Signal Processing Stack Exchange
Signal Processing Stack Exchange

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.

Bayes Estimation (Estimator) - In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation.

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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?
hotpaw2
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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 is the best way to to handle such a…
Paul Molodowitch
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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 an unscented Kalman filter for a number of reasons…
Benjohn
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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 definitive answer. can someone give a definitive…
user24823
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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 background for this post. This is a typical sample of…
Ole-M
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Kalman Filter on Sinusoidal Signal

Suppose a system follows this equation: $$ x(t)=A \cos(\omega t + \phi)+\eta$$ where: $\omega = 2\pi f $ and $\eta$ is a random error using Extended Kalman Filter, how does estimated value $\hat{x}$ be?
unwantednoise
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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 calculated by: $$Y_k =…
Olli Niemitalo
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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 of an object. My state vector ($\bar{x}$)…
bparikh
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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 Kalman filter) I don't have any idea how to determine…
jakeoung
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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 plotting the uncertainty ellipse from the…
Nghia
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Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter

There is sinusoidally controlled signal, which other than being noisy, can change values for amplitude, frequency, phase and offset. At every new sample a new sine is fitted for the last N samples. These fitted signals might be different due to…
user3761419
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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?
IG123
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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). The measurements are independent and the noise…
Nir
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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 Chapter 12 (Linear Bayesian Estimator), Theorem 12.1 (Bayesian Gauss-Markov Theorem) gives the LMMSE…
McZhang
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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 equivenalce of the following expressions: $ \arg…
Royi
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