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

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The Standard Deviation of The Derivative of a Signal

Given a signal with zero mean and a standard deviation of 0.1 sampled at 5000 Hz. What would be the Standard Deviation of its 1st, 2nd and 'n' derivative? For instance, let's say we measure the ...
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1answer
70 views

Maximum Likelihood through a noisy channel

I have random variables $X_1, X_2, \cdots, X_m $, which can take $n$ values and is distributed iid according to $\Theta=(\theta_1, \theta_2, \cdots, \theta_n)$. That is $X_k$ can take values ...
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33 views

Separating fast decaying signal from a slowly decaying signal

I have a discrete signal $x[n]$ which is exponentially decaying but the decay constant is not known. This signal is observed over a certain time period, say $T$. The only known detail about $x[n]$ is ...
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1answer
20 views

Fusing motion and color in particle filter

I am trying to implement particle filter to track a car bounded by a box. First i used color histogram as my likelihood function and implemented PF, where i was using the bhattacharya distance to get ...
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36 views

Bias of transfer function estimate

does anybody know the frequency depending bias of a transfer function estimate between two signals? In very old but interesting paper [Carter et al.(1973), Estimation of the magnitude-squared ...
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28 views

Help in system identification

I am trying to study how to estimate parameters when the signal of interest is embedded in deterministic (chaotic signal) noise and additive white gaussian noise as the measurement noise. A ...
3
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1answer
64 views

Maximum likelihood estimation in presence of colored noise

I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
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35 views

Solving an array signal processing estimation problem based on the Rayleigh quotient

The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by $$ R(\mathbf{C},\mathbf{a}) := ...
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1answer
41 views

Variance of an Implicit Function of Kalman State Vector

Given a state vector given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...
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20 views

What is deterministic noise and its effect

I have few conceptual questions related to application of chaos in communications. Kolmogorov-Sinai Entropy1 , Kolmogorov-Sinai Entropy2 and Kolmogorov-Sinai Entropy3 KS is an entropy metric for ...
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1answer
50 views

What is uncorrelated noise

In many applications such as estimation theory, when we need to estimate a parameter then we usually consider in presence of white gaussian noise of zero mean and some standard deviation. During ...
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1answer
55 views

minimizing the mean squared error?

I'm reading this book "Applied Optimal Estimation" by A. Gelb. In the example 1.0-1, there are two measurements $z_{1}$ and $z_{2}$ with some noise for measuring $x$ as following $$ z_{1} = x + v_{1} ...
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44 views

Spectral estimation from noisy time-series data

This is the first time I'm posting a question on here so I hope I'm doing it right. I've tried searching on here for an answer but haven't found anything particularly relevant. I have some data ...
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2answers
48 views

Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we ...
2
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0answers
76 views

DOA estimation 2 sources time delay estimation uniform array

I am new to signal processing, so sorry if the question is superbanal. I have been spending more days than I would admit on this and can't find the error. I have two triangle waves that are emitted ...
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3answers
57 views

comparison between frequency offset estimators

I have been working frequency offset estimation in OFDM. The objective was to compare different frequency offset estimation techniques. By using MATLAB, I have simulated three different estimation ...
2
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2answers
103 views

How to understand the type of noise

Suppose that I am receiving RF signals contaminated with noise through antenna. This signal is digitally sampled. How can I understand the type of noise(Gaussian,Uniform etc). Any algorithm is there ...
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1answer
123 views

Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
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2answers
159 views

Estimate the transfer function of an unknown system?

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
2
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1answer
71 views

Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in {R}^{NxN} $ Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $. How come the following are equivalent of minimizing $ E[{(\hat{x} - x)}^{T}(\hat{x} - x)] $: $ ...
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49 views

Confusion regarding Dimension of AR model

I have a confusion regarding what is meant by dimension of AR,ARMA,MA model? Considering an AR model $x(t) = a1*x(t-1) + a2*x(t-2)$ is a 2 order AR model with $a1,a2$ as the parameters. This equation ...
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0answers
23 views

Relationship between phase space volume and entropy minimization

I would like to know if there is any analytical proof or relationship which can show that for a dynamical system in presence of chaos signal, if the phase space volume (PSV) minimization leads to the ...
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29 views

Minimizing the sum of squares of autocorrelation function of residuals instead of sum of squares of residuals

I am trying to fit my model to some experimental data and I am using a simulated annealing algorithm. My objective function has so far been the sum of squares of the residuals: $\sum_{i=1}^n (y_i - ...
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1answer
115 views

Carrier frequency offset (CFO) estimation based on Symbols

In (1), it's said that: If two identical training symbols are transmitted consecutively, the corresponding signals with CFO of $\epsilon$ are related with each other as follows: ...
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23 views

Estimating Model Weights for Point-Process Input/Output Systems using Probability Theory

Problem: I have a point-process input & output, x & y and I am attempting to estimate a 2nd order nonlinear Volterra-like model for them in the form: $$ Eq. 1: y[t] = k_0 + ...
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97 views

minimum SNR requirements for maximum likelihood frequency estimation

In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation ...
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2answers
357 views

Carrier frequency offset (CFO) estimation using cyclic prefix

I understand the cyclic prefix, but in (1) it's said that: "If we consider that the channel effect is minimal and can be neglected. then the phase difference of the CP and the OFDM symbol which the ...
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53 views

What are variance and bias in spectral estimation (specifically periodogram spectral estimation)?

