14
2016 Chapter Officers President: Will Paul Vice President: Rich Fultz Secretary: Rich Brown Treasurer: Warren Smith Chapter Director: Keith Spencer Chapter Director: Kevin Genasci Alt. Chapter Dir: Warren Smith Alt. Chapter Dir: Rich Fultz 2016 Chapter Committees By-Laws Committee: Keith Spencer (Chairman) Construction Committee: Open (Chairman) Education Committee: Kevin Genasci (Chairman) Membership Committee: Rich Brown (Chairman) Monument Preservation Committee: Mike Quartaroli (Chairman) Newsletter: Rich Brown (Editor) Professional Practices Committee: Mike Quartaroli (Chairman) San Joaquin County Liaison Committee: Kevin Genasci (Chairman) Stanislaus County Liaison Committee: Rich Fultz (Chairman) Website: Keith Spencer (Web Master) 2016 Chapter Programs Adopt-A-Road: Rich Brown (Coordinator) Boy Scout Merit Badge: Zachary Wong (Coordinator) TrigStar: Bill Koch (Coordinator) Workshops: Rich Brown (Coordinator) September 2016 Volume 6, Issue 5 THE PRISM Date: September 28, 2016 Time: 6:00 p.m. Location: Perko’s @ 901 North Carpenter Road, Modesto Speaker: Dan Schwartz, California DWR Topic: DWR Land Records Date: October 26, 2016 Time: 6:00 p.m. Location: Perko’s @ 901 North Carpenter Road, Modesto Speaker: Justin Height, Praxis Topic: Recent Work of the ACEC Up Coming Meetings! Announcements STATE CLSA PRESIDENT-ELECT UP FOR ELECTION With the resignation of State CLSA Secretary earlier this year, next year’s President- Elect will be decided by membership election. Joe Pedilla will be running against Ron Nelms, who was elected by the Executive Board to replace Jeff Steffans as Secretary, for 2017 President-Elect. ADOPT-A-ROAD CLEANUP DAY The next Adopt-a-Road Cleanup Day is scheduled for September 17th. We are in need of volunteers to help. More information please contact Rich Brown 2017 FRESNO GEOMATICS CONFERENCE ANNOUNCED The 2017 California State University, Fresno Geomatics Conference has been sched- uled for January 27th & 28th. It will be held at the Double Tree Hotel in Downtown Fresno. 2016-17 NCEES PRESIDENT-ELECT ANNOUNCED Former Board member Pat Tami, P.L.S., was installed as 2016–2017 President-Elect at the NCEES Annual Meeting last week. In the 96 year history of NCEES, Mr. Tami will be only the 4th representative from California to serve as President and only the 4th licensed Land Surveyor! NOMINATIONS FOR 2016 COUNTY SURVEYOR OF THE YEAR The nominations for CEAC 2016 County Surveyor of the Year are due October 3rd. For each of the last 6 years, CEAC (the County Engineer’s Association of California) has honored a County Surveyor for their contributions to the profession and/or achievements within the profes- sion. However, County Surveyors rarely get a chance to see what their fellow county surveyors are doing other than the interactions that occur during CEAC or other meetings. For information, please contact Rick Marshall, Napa County Surveyor, at [email protected] or (707) 259-8381. Central Valley Chapter - California Land Surveyors Association www.californiacentralvalleysurveyors.org Central Valley Chapter Table of Contents Page 2 Classes, Training & Education Page 2 Editor’s Message Page 3 Education Page 6 Safety Page 8 Just For Laughs Page 9 Classifieds Page 10 Monument Obituaries Page 10 Pictures of the Issue

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Page 1: THE PRISMcaliforniacentralvalleysurveyors.org/.../CVC-The-Prism_2016-09.pdf · Professional Practices Committee: Mike Quartaroli (Chairman) ... PAGE 6 THE PRISM Safety, safety, safety

2016 Chapter Officers

President: Will Paul

Vice President: Rich Fultz

Secretary: Rich Brown

Treasurer: Warren Smith

Chapter Director: Keith Spencer

Chapter Director: Kevin Genasci

Alt. Chapter Dir: Warren Smith

Alt. Chapter Dir: Rich Fultz

2016 Chapter Committees

By-Laws Committee: Keith Spencer (Chairman)

Construction Committee: Open (Chairman)

Education Committee: Kevin Genasci (Chairman)

Membership Committee: Rich Brown (Chairman)

Monument Preservation Committee: Mike Quartaroli (Chairman)

Newsletter: Rich Brown (Editor)

Professional Practices Committee: Mike Quartaroli (Chairman)

San Joaquin County Liaison Committee: Kevin Genasci (Chairman)

Stanislaus County Liaison Committee: Rich Fultz (Chairman)

Website: Keith Spencer (Web Master)

2016 Chapter Programs

Adopt-A-Road: Rich Brown (Coordinator)

Boy Scout Merit Badge: Zachary Wong (Coordinator)

TrigStar: Bill Koch (Coordinator)

Workshops: Rich Brown (Coordinator)

September 2016 Volume 6, Issue 5

THE PRISM Date: September 28, 2016

Time: 6:00 p.m.

