1. Tier 2:
Case Studies
If you need narration for this, you’re in the wrong profession.

2. Case Studies Table of Contents Chapter 1 Introduction
Useful Computer Tools for Data Reconciliation
Chapter 2 Case Study #1
Steady-State Nonlinear DR and Detection of Gross Errors through Analysis
Chapter 3 Case Study #2
A Gross Error Detection Problem Using Observability and Redundancy Analysis
Chapter 4 Case Study #3
An Unsteady-State Problem
If you need narration for this, you’re in the wrong profession.

3. Useful Computer Tools for Data Reconciliation
Introduction:
Useful Computer Tools for Data Reconciliation

4. Jumping Jiminy Cricket!
Introduction
Jumping Jiminy Cricket!
Excel and
MATLAB!?
This section (Tier 2) will focus on using two widespread software programs, Excel and MATLAB, to solve 3 different case studies in data reconciliation.

5. Introduction Matrix Algebra Data Reconciliation MATLAB EXCEL
As seen in Tier 1, data reconciliation involves using matrix algebra in order to reach a solution. With MATLAB, this is not a problem, as the software is designed for this purpose. However, with Excel, for some operations such as QR Factorization, you will need to download additional software.
MATLAB
EXCEL

6. Introduction Some useful syntax in MATLAB: A = AB AT A-1
QR factorization of A
QR factorization with permutation
A = [ ; ; ]
A*B A’
inv(A)
[Q,R] = qr(A)
Shown here is some useful syntax for data reconciliation in MATLAB, including matrix notation, multiplication, transpose, inverse, and QR factorization.
[Q,R,E] = qr(A)

7. Introduction Some useful syntax in Excel: 1 Suppose A = (cells A1:B2)
Suppose A = (cells A1:B2)
B = (cells D1:E2) 1
And here is the corresponding syntax for Excel. Since Excel is a cell-based format, all operations must be performed using arrays of cells. There is no syntax here for QR factorization, but more on that later.
Then AB AT
A-1
MMULT(A1:B2, D1:E2)
TRANSPOSE(A1:B2)
MINVERSE(A1:B2)

8. Introduction A (2x2), B (2x2) AB = C C (2x2)
In order to calculate C and place it in cells G1:H2:
Highlight cells G1:H2
Type “= MMULT(A1:B2, D1:E2)”
Press Control, Shift and Enter simultaneously
It should be noted that in order to assign values to an array in Excel, Control, Shift, and Enter must be pressed simultaneously after the desired mathematical operation has been entered in. For example, if it is desired to calculate AB=C, this will result in a 2 by 2 matrix. Therefore, an array of 4 cells must be highlighted and equated to AB in order to obtain the whole solution.