Questions tagged [particle-filter]

Particle filters (or sequential Monte Carlo) is a form of genetic simulation algorithm used for filtering problems in signal analysis and time series analysis.

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Sample from a distribution and plot in python

I am trying to understand Particle Filter and Importance Sampling Principle from a UniFreiburg Course and this USNA document on particle filters. Simultaneously, I am also trying to write a document ...
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Particle Filter for navigation through known map

I have some issues with understanding the Particle Filter for navigation through a known map. So, consider a situation where I want to write a Particle filter to navigate through a maze or a map that ...
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Deriving Hyperparameter updates in Online Interactive Collaborative Filtering

I've been going through "Online Interactive Collaborative Filtering Using Multi-Armed Bandit with Dependent Arms" by Wang et al. and am unable to understand how the update equations for the ...
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Particle Filtering: Derivation that mean of weights is the marginal likelihood

I see everywhere the following (for the Bootstrap Filter) $$ p(y_t \mid y_{1:t-1}) \approx \frac{1}{N} \sum_{i=1}^N W(x_{0:t}^i) $$ where $W(x_{0:t}^i)$ are the normalized weights defined as $$W(x_{...
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Estimate sales of product from sales of related products

The sales of product I'm interested in published every quarter. The sales of related products published every month. How the sales of the interesting product could be estimated from the sales of ...
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Which step is to perform after the resampling step in particle filter?

I am implementing my code regarding the particle filter in MATLAB. I am new to this implementation. I have completed particle filtering step till resampling. Now which step should I perform? I have ...
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24 views

Monte Carlo probability approximation vs Histogram

I am trying to learn the sequential Monte Carlo method (particle filter) in data assimilation. In this method, the aim is to approximate the CDF of the target variable having a random sample of the ...
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31 views

Particle Filter with sparse observations: observation vector

I have a very practical question (or maybe I got soemthing completely wrong). I want to approximate two variables A and B at ...
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How to check which weight method to apply on particle filter?

I am working on a project using MatLab. I have to apply the particle filter. But I am stuck at the point that how do I apply weight. I have applied two-weight function, but cannot decide either these ...
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24 views

Values of Weights in particle filter are NaN [closed]

I have implemented particle filter using MATLAB. The main issue in this code is with the last step Calculation of Weights. I have used the formula given in Page No 178, Equation 48. But when I print ...
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Particle Filter for structural credit risk model

Kwon (2012)* proposes a structural credit risk model where the asset value process and the noise are estimated based on the observed equity prices: $S$ - equity prices $V$ - value of the assets $Z$ - ...
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32 views

Modelling Ball Movement using Delayed Measurements with Known Latency

I am a hobby programmer currently developing an algorithm to combine measurements of a dynamically moving ball position (and velocity) from multiple robots. Each robot measure and calculate the ...
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Simplying Bayes Theorem expression: SIS particle filter posteriori

In the book Beyond the Kalman Filter: Particle Filters for Tracking Applications on page 39 the weight update equation for the particle filter is derived. The derivations begins by introducing the ...
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1answer
43 views

Calculating the observation density

In the context of link. For a state space model $$ x_{k+1} = f(x_{k}, u_k, w_k) $$ $$ y_k = H x_k + v_k $$ where the measurement function is assumed linear and Gaussian and the state transition is ...
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Particle filter: Evaluating Optimal importance density

NOTE I posted this in the math stack exchange but I realized this may be the more appropriate place, old post here. I'm not sure if I should delete one of them so I just linked them in both? I am ...
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65 views

Evaluating Likelihood in Bootstrap Particle Filter

I am currently struggling with an attempt to apply a bootstrap particle filter to a linear, Gaussian state-space model $$s_t=A\,s_{t-1}+B\,\nu_t\qquad\text{( transition equation )}$$ $$\qquad z_t=C\,...
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Bootstrap Particle Filter (Gordon, Salmond, Smith, 2003) - Importance Weights

So, my endeavor to apply the is just for my own edificationI am currently struggling with an attempt to apply a bootstrap particle filter (Gordon, Salmond, Smith, 2003) to a linear, Gaussian state-...
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25 views

extension of sequential probability ratio tests to particle filters?

