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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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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1answer
50 views

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 ...
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1answer
20 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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4answers
161 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 ...
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0answers
91 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. ...
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5answers
623 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 ...
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1answer
188 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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2answers
2k 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 ...
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1answer
307 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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1answer
320 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 ...
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2answers
82 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 ...
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1answer
59 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 ...
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2answers
526 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}...
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5answers
2k 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?
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1answer
145 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 ...
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4answers
310 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). ...
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1answer
225 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 ...
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2answers
193 views

Update Sub Set of the State Vector in Kalman Filter

I question about Kalman Filter: If I have system state $$ \mathbf{X} = [x_1\ x_2\ x_3\ x_4\ x_5]^T, $$ these state elements are independent. I have measurement from a sensor to correct the ...
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1answer
67 views

Kalman Filter - Updating the Covariance Matrix Step

I am trying to simulate the Kalman Filter. I have the covariance matrix P_{0|0}. Tell me please, how can I get the predicted (a priori) estimate covariance matrix ...
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1answer
1k 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 ...
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1answer
239 views

Kalman Filter - Non Linear Measurement Model

I'm new to Kalman filters and estimation in general. I'm running a simple test of an EKF to check my understanding, but I'm getting some odd results with a particular case. Given a state vector: $$ \...
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0answers
667 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 ...
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3answers
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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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1answer
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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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2answers
145 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 ...
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2answers
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 ...
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1answer
1k 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 ...
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5answers
6k views

Kalman Filter - Implementation, Parameters and Tuning

First of all, this is the first time I try to make a Kalman filter. I earlier posted the follwoing question Filter out noise and variations from speed values on StackOverflow which describes the ...
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6answers
18k views

What Is the Relationship Between a Kalman Filter and Polynomial Regression?

What is the relationship, if any, between Kalman filtering and (repeated, if necessary) least squares polynomial regression?