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Questions tagged [least-squares]

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4
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1answer
83 views

Use recursive least square as an “actual” filter?

I am currently studying recursive least square (RLS) and as far as I understand, the setup is (for example) that we are given a process with uncertain parameters/noise and we want to adapt parameters ...
1
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1answer
29 views

Why is the concept of a “state covariance matrix” necessary in estimation?

I'm currently taking a course in optimal estimation (and it's still very early in the course). Much of our work is based around the idea of a measurement model $y=Hx + v$ This model assumes our ...
3
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1answer
91 views

Jacobian Computation in Least Squares IIR Filter Design

Long time lurker and first time poster - but unfortunately I haven't had any joy untangling this on my own. I've been studying Mathias Lang's thesis, Algorithms for the Constrained Design of Digital ...
0
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0answers
48 views

System identification with limited bandwidth

Given a FIR filter $h[n]$. Its action can described as: $$ \mathbf{y} = \mathbf{H} \mathbf{x} \\ \mathbf{y} = \mathbf{X} \mathbf{h} $$ where $\mathbf{H}$ and $\mathbf{X}$ is a Toeplitz matrix. If $h$...
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0answers
28 views

Difference Between a 1st Order SG Filter And a Least Squares Moving Average

I have been studying SG filters and i recently found another filter which seem to be commonly used in financial data smoothing which is the least-squares moving average, this filter is also called ...
0
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0answers
73 views

How to find Coefficients of Autoregressive (AR) model using least means square (LMS) Algorithm without having future signal?

I want to do two things. Estimating Coefficients of AR model using LMS Using Coefficients found in step 1 and predict future samples of a signal using AR equation. I don't have a desired signal so I ...
0
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1answer
110 views

Range Estimation Based on Distance Differences

It is a range estimation problem, as shown in the figure. The blue circles are the anchor node' positions, which are produced by one moving anchor (the moving direction is shown with black arrow). ...
0
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0answers
46 views

Non Linear Recursive / Online Least Squares

I am searching for a recursive or online non linear least squares algorithm. I want to spread the computation out as new data is sampled like in the linear Recursive Least Squares or the LMS. ...
0
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0answers
22 views

Can coefficients of a DWT be computed using least squares approximation?

I assume that it can be computed given function values for each sample as a vector and wavelet values for each scale and translation packed in a matrix. Can anyone clarify the matrix construction and ...
1
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1answer
102 views

Equivalence of Maximum Likelihood (ML) and Discrete Fourier Transfrom (DFT) Peak Finding for Single Tone Estimation

My understanding is Maximum Likelihood and DFT Peak Finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the DFT. I was wondering if there was ...
1
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2answers
113 views

Solving a Linear Mean Square Estimation the Easy Way

I have an exercise which is quite trivial. However I got stuck and I'm not sure if this the end-result. I assume there has to be a way to get this result much quicker. Given are two randomly ...
0
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1answer
47 views

Linear Difference Equation and Method of Least Squares

I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a. The author explains how to estimate the parameter of a linear difference equation using Least Squares. We start with a ...
2
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4answers
371 views

Sequential Form of the Least Squares Estimator for Linear Least Squares Model

I'm currently working on a project in which I need to find the tilt of a surface. Let's assume I'm only concerned with a single dimension tilt (i.e. slope) to begin. I currently have the ability to ...
0
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1answer
32 views

Defining Model in Kalman for Getting Position Using

I am stuck at modeling a system model, i.e. getting my state vector and input vector for navigating just using navaid and ins (tactical). My guess is that position is my only state vector and INS ...
1
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1answer
110 views

Adaptive LMS Algorithm MATLAB

I'm having some trouble implementing my LMS Adaptive Filter in MATLAB to separate wideband and narrowband signals from a voice signal. I'm using a delayed version of my input as a reference as well ...
1
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1answer
109 views

Using MATLAB Function `mpiir_l2()`: Results Are Not IIR but FIR Filters - Why and How to Avoid This?

