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1answer
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Is derivative of a Gaussian Signal also Gaussian? How to find variance of signal that is obtained from differentiation of a Gaussian signal?

Could someone please let me know or give appropriate references for the question I have posed above. My main interest lies in applying Kalman filter for state estimation. The noise on sensor ...
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0answers
13 views

A problem with deriving posterior of particle filter [duplicate]

At the normal particle filter, there is an equation to deriving posterior $p(x_{0:k}|z_{1:k})$. In the article ,equation 45 , it says that: ...
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0answers
55 views

Review paper on particle filter

I have found online a draft of an excellent review paper by Zhe Chen entitled "Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond". According to Google Scholar, the citation for ...
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0answers
27 views

How to modeling the movement of an object? [closed]

I have implemented the condensation algorithm in order to track a moving object in video sequences, so I would improve the predictive step. Currently the state includes only the coordinates of the ...
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1answer
67 views

Methods of fitting a dynamic linear model

I'm taking a time series course and am learning about exchangeable time series form of dynamic linear models (DLMs). This is given by: \begin{align*} \mathbf{y}_t' &= ...
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0answers
25 views

How to find the pdf of a time-dependent parameter in a linear regression model with drift?

Suppose there exists a simple linear equation, where the dependent variable y(time series; measurements available) depends on x1 and x2. If the parameter multiplier of x2 is time dependent and the ...
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1answer
160 views

Particle filter (sequential Monte Carlo) for a non-Gaussian hierarchical model

I have the following, which I am attempting to model with a particle filter. \begin{align*} y_{i,t}&\sim\mathrm{Poisson}\left(\lambda_{i,j,t}\right)\\ ...
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0answers
25 views

Is it a problem to have non homogeneus sampling time in Bayes Filter?

I have a doubt related with Recursive State Estimation using Bayes Filter (actually using an aproximation to that through Particle Filters) This algorithm is explained in several sources with ...
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0answers
45 views

Covariance update from Jacobian of transition function

In this paper on particle filtering with gradient descent, the authors sample Xk+1 through gradient descent, then update the covariance matrix P associated with Xk+1 as follows: Pi+1(k + 1|k + 1) = ...
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0answers
27 views

Showing that the variance increases with the dimension of the random vector

This is actually related to a more complex question; but I want to re-ask it by trying to simplifying it as possible: 1- We have $n$ dimensional functions of the form $f_n:\mathbb{R}^{n} \mapsto ...
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0answers
37 views

How to show that the variance of Sequential Importance Sampling estimates increase with the dimension?

I am trying to understand the Particle Filter and the motivation to use it over the regular Sequential Importance Sampling. As far as I understand until now: 1- We try to estimate the expectation of ...
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1answer
86 views

Likelihood score function 101

I have some trouble with score functions in likelihood calculation. I'm not good at statistics or probability, so I'm still confused on formalism and mathematical-probabilistic language. Some ...
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2answers
150 views

Particle filters and loopy belief propagation

I want to implement a loopy belief propagation algorithm for factor graphs with continuous variables and messages represented using particles, that is vectors of samples for an empirical ...
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1answer
116 views

How is the number of particles decided in particle filtering?

Say the observations are $x_i$ and the states are $y_i$ in a sequential model. I understand that particle filtering works by generating "particles" from $p(y_i | x_1,\ldots,x_i)$ for approximating ...
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0answers
157 views

How to generalize Particle Filters (w.r.t. multiple states)

I'm using particle filters for inference in a hidden markov model with an infinite state-space. My current state-variable is multidimensional and there are interdependencies between some dimensions. I ...
2
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0answers
77 views

Rao-Blackwellising state space for a (marginalised) particle filter

I am starting to look at particle filtering for a problem that I have. In particular, I would like to reduce the dimensionality of the particles. The model that I have is able to be partitioned. ...
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1answer
1k views

Time series forecasting using particle filter

I have searched high and low for a practical example of using a particle filter to assist with short term price forecasting using the local trend of a time series. Could someone please share how a ...
2
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1answer
311 views

Particle filtering importance weights

In theory, the importance weight of a particle has to be a probability, i.e., $w_{s_t} = p(z_t|s_t)$. My question is: Since we eventually normalize the weights with their sum and get a probability ...
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1answer
310 views

Rao-Blackwellization of sequential Monte Carlo filters

In the seminal paper "Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks" by A. Doucet et. al. a sequential monte carlo filter (particle filter) is proposed, which makes use of a ...
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1answer
252 views

Using a particle filter for robot localization

I have a robot that has a GPS and velocity sensors. The GPS updates roughly every 1-2 seconds. I've been playing around with a Kalman filter that has been working pretty well. I just learned and ...
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0answers
58 views

A motion model to track a moving object using the condensation algorithm

I have implemented the condensation algorithm in order to track a moving object in video sequences, however the predictive step does not work properly, so the samples moves excessively compared to the ...
1
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1answer
275 views

clustering with particle filters

Suppose we want to cluster a data stream of unknown number of clusters, and estimate them using particle filters. With particle filters, we need to know $P(x_t | x_{t-1})$ and $P(z_t | x_t)$ (where z ...
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3answers
7k views

Very simple particle filters algorithm (sequential monte carlo method) implementation

I'm interested in the simple algorithm for particles filter given here. It seems very simple but I have no idea on how to do it practically. Any idea on how to implement it (just to better understand ...
2
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1answer
356 views

Forecasting a “chaotic” time series

Here are four graphs, 1, autocorrelation, autocovariance, partial-correlation and cross-correlation calculated from a time series are given. 2, The time series I need to do some predictions on ...
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1answer
669 views

Maximum likelihood estimation procedures for state-space linear models

State-space models are represented by a state equation and an observation equation (or system of equations to be more precise). These equations are parametarized by components including a transition ...
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1answer
127 views

Sense of correlation coefficient matrix of particle filter's parameters

I am using a particle filter to estimate the parameters($\Phi_{n\times1}$) of a non-linear model. Say my input (observations) is $t=1:k$, I will have a vector of length $k$ for each of the parameter ...
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1answer
1k views

Particle filter in Matlab - what is going wrong?

I posted this question on Electronics.Stackexchange and someone told me I'll be better off posting it here. Its an implementation of the Particle Filter using MATLAB but the results never follow the ...
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3answers
1k views

Estimating parameters of a dynamic linear model

I want to implement (in R) the following very simple Dynamic Linear Model for which I have 2 unknown time varying parameters (the variance of the observation error $\epsilon^1_t$ and the variance of ...
27
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1answer
6k views

What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?

A particle filter and Kalman filter are both recursive Bayesian estimators. I often encounter Kalman filters in my field, but very rarely see the usage of a particle filter. When would one be used ...