Model-This.com » Least Squares http://www.model-this.com Model What!? Model-This! Sat, 31 Jan 2009 01:53:11 +0000 en hourly 1 http://wordpress.org/?v=3.0 Least Squares Intro http://www.model-this.com/archives/5 http://www.model-this.com/archives/5#comments Fri, 23 Nov 2007 03:55:52 +0000 admin http://www.model-this.com/?p=5 There are many ways to approach modeling data and the one I am going to present here I was taught at ETSU in a class called, at the time, Advanced Surveying Mathematics. It is rooted in the realm of Linear Algebra and Calculus and attempts to model data with constraint equations and the minimizing of residuals.

 

This method uses two matrices to store and model data. The first being matrix J. Matrix J contains one row for each measurement and one column for each unknown variable. Each element contains the derivative with respect to the variable in the column it resides. The second matrix, is matrix k, it contains the residual of that measurement, or the value that the measurement should be minus the calculated value of that measurement.

 Least Squares Solve Block

Matrix J and K are applied in this equation which yields an update to the variables and the process is repeated.

 

  

Pardon this simplistic explanation, I am not a mathematician.

  

I have successfully built models of lines, circles, polynomials, triangulations, trilateralizations and traverses among other things. It is my hope to post examples and maybe even some code snippets in the coming days. 

   

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