# Tagged Questions

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12 views

### Particle filter reducing the covariance matrix of joint normal distribution too much

I am working on developing a particle filter to improve the results of an Unscented Kalman filter (UKF) to satellite attitude determination. The UKF outputs a 12-dimensional joint normal distribution, ...
9 views

### Particle filtering for multiple parameters

There are several ABC algorithms out there relying on the use of importance sampling/particle filtering in which a value of a parameter is chosen based on its weight. I was wondering what happens if ...
27 views

### Difference between particle filter (PF) and recurrent neural network (RNN) for time series

Both method are used to estimate time series from data. The question is, when should I use one method or other? Is any advantage to use one instead of the other? I know that in a PF there is a hidden ...
176 views

### Mathematical and statistical prerequisites to understand particle filters?

I am currently trying to understand particle filters and their possible uses in finance and I'm struggling quite a bit. What are the mathematical and statistical prerequisites I should revisit (coming ...
82 views

### Are particle filters necessarily linked to state-space models?

I have been asked to look into using particle filters on financial time series. All the sources I have found describe particles filters in the context of state-space models. Are particle filters and ...
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### How to compute initial weights of SMC, when you initialize the algorithm with MCMC draws

Let $$y_t | \alpha_t \sim N(0, \exp(\alpha_t)), \\ \alpha_t = \phi_0 + \phi_1\alpha_{t-1} + \sigma \epsilon_t, \\ \text{ where } \epsilon_t \sim N(0,1) \text{ i.i.d.},\\ t=1,2,\cdots,T$$ The unknown ...
124 views

### Likelihood calculation in Particle Filtering

I have a doubt with likelihood calculation in particle filtering. In my understanding the particle filter consists of the following steps Generate particles from initial point Propagate through ...
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### What is the relationship between sequential Monte Carlo (SMC) and sequential importance sampling (SIS)?

The papers which develop SMC (eg. [1]) often begin by describing SIS. The two terms, SMC and SIS, don't seem to be synonyms. But neither does SIS seem to be just one "type" of SMC method. So how ...
40 views

### Can we apply bootstrap filter/particle filters on a time-series?

The task at hand is to find out the probabilities of occurrence of metric values in a time-series. For example, this time-series can be assumed as the CPU utilization of a VM. There are several such ...
60 views

### Can we modify the weight function of particle filters?

I am doing some experiments on particle filtering and I have a problem calculating the weights. Normally, the weights should be decided based on a function $w_{s_t}=p(z_t|s_t)$, if this distribution ...
21 views

### How can independence be represented efficiently?

Consider a probability distribution over a high dimensional space. We would like to find an encoding describing the distribution, so that we can approximately compute the expected value of most random ...
40 views

### Passive particle filter for x, y coordinates

I've implemented a histogram-based computer vision (CV) algorithm that estimates a webcam's x, y position based on the camera images. These estimations are naturally noisy, and ambiguous (for example, ...
2k views

### Difference between Hidden Markov models and Particle Filter (and Kalman Filter)

Here is my old question I would like to ask if someone knows the difference (if there is any difference) between Hidden Markov models (HMM) and Particle Filter (PF), and as a consequence Kalman ...
207 views

### How to re-sample particle filter's particles for a 1D door/wall problem

So assuming your implementation of the motion model and sensor model is at a somewhat satisfying level, the question then is how do I stabilize localization with the re-sampling step. I'm currently ...
69 views

### convergence of MSE (mean square error) using Sequential monte carlo

I am using sequential monte carlo method for a regression problem with bayesian estimation . I am trying to find a measure to confirm that my distribution has converged to the actual posterior ...
117 views

### Particle filter for estimation of static parameters

I am considering particle filtering methods for the estimation of static and dynamic parameters. For the static parameters $\theta$, Liu and West (page 7, equation 3.1) describe an "artificial" ...
105 views

### How to use a particle filter for Bayesian inference?

I'm not very well versed in probability theory, so I'm not sure how to assess if my approach is correct. I hope this is the right place to ask. I have implemented a particle filter to get an estimate ...
49 views

### Particle Filter Inefficiency

As I understand it, Particle Filters are a Monte Carlo method to narrow down a search space and find a posterior through a survival-of-the-fittest type method. The particular application of Particle ...
59 views

### Particle Filter and Gaussian Mixture

Let an observation model be given as $f(y_t|x_t)$ - this pdf is assumed to be nontrivial (not normal, not linear). The observation model is assumed to be known. Despite there is a state evolution ...
142 views

### 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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198 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 ...
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### 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. ...
2k 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 ...
1k 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 ...
501 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 ...
450 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 ...
66 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 ...
383 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 ...
14k 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 ...
420 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 ...
1k 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 ...
168 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 ...
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 ...
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 ...