# Questions tagged [least-squares]

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### Solving Sparse Model with given Dictionary Using LASSO

I was trying to solve a problem where the basis matrix contains the components of $\sin(nx)$, $\cos(nx)$, $\sinh(nx)$ and $\cosh(nx)$. Say the $n$ varies from 1 to 100. While solving the lasso linear ...
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### How to find the solution of nonlinear least square (NLS) equation for freqeuncy estimation

I am struggling to understand the theory of parametric methods for power spectral estimations of line spectra. And I want to find the solution of nonlinear least square (NLS) method for estimating ...
83 views

### numpy.linalg.lstsq underdetermined case

I would like to understand what I am doing wrong here. I am trying to perform polynomial regression by minimizing the least squares, ||Au-y||^2, where y is the given data and A is the matrix where the ...
100 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 ...
38 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 ...
107 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 ...
127 views

### System Identification with a Limited Bandwidth Input Signal and Region of Interest

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 $h$...
39 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 ...
130 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 ...
115 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). ...
61 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. ...
122 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 ...
126 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 ...
54 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 ...
537 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 ...
34 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 ...
220 views

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 ...
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### 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 ...
97 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 ...
374 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 ...
395 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 ...
130 views

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### Question About Kailath's Paper - An Innovations Approach to Least Squares Estimation Part I: Linear Filtering in Additive White Noise

I'm reading the paper at the link below and I was following it for about 2 pages until I hit a road block on the bottom of page 648 where the author says: putting together 9-11, we obtain and ...
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 ...
586 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 ...
332 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 ...
124 views

### Least Squares with Blocks / Updates

I have a continuous-time system that I want to fit via least squares. I just send $N$ digital samples $x[n]$ through the system and receive (via analog signal chain, ADC etc) $N$ digital samples $y[n]$...
287 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 ...
3k 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 ...
291 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 (...
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### 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 ...
116 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 ...