I've been wondering if there are extensions of the sequential probability ratio test to account for particle filters. I ask because, in my research, I'm working with distributions that cannot be ...
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66 views

Finite grid approximation to the Bayesian filtering problem

I need some hints for solving Ecercise 4.4 from Bayesian Filtering & Smoothing by Simo Särkkä: Select a finite interval in the state space, say, $x \in [-10, 10]$ and discretize it evenly to N ...
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41 views

Predictions after SMC

I have a statistical model given by $$ y_t\sim p(y_t|x_t, \theta)\\ x_t\sim p(x_t|x_{t-1},\theta)\\ \theta\sim p(\theta) $$ where $y$ is the only observed component. Using a sequential Monte Carlo ...
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What are the differences between Bayesian filters and adaptive filters?

I am learning about state estimation and I am having difficulty understanding the difference between Bayesian filters such as Kalman filter and particle filters compared to adaptive filters. According ...
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45 views

Particle filter for diagnosis

I have two annual measurements taken on medical images depicting a lung cancer tumor 's condition. I have likelihood function that taken in the measurement values and estimates malignancy of the tumor....
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93 views

Posterior as prior for correlated parameters [closed]

I want to use the posterior distribution of the model parameters $\theta$ given data in the time frame $[0,t]$ days, $P(\theta|y_{0:t})$; as a prior for the parameters in the time frame $[t+1, t+n]$ ...
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151 views

sequential Monte Carlo sampler, why the extended space and backward kernel?

Hello cross validated, I am currently studying sequential Monte Carlo samplers. My current understanding is as follows: We are interested in the marginal distribution of some sequence of joint ...
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1answer
83 views

Kernel for MCMC moves in sequential monte carlo

I'm trying to understand how to employ MCMC moves in a sequential Monte Carlo procedure for estimating static parameters as in the setting described by Chopin. He proposes, for example, the usage of a ...
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120 views

boostrap particle filter marginal likelihood

I want to calculate the marginal likelihood $p(y|\Theta)$ of the parameters of a Markov state space model with unknown parameters $\Theta$ that I am trying to estimate the marginal likelihood (...
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247 views

Why is it necessary to perform resampling step in particle filtering (or sequential monte carlo)?

I read the Wikipedia page on particle filter, it says that during 'prediction-updating', the samples from the distribution are weighted by a likelihood that represents the probability of that particle ...
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Inference for Maximum Likelihood Estimator Using Particle Filter

How does one compute standard errors for the MLE when using a particle filter approximation to the likelihood? I know that the estimator is asymptotically normal and that the variance-covariance ...
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1answer
112 views

Particle filter - expectations

I've recently been implementing some particle filter algorithms and I've realized there is a small detail I might have been doing incorrectly. Unfortunately the descriptions of the algorithms in ...
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147 views

Sequential monte carlo, resampling

In particle filters when one is doing sequential importance sampling, the quantity of interest that is being approximated is usually a weighted sum: $$\hat x_t = \sum_{i=1}^M \Bigl [f(v^{(i)}_{t}) \...
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125 views

Are the Sequential Monte Carlo algorithm invariant to the step at which we resample?

In a usual textual description (according to SMC in Practice book ) of a SMC algorithm for State-Space models, we usually expand the particles according to the distribution from the transition ...
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96 views

A doubt on the formula for updating the weights in Sequential Importance Sampling in a State-Space model

Let $x_{0:t}^{(i)}$ be the states from time $0$ to $t$ from sample $i$. Similarly for the observations $y_{1:t}$. The normalized weights are updated according to Where does the term $p(y_t|x_t^{(i)})...
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32 views

Bayes filter with delayed measurements

I have some straight and curve pieces with numbers, they are used to build tracks (of $5$ lanes) for my cars (figure $1$), I can send commands to the cars using an SDK on the Raspberry (set the speed ...
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98 views

Particle filter maximum likelihood with a discrete (Bernoulli) state variable, non-smooth loglikelihood

