Questions tagged [estimation]

In signal processing, estimation is a technique for approximating an unobserved signal from an observed signal containing noise.

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SNR estimation: signal with unknown amplitude and Gaussian noise

I would like to know can anyone suggest me techniques to estimate the SNR for a given noisy signal. I do not know the amplitude of my signal but I do know that noise is Gaussian. I have tried to do ...
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1answer
601 views

What is the computational complexity of Spectrum Estimation Algorthms and What they depend upon?

There are lots of spectrum estimation techniques, each with some pros and cons. Algorithms like: Music Welch's method Yule-Walker AR method Periodogram modified covariance method multitaper method (...
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72 views

Help in problem formulation for estimation of image as a feature vector - SISO or MIMO FIR channel model?

Based on the paper Blind Image deconvolution: A feature vector is a list of numbers used to represent an image. The feature vector for my case takes values as symbols $-1,1$. An instance or an ...
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1answer
866 views

What are the advantages of higher order Kalman Filters like EKF, UKF?

Kalman Filter provides the optimal estimate of the states of a stochastic dynamical system if the system is linear, the measurements are also linear functions of states and the errors in system ...
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157 views

Different results for different orders of estimating AR model using Yule-Walker equations

I'm trying to use MATLAB to estimate the AR parameters to the following filter: $$H(z) = \frac{1}{1-0.5z^{-1}+0.25z^{-2} -0.25z^{-4}}$$ As I can see, the process at the output of this filter depends ...
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47 views

Estimate/Compute parameters of image dataset

I have a dataset of images taken by Kinect (RGB and D) How can I extract the following information only from the images: Frame rate Camera height The dataset containes images of person (s) moving ...
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27 views

Any estimation algorithms that allow a user to indicate that certain Solutions are impossible?

Variations of the Kalman filter and other algorithms are used for navigation and target tracking. Often times certain solutions might as well be deemed impossible based on known topography in the area....
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69 views

Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)

My apologies for perhaps the stupidity of this question. Presume that one has the 'frequency response' $Y_{data}(k)$ of a system and also has an estimated model $Y_{syn}(k)$ that fits the data. How ...
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1answer
60 views

Good Reference Problem to Test Filtering/Estimation Algorithms

I am looking to figure out if a current filter algorithm I have built could be useful for some problems I am looking into at work. It isn't a Kalman filter, but is instead making estimations using a ...
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125 views

Estimation of accelerating target using position measurements only

I am currently thinking about approaches to estimating the position and velocity of an accelerating target. At this time, I have tried a few approaches that work alright. I have tried two variations ...
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1answer
82 views

Which is correct representation for function of variable?

I have a function as $$E=\int_\Omega -\log\big( p_i(x)\big) dx$$ where $p_i(x)$ is density distribution which estimated by Parzen window method. $$p_i(x)=\frac{1}{\Omega_i} \int_{\Omega_i}K_\sigma\...
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60 views

How to validate an estimated model in case of output-only data (in frequency domain)?

Before moving to the actual question, I would like to emphasize on the following points (maybe they are obvious to some of you, but I still would like to list them, since they make the difference): ...
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1answer
248 views

Frequency estimation of N FFTs of one sine signal in AWGN

Assume N receivers, detecting the same sine signal in AWGN with FFT, then we have N peaks for the same frequency corrupted by noise. How to use the N FFT observations of the same signal to get a more ...
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435 views

Maximum Likelihood for Colored Noise

I have the following question about the maximum likelihood (ML) in presence of inter-symbol interference and colored noise. Assume the communication system is as follows. Information source, ...
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1answer
281 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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Methods of combing two parameter estimates

If you have two different methods of calculating a continuous parameter (eg. heart rate), each with their own uncertainty, what would be some common methods of combining these parameters to create a ...
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2k views

1/f noise parameter characterization

I would like to characterize 1/f noise in some time series data. I would like to estimate the 1/f noise corner, and the standard deviation of the 1/f noise component and white noise component. The ...
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146 views

