# 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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### Bayes rule and terms with expectation

I am reading the following paper in economics; link On page 495, authors give an expression with Bayes rule. As an example, say that there is a random variable $\beta$ which can be either $\beta_L$ or ...
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### regression model with arma errors: forecasting the residuals

Suppose I estimate the following model: $$y_t = \beta_0 + \beta_1 x_t + \eta_t$$ where $\eta_t$ is an AR(1) model, say. I can do that with forecast::Arima() as ...
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### What is the "process noise" (Q) parameter to a Kalman filter?

I'm teaching myself about Kalman filters; I've studied a number of videos and articles and have enough of an understanding now that I can effectively construct and use them. However, most of what I've ...
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### Using Bayesian statistics in time series forecasting

I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal ...
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### How can mahalanobis and chi2-test be used to determine of an observation is acceptable?

Assume that you have a model $$\dot x = Ax + Bu$$ $$y = Cx$$ And this model is SISO. Single input and single output. You got the mission to determine of an observation is acceptable for the kalman ...
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### Assessing probability that one set of measurements extends the other with Kalman smoother

I have two sets of N-dimensional measurements following each other with a certain time gap in between. Let's name those sets $A$ and $B$, respectively. All observations have constant Gaussian white ...
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### Exact diffuse initialization of the Kalman Filter: what does the design matrix look like?

I am using Python (statsmodels) to create a dynamic factor model on which I apply the Kalman filter. Thanks to earlier questions on this forum, I landed upon using exact diffuse initialization. My ...
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### Kalman Filter Terminology: Prediction vs Estimation

The linear dynamical system model underlying the Kalman filter technique involves a random process $(x_{0}, v_{1}, w_{1}, x_{1}, z_{1}, v_{2}, w_{2}, x_{2}, z_{2}, \ldots)$ where $x_{k}$ represents ...
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### Why do popular ML and statistical packages simply ignore classical estimation and detection algorithms for statistical signal processing? [closed]

For those who had a hard time to study and understand classical estimation and detection algorithms, and unfortunately realized that these algorithms are simply ignored by many packages that have the ...
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### Proving consistent/inconsistency of a fusion of KF estimates

I have a distributed fusion scenario with a single target where two sensor nodes $i,j$ estimate the true state $\mathbf{x}$ using a local Kalman filter. The (linear, Gaussian) measurement errors of ...
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### Smoothing of GPS tracks - remove noise and stop-go clusters

I know there are several posts about this, but I could not find exactly what I need. I have GPS track data (from an underwater vehicle) for short intervals of 1 second (time-stamps on data). The data ...
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### Instantaneous propagation of process covariance matrix modification's effect on state

I am trying to build a zero-delay kalman filter which udates its process noise covariance matrix $Q_k$ depending on the value of the residues $z_k - H\cdot x_k$. My problem is, I have adopted a 1D ...
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### Inferring a random walk from noisy "images"

I'm interested in the following inference / filtering problem in a hidden Markov model setting. Suppose we have a simple random walk $x_t\in\mathbb{Z}$ and observations are "images" ...
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### Negative value of likelihood function in Kalman filter

I use kalman filter algorithm, where I minimize the value of likelihood function. But after some iteration I got negative value of likelihood function. Is that a problem?
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### What is the scope of application of Kalman filter?

Recently I learned some basics about Kalman Filter 1D As I know, Kalman Filter is useful in Telecommunication and GPS positioning. My estimation goal is to measure the reliability of the Circuit using ...
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### Approximating a 1-d Kalman Filter with non-Gaussian Observation Noise

I'm looking for a Bayesian filter where observations are generated according to $s_t = \gamma s_{t-1} + w_p$ and $w_p \sim Normal(0, \sigma_p^2)$. Both $\gamma$ and the variance of the process noise \$\...
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