I'm using mpiir_l2() from user Matt L's PhD thesis to design IIR filters. I set the number of numerator and denominator coefficients both to the same value (between ...
0
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1answer
89 views

Equalizers with low data rate systems

In case of using equalizers with ZigBee systems, what type of fading does the channel show, flat or frequency selective, fast or slow? Is the inter-symbol interference (ISI) problem encountered in ...
0
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1answer
255 views

Recursive Least Square Adaptive Linear Equalizer

For the adaptive filter to work properly, a desired signal d(n) needs to be provided. The output from the equalizer y(n) is subtracted from d(n) to produce an error signal, which is used to adjust the ...
0
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1answer
319 views

Design of FIR Filters with Arbitrary Magnitude and Phase Responses

I found many information in this thesis "Algorithms for the Constrained Design of Digital Filters with Arbitrary Magnitude and Phase Responses",i want to understand it. This question is a ...
1
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1answer
119 views

Sequential Non Linear Least Squares Problem

I have the the following non-linear function, $$s(x;A_k,\mu_k,\sigma_k)=\sum_{k=1}^2 A_k \exp\left(\frac{-(x-\mu_k)^2}{\sigma_k^2}\right)$$ with unknown (but deterministic) parameters $A_k,\mu_k,\...
1
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3answers
166 views

Complex Least Squares Approximation

In the case of frequency domain FIR filter design, the error function given by : $$E(\omega)=H(e^{j\omega})-D(e^{j\omega}) \tag{1}$$ is a linear function with respect to the unknown filter ...
0
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1answer
65 views

Why Isn't the ML Estimator (MLE) in MIMO Spatial Multiplexing Obtained by the Least Squares Solution?

In the simplest scenario of MIMO spatial multiplexing: $$\mathbf{y} = H\mathbf{s} + \mathbf{n}$$ where: $\mathbf{s}=[s_0,s_1,...s_{M-1}] \\\mathbf{y}=[y_0,y_1,...y_{N-1}]$ $\mathbf{n}=[n_0,n_1,......
1
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2answers
62 views

What Is the Definition of Linear Predictive Coefficients When the Optimal Value Aren't Unique?

Linear predictive coefficients of signal y are defined as the best $k$ coefficients $a_i, i = 1, \ldots, k$, that will approximate $y_n$ by $-\sum_{i=1}^k{a_iy_{n-i}}$. (Best approximation is that ...
0
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2answers
491 views

Why Is Non Linear Least Squares Method from MATLAB and Alglib Gives Different Results on the Same Data?

i'm trying to rewrite my Matalab prototype for some DSP to C++ and encountering a displeasing problem. I'm trying to fit data to a function $y = a * (\pi / 2 + arctg(b * x))$. In Matlab it works well ...
2
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2answers
232 views

Finding the Best Gaussian Smoothing Kernel to Minimize the Discrepancy Between Two Images

Suppose we have two grayscale images, $A$ and $B$. $A$ and $B$ very strongly resemble each other, such that the mean of the absolute difference $\lvert A - B\rvert$ is fairly small. Suppose further ...
0
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2answers
147 views

Solving LASSO ($ {L}_{1} $ Regularized Least Squares) with Gradient Descent

To the best of my knowledge, state of the art methods for optimizing the LASSO objective function include the LARS algorithm and proximal gradient methods. I was wondering however, if the LASSO ...
3
votes
1answer
2k views

Python: Least Squares Support Vector Machine (LS-SVM)

I'm looking for a Python package for a LS-SVM or a way to tune a normal SVM from scikit-learn to a Least-Squares Support Vector Machine for a classification problem. The goal of a SVM is to maximize ...
1
vote
1answer
190 views

Obtaining Correct (Least Squares Sense) Affine Transform Parameters Between Two Images

I have two images that I want to compute the affine motion model parameters. The model that I use is $$x' = a_1x+a_2y+a_3$$ $$y' = a_4x+a_5y+a_6$$ To calculate those 6 parameters, I picked 6 points (...
1
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2answers
454 views

Least Squares Fitting to Inverse Exponential Function

I have a time series of measurements that resembles the shape of an exponential function. The samples are a bit noisy and sometimes there is a weak sine like ripple signal ontop of it. Simplified the ...
0
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1answer
110 views

Received Signal Error vs. BER

It is my understanding that the least squares algorithm (e.g., in equalization) minimizes the received signal error. However, minimizing the received signal error does not necessarily equate to ...
1
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1answer
283 views

Least Squares Linear Phase FIR Filter Design

In explication ''the geometric interpretation of least squares'' Typically, the number of frequency constraints is much greater than the number of design variables (filter coefficients). In these ...
1
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1answer
173 views

RLS Algorithm (Memoryless)

I have been studying the adaptive filters lately and now when I am at RLS (Recursive Least Squar) Algorithm I came across the term used in the weighting function of the RLS called forgetting factor ($\...
-1
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1answer
136 views

Properties of Optimization Techniques in Filter Design

I have this design: Can you tell me about the type of filter and the algorithm just viewing this design, or should there be other information?
3
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0answers
242 views

Least Squares Approximation for FIR Filter Design

Following this paper , I am trying to make a least-squares algorithm in MATLAB, but for type I (I know about firls()). ...
2
votes
1answer
352 views

How to Use the DFT (FFT) to Solve a Least Squares Regularization Problem (Inverse Problem)?

Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively. The blur image $B$ is obtained as follows $$B = X * K$$ I want to solve the following general regularization problem $$...
4
votes
1answer
288 views

Direct Correlation (DC) Time Delay Estimation: Variance Keeps Decreasing for Increasing SNR?

I'm trying to reproduce the results from this paper "Discrete time techniques for Time Delay Estimation" doi:10.1109/78.193195, for both the correlation and Least Squares. I've generated a random (...
1
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0answers
83 views

Solve for Transfer Function Coefficients Embedded in a Non Linear System

Given a complex input signal $x$ and real input signal $v$, a 4th order (for simplicity) transfer function $H(z)$ is first applied to $v$ to obtain $w$, which in the time domain is represented by the ...
0
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1answer
299 views

Estimate a Transfer Function from ARX Models vs. ARIMAX?

There is diffrent models which can be used to create a dynamical model by using least squares. Those models are following: ARX ARMAX ARIMAX OE BJ But if my goal with creating a dynamical model is to ...
0
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1answer
354 views

Difference between Leaking Factor and Forgetting Factor

I am using a Recursive least square adaptive filter to process electromyography signals and it is working decently so far. I decided to implement an LMS adaptive filter as a noise cancellation, so ...
1
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0answers
37 views

Digital Filter Design Accuracy [duplicate]

Having only dealt with digital filter scarcely, the question dawned to me when I used the firls function in matlab to design an equalizer with a certain gain response. In general, can we prescribe ...
4
votes
6answers
382 views

The Least Norm Solution of Under Determined Linear System

Suppose I have a matrix $$A= \begin{pmatrix} 1 & 0 & 1 & 0\\ 0 & 1 & 1& 0\\ \end{pmatrix} $$ where the variables are channel information like assume $X_1$, $X_2$, $X_3$ ...
0
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1answer
872 views

Maximum Likelihood Estimator (MLE), MMSE and LS - Are All of Them Regressor, Estimator and Predictor?

Can all three criteria ML, MMSE, and LS be called regressor, estimator, and predictor ? If not, an intuitive explanation of why they can't be would be good.
0
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1answer
67 views

$ \frac{1}{f^2} $ Weighting for Least Squares FIR

I am currently modifying the firls.m from Octave to allow all types of FIRs, differentiators, and Hilbert transformers, while taking a peak at Matlab's. I see there ...
0
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1answer
126 views

Least Squares FIR for Type II

Following this paper (see the Matlab example at the end), I am trying to make a least-squares algorithm in Octave, but for type II (I know about firls). For type I ...
0
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2answers
364 views

How to Add Group Delay?

I was confused about the value of group delay, I am not sure whether my opinion is correct. For example, if I want to add a group delay of $0.25$ time units to a zero-phase signal, does it mean that I ...
1
vote
2answers
116 views

MATLAB: Implementing Least Squares Estimator for a Given Model

The formula to estimate $\mathbf{h}$ is then $$\hat{\mathbf{h}} = (X^T X)^{-1} X^T \vec{y}\tag{2}$$ I think this can be implemented in Matlab using ...
0
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1answer
138 views

How to Apply Least Squares Estimation for Sparse Coefficient Estimation?

The model is expressed as, $$y(n) = \sum_{i=0}^{p-1} r(i) x(n-i) + v(n) \tag{1}$$ where $\mathbf{r} = [r_1,r_2,\ldots,r_p]^T$ is the sparse channel coefficients of length $p$, $\mathbf{x} = [x_1,x_2,....
4
votes
1answer
616 views

What Is the Difference between RLS, LMS and Wiener Filter? When Is One Preferred Over Another?

I'm dealing with a channel equalization problem where the channel is modeled as a WSS process. I understand LMS utilities a Wiener-like approach, ie it converges to the optimal (wiener) solution. I ...
21
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3answers
4k views

FIR Filter Design: Window vs Parks McClellan and Least Squares

Are there any advantages to use a window approach over Parks-McClellan (further abbreviated here as PMcC) or Least Squares algorithms for FIR filter design of a low pass filter? Assume with today's ...
7
votes
2answers
916 views

Zero Phase Filter: Determining Initial Conditions for Forward Backward Filtering

Is anybody familiar with Gustafson's algorithm for minimizing transients in forward backward filtering [1]? I'm trying to implement it and my first guess was to check Matlab's filtfilt.m, since they ...