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31 views

Instability problem in NLMS adaptive algorithm

I have been used NLMS algorithm to equalize 4x4 MIMO signals, but the bit-error-rate (BER) after equalization is unstable with iterations. I don't know if it is the normal behavior of the adaptive ...
3
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3answers
52 views

LMS filter weight update

I have a general question regarding Least mean squares adaptive filters. Using the example of noise cancellation, I understand that if you have a set of reference signals (S) and corrupted signals (S+...
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0answers
58 views

RLS or another way to solve Ax=b in batches

I need to solve a system of linear equations to do the imaging. My A is 60k by 10k or so and not full-rank. What are the ways to proceed? I tried matlab built-in LSQR algorithm, which allows ...
3
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1answer
68 views

What is difference between LMS and gradient-descent adaptation?

I found algorithms that seems the same to me, but they are described with different names (in field of adaptive filtering). For example: LMS - least-mean-squares seems to be GD - stochastic ...
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2answers
135 views

Is the Kalman Filter a Best Linear Unbiased Estimator (BLUE) for Heteroscedastic Noise?

According to the Gauss-Markov Theorem, a ordinary least squares estimator is BLUE if the noise entering a system is uncorrelated with zero mean and is homoscedastic (has a constant finite variance). I ...
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0answers
10 views

Why would prefiltering 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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1answer
53 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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103 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
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1answer
180 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 Transpose ...
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0answers
97 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 ...
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1answer
178 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 ...
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0answers
46 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}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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0answers
97 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 ...
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2answers
2k 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
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2answers
990 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 ...
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3answers
229 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?
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4answers
201 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 ...
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1answer
81 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 ...
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0answers
58 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 $...
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2answers
209 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
220 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 + \begin{...
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3answers
3k 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
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1answer
130 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 $b$ in ...
2
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2answers
141 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 $b$ ...
15
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1answer
661 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 ...
14
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1answer
512 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 ...