# Questions tagged [bayesian-estimation]

Use this tag for any question regarding or utilizing Bayesian Estimation (Bayesian Estimator). This family includes (Among others) the Kalman Filter, the MAP Estimator and the MMSE.

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### Deriving a Kalman Filter Equation for a Linear Gaussian Filtering Model with Non Zero Mean Noise

I am trying to answer an exercise question from the book Simo Sarkka - Bayesian Filtering and Smoothing. The question is: Does anyone know if there is a resource that has the solutions for this book?
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### Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

I am learning estimation theory through Steven M. Kay - Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. In the ...
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### Bayesian Information criterion is independent of prior - What does 'prior' mean here?

I am trying to identify the possible number of states in my data. Each state corresponds to a different scenario. For example, I am measuring humidity and trying to identify the number of states in ...
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### Kalman Filter | Difference Between Minimizing the Mean Square Error (MMSE) & Maximizing Likelihood Value in Bayesian Estimation

I am going through data assimilation slides on Multi Sensor Data Fusion by Hugh Durrant Whyte and it mentions: The Kalman Filter, and indeed any mean-squared-error estimator, computes an estimate ...
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### How to update Kalman Filter with n-th order state translation?

In Kalman Filter, the hidden state translation is defined by $X_t=F_tX_{t-1}+W_t$, where $X_t$ can be a vector or a single value. This is actually derived from Bayes filter, in which 1-th order markov ...
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### Kalman fitler to estimate position from velocity measurement

I am using the Kalman filter to estimate the position from velocity measurements. I implemented the filter, but the position estimate is not well enough (large RMSE and Covariance value). Some time ...
30 views

### Particle filter localization with different types of measures

I want to implement a localization system using particle filter or other bayesian filter. I have a motion model based on odometry and different types of sensors for measurement. During the navigation, ...
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### Layman Description of the Kalman Filter

I want to know about Kalman Filter but i tried searching different links including Electrical Engineering StackExchange but the information available there was hardly digestible. All I am able to ...
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### Sparse Bayesian Learning Algorithm in Python - MSE vs. SNR

I am implementing SBL in python. I have plotted a graph between MSE (mean squared error) and SNR (Signal to Noise ratio) The graph must be decreasing, but mine is decreasing till the SNR is negative. ...
663 views

### Estimators for improved spectral subtraction of noise

Real zero-mean Gaussian white noise, independent of a clean signal $x$ and of known variance is added to $x$ producing a noisy signal $y.$ Discrete Fourier transform (DFT) $Y$ of the noisy signal is ...
233 views

### “Bi Directional” Kalman Filter

I am working on a project in Object Tracking, i.e. need to predict the location of next bounding box. I used a Hungarian algorithm with a Kalman Filter (which is a common method in this domain) which ...
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### Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

I'm new to Kalman filtering and state estimation and I'd like some guidance on EKFs. Currently, I'm trying to use a linear prediction model coupled with nonlinear measurements to estimate the state ...
420 views

### How to Realize the Sigma Point Sampling Function in Unscented Kalman Filter?

Recently I'm learning the unscented kalman filter (UKF). When designing the unscented kalman filter, it involves a non-linear function to generate the sigma points and then use the system non-linear ...
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### Unscented Kalman Filter - Multiple Consecutive Measurement Updates

In trying to implement an Unscented Kalman Filter (UKF), I have come across the issue of what to do when my measurement signals come in at a different rate than my control inputs, which I use in the ...
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### Question About Kailath's Paper - An Innovations Approach to Least Squares Estimation Part I: Linear Filtering in Additive White Noise

I'm reading the paper at the link below and I was following it for about 2 pages until I hit a road block on the bottom of page 648 where the author says: putting together 9-11, we obtain and ...
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### Question on the update step of Bayesian filter

The update step in Bayesian filtering is given as follows, in a textbook $p(x_k|y_{1:k}) = \frac{1}{Z_k}p(y_k | x_k)p(x_k|y_{1:k-1})$, $Z_k$ is defined as $\int p(y_k|x_{k})p(x_k|y_{1:k-1})dx_k$ I ...
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### Will an Unscented Kalman Filter Be “As Good” as Other Optimization Algorithms for This Problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
9k views

### When Is a Kalman Filter Different from a Moving Average?

this thread asks when a discrete time Kalman filter is better/different from a simple moving average of the observations: Why use a Kalman filter instead of keeping a running average? there's no ...
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### How to Determine Covariance Matrix $Q$ and $R$ in Kalman Filter

I am implementing getting orientation from smartphone. I want to use Kalman filter and should determine process noise covariance matrix $Q$ and measurement noise covariance matrix $R$. (newbie to ...
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### Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $M \in \mathbb{R}^{N \times N}$ which is a Positive Definite Matrix. Let $\hat{x}$ the MMSE of $x$ given $z$, namely $\hat{x} = \mathbb{E} \left[ x \mid z \right]$. Prove the ...
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### Kalman Filter Covariance

I've recently started playing with the Kalman filter for a simple 2D (x,y,dx,dy) tracking toy problem. But I seem to have some misunderstanding on what I can expect from the filter. I'm interested in ...
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### Kalman Filter - Optimal Way to Handle “Derived” Measurements?

Ie, if you have as state variables position (p) and velocity (v), and I make low-frequency measurements of p, this also indirectly gives me information about v (since it's the derivative of p). What ...