Location: Perko’s @ 901 North Carpenter Road, Modesto

Speaker: Dan Schwartz, California DWR

Topic: DWR Land Records 

 

Date: October 26, 2016

Time: 6:00 p.m.

Location: Perko’s @ 901 North Carpenter Road, Modesto

Speaker: Justin Height, Praxis

Topic: Recent Work of the ACEC

Up Coming

Meetings!

Announcements STATE CLSA PRESIDENT-ELECT UP FOR ELECTION With the resignation of State CLSA Secretary earlier this year, next year’s President-Elect will be decided by membership election. Joe Pedilla will be running against Ron Nelms, who was elected by the Executive Board to replace Jeff Steffans as Secretary, for 2017 President-Elect. ADOPT-A-ROAD CLEANUP DAY The next Adopt-a-Road Cleanup Day is scheduled for September 17th. We are in need of volunteers to help. More information please contact Rich Brown 2017 FRESNO GEOMATICS CONFERENCE ANNOUNCED The 2017 California State University, Fresno Geomatics Conference has been sched-uled for January 27th & 28th. It will be held at the Double Tree Hotel in Downtown Fresno. 2016-17 NCEES PRESIDENT-ELECT ANNOUNCED Former Board member Pat Tami, P.L.S., was installed as 2016–2017 President-Elect at the NCEES Annual Meeting last week. In the 96 year history of NCEES, Mr. Tami will be only the 4th representative from California to serve as President and only the 4th licensed Land Surveyor! NOMINATIONS FOR 2016 COUNTY SURVEYOR OF THE YEAR The nominations for CEAC 2016 County Surveyor of the Year are due October 3rd. For each of the last 6 years, CEAC (the County Engineer’s Association of California) has honored a County Surveyor for their contributions to the profession and/or achievements within the profes-sion. However, County Surveyors rarely get a chance to see what their fellow county surveyors are doing other than the interactions that occur during CEAC or other meetings.

For information, please contact Rick Marshall, Napa County Surveyor, at [email protected] or (707) 259-8381.

Central Val ley Chapter - Cal i fornia Land Surveyors Association www.cal i forniacentralval leysurveyors .org

Central Val ley Chapter

Table of Contents

Page 2 Classes, Training & Education

Page 2 Editor’s Message

Page 3 Education

Page 6 Safety

Page 8 Just For Laughs

Page 9 Classifieds

Page 10 Monument Obituaries

Page 10 Pictures of the Issue

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PAGE 2 THE PRISM

Editor’s Message

If you have information about a training or class, please submit to:[email protected]

If you would like to comment on this topic or suggest another, please submit it to:[email protected]

With the economy continuing to improve, construction projects in many areas are going full force. That is great for the communities and the work force, but bad for existing survey monuments. Though improving, monument preservation is still under attack by construction companies that are trying to “save a buck”, and local government agencies that just don’t seem to care. 8771 of the Busi-ness and Professions Code requires to protect and/or replace existing monuments. To me, that is re-ally simple. If you are working in an area that has any Monumentation, PROTECT IT! They may think they are saving money, but it actually will cost the land owners and the Surveying Profession a lot more in the future. When a corner is taken out by construction, or any other means, and not re-placed will cause any work that needs to be done in the area a lot more expensive. Instead of being able to go to the nearest corner, the surveyor might need to go several sections area just to tie the

project out. Think about it. You may save a few dollars taking short cuts, but look at the damage you will be causing. Then ask yourselves this, Is it really worth it?

On a good note, there are several Surveyors that have gone above and beyond their duty to protect and save our treasured monuments. Thank you to Rich Fultz, City Surveyor for Turlock, Ron Nelms, Chairman of the CLSA State Monument Con-servation Committee, and Mike Quartaroli, author of Monument Obituaries. You gentlemen are a great example for the current and new generation of surveyors.