Problem using MMSE estimation of channel frequency response

I need to model the minimum mean square error (MMSE) performance in estimating channel frequency response. I have channel's power delay profile (PDP) as a table with tap delays and powers. The ...
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160 views

RLS Algorithm Convergence

I am looking for some help to understand the concept how RLS converges? If possible to present it graphically that would be best. It is very easy to understand the understanding of convergence in case ...
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1answer
300 views

Cost function for adaptive algorithms

I am having little difficulty to understand that why most of the adaptive algorithms use error power or addition of error power as cost function/minimization criterion. I have read that minimization ...
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2answers
292 views

Estimate camera generalized velocity from consecutive frames

Let's suppose I have a camera which can move freely in 3D space and has 6 degrees of freedom. Is it possible to estimate the linear and angular velocity of the camera from 2 or more consecutive frames?...
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1answer
644 views

Cross-Correlation Signal Delay Estimation Variance

I am working on a project which intends to use Time Difference of Arrival (TDoA) for localization. Firstly, my understanding is that a matched filter is the most common method for estimating signal-...
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1answer
388 views

Channel Estimation / Equalization - Estimate Channel Inverse Using White Noise Statistics Only

Given the system defined in the following figure: We have a system $ G \left( f \right) $ which is unknown yet can be defined by $ {N}_{p} $ poles and $ {N}_{z} $ zeros. The signal $ x \left( t \...
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Kalman Filter for estimating position with nonconstant velocity & acceleration

I am trying to estimate the position & head direction of a rodent going through a 2D environment (a circular surface of 1m radius). Above his head is an overhead camera which records 4 LEDs ...
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2answers
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Determining channel frequency response from measured data via IFFT

I've been working on a small system that transmits a linear chirp over the 35Hz-20kHz frequency range in a room and simultaneously records the transmitted signal with echoes (from the floor, walls, ...
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1answer
79 views

Why Would Pre Filtering Measurement Data Affect the Least Squares Estimate?

In estimating parameters in a discrete time model I've often seen the use of filters applied to the input data, before its applied to least squares processing. I've been told that the filters are ...
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293 views

Optimality of Kalman Filter for Process Noise dependent on magnitude of state

Consider I have a dynamical system $\dot{x} = Ax + w(t)$, $x \in \mathbb{R^2}$ where $w(t)$ is a Gaussian random variable with mean $E(w(t)) = C\|x\|^2$ where $C \in R^2$ is a constant and covariance ...
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48 views

Estimate High Frequency

I'm smoothing a signal with an little algorithme and I can control the amount of smoothing dynamically. Now it could be interesting to drive that amount with a measure depending of the frequency ...
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1answer
216 views

Making sense of the delay formula between two sensors in an antenna array?

In the image above, there is a formula for the delay of a signal at a given sensor 'i' in an antenna array. I don't understand how they arrived at that formula. Each antenna array element is ...
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1answer
690 views

Estimating a Low Frequency Signal Corrupted by High Frequency Noise

This is a follow up to the question How to Pick a Journal for Publishing a Research Work? question. Suppose we take discrete samples of a low frequency signal corrupted by high frequency noise. We ...
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Temporal window $\{v(t)\}$ of Welch estimator

The Welch estimate [1] of PSD (power spectral density) is determined as: $$\hat{\phi}_W(\omega)=\frac{1}{S}\sum_{j=1}^S \hat{\phi}_j(\omega)$$ where $$\hat{\phi}_j(\omega)=\frac{1}{MP}\left|\sum_{t=1}^...
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1answer
2k views

MUSIC algorithm for peak detection

On Wikipedia, is written that MUltiple SIgnal Classification (MUSIC) is an algorithm used for frequency estimation. One purpose of estimating the spectral density is to detect any periodicities in ...
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98 views

How to Pick a Journal for Publishing a Research Work?

I got my MS in EE way back in 1994 and have not presented at a conference, or published in a journal before, but I had and still have an intense interest in the applied math that I learned. I have ...
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159 views

Optimal method to calculate Fractional Fourier for Chirp signals

There are several method exist in the literature to calculate fractional Fourier transform. My interest is in chirp signals and want to find time delay estimation using fractional Fourier transform (...
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2answers
3k views

An explanation of parts of the MUSIC Algorithm for someone without a background in signal processing?

