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# 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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13 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, ...
102 views

### 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 ...
55 views

### 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. ...
20 views

### When we set a State vector during bayesian process, can we use only velocity or location?

When we use a bayesian framework, we firstly set a state. The state is what we want to know. At this time, Can we use just location or velocity as below? For example, $$\mathbf{x} = [x\ y]^T$$ ...
528 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 ...
1k views

### 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 ...
184 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 ...
215 views

### 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 ...
62 views

### 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 ...
52 views

### 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 ...
411 views

### Alternative to Extended Kalman Filter when prediction function is not differentiable

I am looking at a tracking problem. It can be modelled similarly to the Extended Kalman Filter:  \begin{array}{rcl} \mathbf{x}_k &=& \mathbf{f}(\mathbf{x}_{k-1}, \mathbf{u}_k) + \mathbf{w}...
1k views

### Why does the Kalman filter remove only Gaussian noise?

What and where in the derivation of the Kalman filter is the assumption of Gaussian noise? Why and how does this assumption help?
120 views

### How to derive an expression for the optimal importance distribution?

I'm trying to answer the exercise 7.6 letter b of this book: https://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf page 133 but I'm having some problems in understanding the question ...
262 views

### MMSE Estimation - Fusion of 2 Measurements

Let's say I have 2 measurements of the same phenomenon (for example current temperature) and I want to find the MMSE (minimum mean square error) estimator, i.e to minimize the MSE (mean square error). ...
183 views

### General questions on Kalman filter and difference

In the wikipedia Kalman filter link, the state variable $x_k$ takes a continuous value say a floating point number, but what if the values are integer say symbols from an alphabet set, then how does ...
873 views

### Derivation of Transfer Functions for Kalman Filter

Hi All: I'm somewhat familiar with the kalman filter from a statistical point of view. But lately I've been trying to familarize myself with the linear systems-EE way of looking at it. So, I've been ...
646 views

### 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 ...
7k 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 ...
10k views

### 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 ...
139 views

### 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 ...
2k views

### 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 ...
924 views

### 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 ...