Classes, Training, and Continuing Education CAD Masters - AutoCAD Level I (3-Day Course) Sept 12-15, 2016, Sacramento Sept 19-21, 2016 Walnut Creek Oct 11-13, 2016, Sacramento Oct 24-26, 2016 Walnut Creek Nov 7-9, 2016, Sacramento Register here

CAD Masters - AutoCAD Level II (2-Day Course) Sept 15-16, 2016 Sacramento Sept 29-30, 2016 Walnut Creek Oct 24-25, 2016 Sacramento Nov 14-15, 2016 Walnut Creek Register here

CAD Masters - AutoCAD Level III (1-Day Course) Oct 14, 2016 Sacramento Register here

CAD Masters - AutoCAD Civil 3D Intro (3-Day Course) Sept 6-8, 2016, Sacramento Sept 20-22, 2016, Walnut Creek Oct 3-5, 2016, Sacramento Oct 17-19, 2016, Walnut Creek Oct 31-2, 2016, Sacramento Nov 14-16, 2016, Walnut Creek Register here

CAD Masters - AutoCAD Civil 3D Adv. (2-Day Course) Oct 5-6, 2016, Walnut Creek Oct 26-27, Sacramento Register here

CLSA - The End of Coordinates and Elevations As We Know It!

Sept 14, 2016, Webinar Register here

CalPoly Pomona 2016 CLSA Conference October 6-7, 2016 More details to follow

Fresno State 2017 Geomatics Engineering Conference January 27-28, 2017, Double Tree Hotel, Fresno

2017 National Geodetic Survey Geospatial Summit April 24-25, 2017, Silver Spring, Maryland

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Education What is a Least Squares Adjustment Anyway? By Charles D. Ghilani, Ph.D.

Continued on page 12

Up to now I have talked about a least squares adjustment as if everyone knows what it involves. In this article, I discuss what a least squares adjustment is and what makes it so valuable in adjusting observational data.

Least squares adjustments have their roots in the normal distribution, which is pictured in Figure 1. The equation for the normal distribution curve is Equation (1) where: • v represents the residual of the observations and is plotted on the x axis,

• y the probability of the residual occurring, • σ2 the variance of the observations, and • e the exponential number, which is the transcendental number 2.718281828.... To maximize the probability of this function, the sum of the weighted, squared residuals (∑wv2 ) must be minimized.

This process can be done by writing equations for every observation in terms of their unknown parameters. For a hori-zontal survey this would mean a system of equations representing the angles, azimuths, and distances, which are written in terms of their unknown station coordinates (n, e).

However, each of these equations is nonlinear. To solve a system of nonlinear equations, they must first be linearized using a first-order Taylor series expansion. For example, the familiar nonlinear distance equation with its residual is Equa-tion (2) where (n, e) are the northing and easting coordinates of the endpoint stations i and j for the distance observation lij with a residual error of vl.

The linearized equation for the distance equation is Equation (3) where:

• (dn, de) are corrections to approximate values for the unknown parameters (n, e), • zero subscripts indicate values determined using the approximate coordinate values, • K is the difference between the observed and computed length of the distance where the computed length IJ is deter-

mined from the approximate coordinate values, and

• v is the residual error. In the solution of these equations, the residual v is dropped,

and the solution is iterated applying the corrections dn and de to the approximate unknown parameters n and e until the correc-tions to the corrected coordinates become negligibly small (in essence, until the coordinate values for the stations are resolved to less than the accuracy of the survey, which is typically less than 0.005 ft or 0.0005 mm). Linearized equations are written similarly for the azimuth and angle observations.

Performing the Adjustment

To minimize the sum of the weighted, squared residuals, that is, to perform a least squares adjustment, all of the observa-tion equations are written in matrix form. However, as we all know from our Algebra I class in high school, they could be solved by hand if it weren’t so time-consuming and hard. Thus, it was the availability of computers and their ability to be pro-grammed to solve large systems of equations that made the least squares process available to us.

(The derivation and application of the least squares method occurred at the end of the 18th century and is attributed to Karl Gauss while he was a graduate student. Thus the method has been available a long time, but it wasn’t until the advent of the micro-computer that it became available to most surveyors.)

By forming the matrices as shown in Equation (4) and then solving this system of equations, the resultant solution yields the minimized sum of the squared residuals. This statement is shown in my book Adjustment Computations: Spatial Data Anal-ysis.