My model looks like this \begin{align} \begin{split} dY_{t} & = \sigma_{t} dW_{t} + Z_t dN_t \\ d\lambda_t & = \alpha(\lambda_\infty - \lambda_t)dt + \beta dN_t \end{split} \end{...
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176 views

Importance weight of conditioned particle in conditional SMC

In a generic particle filter, I understand the importance weights for each particle are calculated as $w_t^s \propto w_{t-1}^s \frac{p(y_t \mid z_t^s) p(z_t^s \mid z_{t-1}^s)}{q(z_t^s \mid z_{t-1}^s, ...
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989 views

Understanding Sequential Importance Sampling and Particle Filtering

I am struggling with SIS for particle filtering in the following aspect: In particle filtering (as per this book), the objective is to estimate the full posterior $p( x_{0:k} \mid y_{1:k} )$ rather ...
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184 views

notation conditional normal distribution [duplicate]

I'm describing parameter search using a particle filter, for which I use West M. (1993) Approximating Posterior Distributions by Mixture. On page 8 of the document, he states "and $p(\theta)$ is (...
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Soft Question: What background do I need to understand Feynmann Kac Formulae by Pierre Del Moral?

I am attempting to understand Sequential Monte Carlo(SMC) deeply, but with little theoretical background on probability theory and stochastic processes. Usually, the 'statistics' perspective of markov ...
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613 views

How to calculate importance weights for update step of an SIR (Sequential Importance Resampling) Particle filter?

I understand that one may use a particle filter to solve the filtering problem (estimating the hidden state of a system which can be described as a Hidden Markov Model). If I have a system where I ...
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2answers
473 views

Resample-move algorithm for Sequential Monte Carlo

I'm reading about the resample-move strategy, originally by Gilks and Berzuini, but my question will use the slightly more verbose description from the review of Doucet and Johansen, section 4.4, PDF ...
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Stochastic models: freedom in choosing error type?

I have a general question concerning probabilistic models. Imagine that I have a system with a high-dimensional state $x$ with a pdf $p(x)$. The state $x$ is time-dependent, and a propagating ...
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416 views

Stochastic volatility: particle filter vs Metropolis-Hastings

In many of the papers on particle filter I've read (e.g. Douc, Moulines and Olsson, 2007), stochastic volatility is a common example to show that a newly-proposed filter is working. At the same time, ...
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96 views

Multi-Target Tracking Filters

I am trying to solve a multi-target tracking problem, which is in some parts different to some filters I have already researched such as the PHD filter. I am asking for advise which filters to start ...
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1answer
259 views

Bootstrap filter

I am trying to implement bootstrap filter and I'm trying to understand it based on Bootstrap filter/ Particle filter algorithm(Understanding) EDIT: Following is the example that I'm trying to solve: ...
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27 views

Estimating Gamma PDF parameters from data with negative increments

Say we have collected data, and from a physical perspective we know that the collected data should increase positively with time. However the data looks more like this: This data shown in the figure ...
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1answer
983 views

What is the best way to apply the log-sum-exp trick in this situation?

I am aware of the "log-sum-exp" trick for calculating the logarithm of sums that handles overflow and underflow issues. However, I would like to know more about how it works. In particular, I am ...
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1answer
135 views

weights versus shifted log-weights

I'm having a hard time checking an equality in https://arxiv.org/pdf/1511.01707.pdf. It is unnumbered, immediately before (24), on page 13. Any help would be appreciated. Here is some simplified ...
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911 views

SMC (Particle Filtering) code [closed]

Does anyone know where I can find particle filtering code for R? In particular I'm looking for code for filtering a forward-rate curve.
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229 views

Techniques to estimate constant states with particle filter?

I have an application where some of my states are constant and therefore have no process noise. Over the course of the estimation process, the uncertainty in these states drops several orders of ...
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99 views

Calculate projectile trajectory from 3d points

I am trying to calculate the trajectory of a moving object (specifically, a thrown object) through a series of video frames. My tracking algorithm can reliably detect ~90% of the object occurrences ...