The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
0answers
11 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, ...
0
votes
0answers
47 views

Least Square Channel Estimation Technique

A communications channel is modeled by a finite-impulse-response (FIR) filter: $$y[n] = Hs[n] + w[n]$$ where $H$ is the channel coefficients, $s$ is the binary source and $w$ is AWGN A least Square ...
3
votes
1answer
85 views

Constant Modulus Algorithm and the gradient operation

CMA is a blind channel equalization algorithm with the details presented above. I am facing 3 difficulties and shall appreciate help Q1: Does $H$ and the bar over $\bar{y_k}$ represent the ...
1
vote
0answers
43 views

Motion artifact cancellation from ECG signal using 3-axis accelerometer data

I have a ECG signal measured as a test subject is performing 3 different activities - sitting, walking(2mph) and jogging(5mph) and also the corresponding 3-axis accelerometer(X,Y and Z) signals. I can ...
0
votes
0answers
51 views

How to apply the least squares method to built-in models of Levenberg-Marquardt algorithm

I am trying to apply the least squares to my data using the built-in Voigt model from lmfit. But I have to call the Minimizer class to apply the least squares method, which requires a function. And ...
1
vote
1answer
110 views

Least squares and auto and cross correlation

I am trying to understand why auto and cross correlation helps find the best fit line in least squares. I have an equation as stated here: $Ax=b$ -- I have not exact solution, so I use the least ...
0
votes
0answers
31 views

Prediction error in least squares with a linear model

In the classical linear model with $$Y=X\beta +\epsilon,$$ where $Y \in \mathbb{R}^n$ is the observation, $X\in \mathbb{R}^{n\times p}$ is the known covariates, $\beta \in \mathbb{R}^p$ is the ...
0
votes
0answers
30 views

detecting frequency bursts in GSM using ALE, mystery peaks

http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=1404796 I've implemented the algorithm in the mentioned paper. From the error function, I can clearly see the filter converging to the FCH (Frequency ...
1
vote
0answers
42 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}) := ...
2
votes
0answers
90 views

Least Angle without matrix inversion?

Sorry if this is too damned long. I did what I could to abbreviate it. I'm new to numerical work with matrices. I believe I have a way to compute Least Angle without explicit matrix inversion. I'm ...
1
vote
2answers
819 views

Difference between Equiripple & Least Squares design for FIR digital filters

For an efficient and optimized digital FIR filter design, there are two methods available broadly, Equiripple filter design & Least Squares filter design. A general method for designing a filter ...
4
votes
2answers
554 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 ...
1
vote
3answers
194 views

Force Linear Phase for a FIR filter synthesized using Berchin's FDLS?

As a follow-on to this post, how would you force linear phase for a FIR filter you synthesized using Berchin's FDLS?
1
vote
4answers
199 views

Best signal processing method for this application?

I have a signal I'm getting from a sensor (shown below in the photo of an excel plot) and I need to process it to get it to look something like the red line I've overdrawn on it. Sort of a moving ...
0
votes
1answer
75 views

Estimation of input signal to obtain the desired output signal for an unknown filter

Suppose $h(n)$ is a finite impulse response which is unknown. We can feed any input signal $x(n)$ into the system and observe the corresponding output signal $y(n)$. From this, is it possible to ...
1
vote
0answers
53 views

How to fit a function (find a lower bound) to (for) the plots?

I am dealing with a complicated optimization problem with two parameters $N, K$. Setting $K =$ constant and finding the minimum for different $N$'s lead to a set of function values. I can do this for ...
1
vote
2answers
198 views

Conceptual question on least square estimation method

What is meant by Least square plus Gaussian method of estimating the parameters of an unknown system? I am aware of least squares in general but some works refer it as least square+gaussian method. ...
3
votes
2answers
200 views

How do you combine 2 least squares estimates?

Say you want to compute the least squares estimate of $w$ from a data-set: $$ \begin{bmatrix}d_1 \\d_2 \\\vdots\\d_N \end{bmatrix} =\begin{bmatrix} x_1 \\x_2 \\ \vdots \\x_N\end{bmatrix}w + ...
4
votes
3answers
2k views

How to remove the periodic oscillations from a signal

The task that I have is to remove the annual and semiannual oscillation from a set of temperature measurements, taken over several years, by means of least squares method. I found the method ...
2
votes
1answer
124 views

Doubt on Weighted Least Square Estimation

This is a page from the book linear algebra,geodesy and gps by Gilbert Strang.... the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ ...
2
votes
2answers
133 views

Least Square Error Estimation doubt when can we write $(A^TA)^{ -1} = A^{-1}(A^T)^{-1}$?

I am new to linear algebra and have this simple question... in least sqaure estimation...the best estimation of the equation $Ax = b$ is $x_{Estimated} = A (A^t A )^{-1} A^t b$...the projection of $b$ ...
13
votes
1answer
477 views

How to tell if an error surface is convex? (Is it determined by the Covarinace matrix or the Hessian)?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...
13
votes
1answer
449 views

How do I improve LMS / NLMS filter performance?

Are there ways to increase computational performance of a normalized least squares (NLMS) filter? Multidelay block frequency-domain (MDF) filters have been proposed to do this, but they also take away ...