$ $Y=HX_t+W_t$ $V_t \sim N(0,Q)$ $W_t \sim N(0,R)$ I am interested in the ...
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2answers
64 views

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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21 views

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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32 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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1answer
35 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
53 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
43 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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1answer
86 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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21 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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14 views

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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17 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
111 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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55 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
49 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
29 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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50 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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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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236 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
72 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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161 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
154 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
51 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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642 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
163 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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18 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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38 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
50 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
139 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
170 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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54 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
158 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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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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2answers
82 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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2answers
121 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
298 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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2answers
175 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 ...
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1answer
134 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
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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: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...