So far, I have read that all the non-parametric estimation techniques decrease the frequency resolution in order to decrease the variance in the spectral estimate What is the general "overview" ...
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72 views

Prony method for undamped signal

i have one question related to sinusoidal model,as i know Prony's method for parameter estimation is used for damped signal,when amplitude of signal decreases as time varies,but is it relevant to ...
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3answers
98 views

How to determine, calculate and plot a probability distribution for a given set of numbers?

A device is rotating with a particular wind speed and producing such pulse frequencies in a minute: ...
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2answers
71 views

Estimating the amplitude of a particular frequency

I am relatively new to DSP and have been reading a lot on the internet. I have a couple of questions. I have a signal in the form of a function $$ f(x) = A_0 + A_1 \cos(\omega_1 x) + A_2 ...
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31 views

Kalman Filter Properties with Biased (By Constant) Measurements

Assuming I have a filter with the following form: $$ \begin{bmatrix} {r}_{k} \\ {\dot{r}}_{k} \end{bmatrix} = {F}_{k} \begin{bmatrix} {r}_{k - 1} \\ {\dot{r}}_{k - 1} \end{bmatrix} + {v}_{k} $$ $$ ...
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26 views

If test statistic is $T(\textbf{Y})=\frac{1}{N}\sum\limits_{n=1}^N |Y[n]|^2$ then what is $T(\textbf{Y}|H_1)$?

There are two hypothesis: $H_0:Y[n]=W[n]$. $H_1:Y[n]=X[n]+W[n]$. $X[n]$ and $W[n]$ are independent of each other. $W[n]$ is zero mean Gaussian with variance = $\sigma^2$; however we only know the ...
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128 views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
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42 views

Incorporating delayed data in Kalman filter

my guide has told me to get familiarized with state estimates and kalman filter ....the problem is that: 1) I am totally new to this topic and finding it really difficult to understand due to lack of ...
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2answers
64 views

DFT detemine frequencies

I am just begining learning about DFT and I am bit unsure on what is happening mathematically during DFT. I've sampled a signal , a sine wave sin(1000*2*pi*t). And performed DFT to calculate the ...
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1answer
42 views

How to identify stable deltas in a noisy signal

This is a problem I have had to deal with in several different contexts now. Given a real time signal which you expect to act as a noisy step function (periods of stability separated by quick changes ...
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1answer
95 views

Frequency and damping estimation with Prony method?

I have a sinusoidal time domain signal with few damped exponential components. i.e. ...
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1answer
45 views

What is the set of most predictable or in other words most self-correlated signals?

Which signals or set of signals is the most predictable or in other words most self-correlated (autocorrelation)? I think one of them is $x(t)=c$, for all $t$, where $c$ is a scalar constant. The ...
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53 views

Sampling Clock Offset estimation

I want to estimate sampling clock offset. I am currently referring this paper " CRAMER-RAO BOUNDS FOR DATA-AIDED SAMPLING CLOCK OFFSET AND CHANNEL ESTIMATION ". Is there any other method to estimate? ...
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30 views

MMSE Estimation of Noise Corrupted Signal

I just learnt the MMSE (minimum mean square estimate) in my stochastic processes course and I am experimenting it on matlab. So I have a noise corrupted signal Z. ...
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7answers
729 views

Obtain a signal's peak value if it's frequency lies between two bin centers

Please suppose the following: The frequency of a signal's fundamental has been estimated using FFT and some frequency estimation methods and is lying between two bin centers The sampling frequency ...
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73 views

Symbol timing recovery algorithms

I am trying to implement the symbol timing recovery loop and for that I have chosen two algorithm to compare my results one is feedforward and Gardner TED. One thing that is confusing me is smoothing ...
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54 views

Estimating Position Based on Range Measurement

I want to present Kalman Filter problem. For simplicity I'd assume the simplest dynamic model - Piece Wise Constant Velocity. The state vector and dynamic model are given by: $$ \begin{bmatrix} ...
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2answers
98 views

Relation between Kalman filter and Sequential linear MMSE estimation

Are the results of applying Kalman filter and recursive linear MMSE estimation process the same ?
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2answers
107 views

Why is PSD estimated, and not simply computed?

I apologize if this comes as a basic question, but I am struggling to understand why the PSD can only be estimated and not directly computed. For example, this thread discusses several such PSD ...
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58 views

Cleaning accelerometer output

I am working on an accelerometer on a mobile device. When an event occurs, I record around 30 acceleration values. The accelerometer, being extremely noisy is very unreliable. What makes it worse is ...
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183 views

How to detect specific behavior in time series?

I was not quite sure what the right SE for this was, so I posted this also here on SciComp. Please tell me which one to remove :) Problem statement I have a few hundred unrelated time series, say ...
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99 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
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133 views

Estimation of the amplitude of a frequency component in a signal

I'm working on a device that produces a signal with sampling rate of 100 kHz. Every 40 ms, I receive 16000 points, from which I have to extract a frequency close to 3.55 kHz. I have developed a method ...