# Questions tagged [kalman-filter]

The Kalman filter is an algorithm for estimating the mean vector and variance-covariance matrix of the unknown state in a state space model.

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### Estimation of ARMA: state space vs. alternatives

I am interested in estimation of ARMA models. I understand that a popular approach is to write the model down in the state space form and then maximize the likelihood of the model using some ...
4k views

### Unscented Kalman filter-negative covariance matrix

I have recently started working on the unscented Kalman filter. I coded the numerically stable version (i.e., square root Kalman filter) and used MATLAB for implementing. In the final update step, ...
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### Is there something analogous to a Kalman filter for estimating continuous variables that are supported over bounded intervals?

Suppose that I have a robot which is somewhere in a $100 \times 100$ arena. A Kalman filter could be used to estimate its position from noisy measurements. The estimate produced from the Kalman ...
3k views

### Possible causes for the state noise variance to become negative in a Kalman Filter?

I am having some trouble debugging an application of a linear discreet Kalman Filter. From time to time, I find that there are diagonal elements of the covariance matrix that become negative. This is ...
400 views

### traditional state-space models and LSTMs

I am trying to understand the nature of LSTMs in relation to intuitions from traditional state-space models (e.g., Kalman filtering). The code below aims to simulate a simple univariate linear state-...
786 views

### Trouble training LSTM for sequence to sequence learning of sensor time series

I'm experimenting with using RNNs/LSTMs in place of a Kalman Filter (KF) for sensor fusion. I'm struggling to make much progress, and would appreciate some feedback/advice. I have several multi-...
290 views

### Relation between Wiener and Kalman filtering

What is the relationship from an historical point of view between Kalman and Wiener filtering? Can the first be logically seen a consequence of the latter?
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### What state-space representation of VARMA is commonly used for fitting

What state-space representation of VARMA is commonly used for fitting? Is Kalman filter + MLE approach used for fitting VARMA model as a common practice? Does the choice of which state-space ...
268 views

### Better prediction models with polling data?

I've been working on a project on measuring polls' accuracy in complex contexts (more than two candidates) where there are a small number of inaccurate polling data points. I thought it would be the ...
107 views

### RNN vs Kalman filter : learning the underlying dynamics?

Being recently interested in Kalman filters and Recurrent neural networks, it appears to me that the two are closely related, yet I can't find relevant enough litterature : In a Kalman filter, the ...
218 views

### ARMA process forecasts and maximum likelihood parameters

I have some trouble understanding the forecasting/inference process of ARMA models. From Hamilton (which I am reading now), we can obtain forecasts at $Y$ from any linear process with r.v. values $X$...
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### Is a Kalman Filter applicable for irregular, infrequent measurement?

I have taken on a project previously approached by someone else, looking at sensor data. Each sensor produces about three days of data (sampling about once a second), and each day a calibration is ...
476 views

### Implementing ARMA Log Likelihood with the Kalman Filter Algorithm

A popular algorithm to determine the (complex) log likelihood function of an ARMA(p,q) process involves generating it through the use of a state-space model and the Kalman Filter. I started reading ...
185 views

### How to add stochastic drift in dynamic linear model?

As I'm not able to comment (yet), my question follows the one raised by @mzuba here I would like to use the DLM R package to model the local linear trend model, which unlike mzuba specified, has a ...
222 views

### Unscented Transform of non-Gaussian data

I'm interested in the unscented transformation, but have a slightly unusual problem. The typical unscented transformation has several parameters which are optionally tuned by the researcher, but, let'...
1k views

### Kalman Filter to correct model simulation bias

I am working with a large scale deterministic model, which attempts to simulate CO2 emissions in different regions. When compared to historic data, the model output suffers from systematic biases. ...
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### Kalman filter: asymptotic of state estimate

Assume we have a linear state-space model: $$z_{k} = Hx_{k} + v_{k}\\ x_{k} = F x_{k-1} + Bu + w_{k},$$ where $u$ is some control variable (constant intercept is the simplest case). Kalman filter, ...
89 views