I've been looking at every tutorial and paper I can find, but I keep losing the intuition behind what's going on when they get into the matrix operations. There is a step in which the signal vector ...
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1answer
52 views

What would be the best way to estimate velocity from a video?

I am not from an EE background, so I am looking for answers to some open-ended questions. I want to calculate how fast water is flowing during a flood. With or maybe even without debris in it. I have ...
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1answer
518 views

How to estimate filter coefficients of an all-pole system?

Suppose we have measured the frequency response of a system that is known to be all-pole; measuring impulse response is not possible. What are the methods available, if any, to estimate the ...
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3answers
111 views

Visual Tracking / Object Tracking: Estimate the Direction the Whale Is Moving

I am trying to find out which way the whale is moving. So I have an image of the whale swimming in the water and I want to find out where is it located and which direction does it swim (with respect ...
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4answers
896 views

Estimate Delay of a Known Signal Delayed by Sub Sample Resolution

Given a known signal $ x \left( t \right) $ and its delayed version $ y \left(t, \tau \right) = x \left( t - \tau \right) $. Both are sampled by Sampling Frequency $ {F}_{s} $ to generate the signals $...
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0answers
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Digital low pass filter vs Kalman filter

I have experience with the design of FIR, IIR digital filters. I also know about the Kalman filter, but I am not skilled at using them. Consider the case of a low frequency signal from discrete ...
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1answer
188 views

Equalization knowing the Channel State Information

I am trying to simulate a simple communication system using channel estimation. I was able to estimate the channel response using the Least Squares channel estimator, and it is working properly (...
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2answers
2k views

Estimating the Variance of Noise Using Median Function Applies on the Gradient of the Image

By investigating the implemented code of an accepted paper, I encounter with following relation to estimate the variance of noise in an image: $$ \sigma = \frac{median (|\nabla^hx-median(\nabla^hx)|)}...
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1answer
126 views

What is the Technique to Find Variance of Estimation Error

Given an $n$-vector $y$ (responses) and a design matrix $X$, I wish to fit them with a simple linear regression model $$y=X\beta+e,$$ or, $y_t = x_t'\beta_0 + e_t$ where $e\sim\mathcal{N}(0, \sigma^...
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1answer
146 views

Looking for the Concept About All In One Curve Fitting

I know that there are some Technic for finding curve fitting like polyfit() or pinv(). so we can get a some polynomial equation. it's OK good. I can get successively a polynomial equation for each ...
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1answer
129 views

Confusion related to PN sequence : Terminology and application in statistical signal processing

A Pseudo-random Noise (PN) sequence is a sequence of binary numbers, e.g. ±1, which appears to be random; but is in fact perfectly deterministic. The sequence appears to be random in the sense that ...
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1answer
620 views

Subsample Time Delay Estimation

Often we need to estimate the time difference of arrival between two signals to find the location of a target. Many algorithms gives the time delay corresponding to a sample number or time delay is a ...
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1answer
166 views

What is the estimator used in this paper for system identification?

The paper System Identification using Symbolic Chaotic Sequence proposes EM-UKS estimator for system identification of a linear FIR channel when excited by non linear input. In Fig 3 of the paper ...
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1answer
188 views

Expectation maximization of moving average with binary source input

I am trying to do blind system identification of a univariate linear FIR model: I am unsure if the approach is correct or not and any help to further proceed with the maximization will be great. ...
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1answer
107 views

Performance of Viterbi detector over non-minimum phase channels

For sequences that are transmitted over channels with memory $\mu=n$ and response H=$[h_0 h_1 \ldots h_n]$,Viterbi algorithm implements Maximum Likelihood (ML) detection and BCJR implements Maximum A-...
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428 views

how to extract meaning from signal (distance estimation)?

I have 3 times series representing detected rssi signal power from 3 emitting devices. The devices are at 1 meter distance from the receptor, plotting the 3 time-series gives the following results : ...

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