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Safety, safety, safety. With advances in technology and the tightening of purse strings, it can be tempting, at times, for companies to adopt one man crews. However, this practice can lead to some serious safety issues. While one man crews can be easily justifiable in certain environments, it is truly dangerous to operate a one man crew when working on roadways. The One Man Crew and the Distracted Driver The biggest safety problem associated with operating a one man crew may be the distracted driving epidemic current-ly happening nationwide. Even with laws being enacted against using cell phones while driving, there are people that continue to use their phones while operating a moving vehicle. How many times have you been sitting at a light and continued waiting after the light turned green because the person in front of you was checking their phone? It hap-pens all the time. "Motorists engage in secondary behavior during more than half of their time spent driving--an action that is a factor in more than one million national car crashes and 16% of fatal accidents annually. And texting is the number one dis-tracted driving activity by a long-shot. With technology at drivers' fingertips, drivers are becoming more and more tempted to send and read quick text messages that they by-and-large assume to be harmless. The truth is, texting while driving takes a driver's eyes off the road for an average of 4.6 seconds and increases the chances of a crash by 23 percent. To put that into perspective, if a vehicle is traveling at 55mph, the average driver doesn't look at the road for about the length of an entire football field while sending a text." --Kiernan Hopkins: distracteddriveraccidents.com So, a driver is looking down at their phone wheeling around town on the streets that they have driven for years. They assume they know what is around every corner and where every straight away is located. What they do not count on, however, is that a land surveyor might be in the middle of the road with his head down looking at a data collector. Maybe not even looking at a data collector, but looking down at a monument or in a manhole. Sometimes making eye contact with every driver is impossible and, even when a surveyor attempts to make eye contact, the approaching driver might have their head down looking at their cell phone. In that case, the surveyor may have a chance to move out of the way of potential calamity. But when both the driver and the surveyor are looking down, it is a recipe for disaster. This is why it is imperative that the survey profession begin using two man crews whenever working in the street. Cell Phones and Drunk Drivers In preparing to write this article, I found several pieces of research detailing the similarities between drunk driving and cell phone use while driving. The first research I found was from the following site detailing the similarities be-tween the two: http://goo.gl/yZMEfQ It is important to keep in mind that this research was done in 2006, long before the advent of our modern smart phones, which can be even more of a distraction with their ease of access to the internet, social media, email and other applications. As the charts above indicate, drunk drivers were applying greater force to their vehicles' brakes, when necessary, as compared to cell phone users (slower to apply their brakes). Based on the research conducted, cell phone drivers showed delayed responses to events while driving and were more likely to be involved in an accident than drunk driv-ers. This is a disturbing fact, especially considering the fact that there are far more people driving while using a cell phone than people driving while drunk during the day, when a surveyor is more likely to be in the street. This re-search also indicated that drivers using cell phones had slower reaction times and were involved in more accidents than drunk drivers. As I indicated previously, this research was performed in 2006 when cell phones were primarily used for phone calls and text messaging wasn't nearly as prevalent. This same 2006 study also indicated that hands-free devices were not any less dangerous than regular cell phone us-age. "Between 2005 and 2012, the number of drunk driving fatalities per person decreased 28%. In the same time period, the percentage of people observed "visibly manipulating" their phones while driving increased a staggering 650%. The

Safety One Man Crews Written by Micah Paulk

Continued on page 7

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PAGE 7 THE PRISM

number of fatalities caused by distracted driving increased 28% between 2005 and 2008 alone. In 2012, 3,328 Ameri-cans died in crashes involving a distracted driver, while 10,322 people were killed in alcohol-related crashes." As you can see from the quote above, instances of distracted driving that contribute to fatalities have increased at the same rate that drunken driving fatalities have decreased. California Fines for Using a Cell Phone While Driving While fines and other penalties for driving while using a cell phone have increased over the years, it does not appear that is has stemmed their actual usage with drivers. California fines for using a cell phone while driving are relatively low with $20 for the first offense and $50 for each subsequent offense. These fines don't do much to stem the use of cell phones while driving. California also allows for GPS usage while driving, as long as the driver does not have the cell phone in hand while doing so. Blue tooth or hands-free cell phones usage is also permitted while driving. There are also statutory loopholes stating that if you read, enter, or select a phone number or the name of a contact on your phone with the intent to (a) communicate with this person through a hands-free device, or (b) deactivate your device, you are not violating Califor-nia law. The disturbing part about these exemptions is that, even when using these functions, the driver is still distracted. An unintended consequence of these laws is that drivers will now hide their cell phones in their laps while texting and driving to avoid detection from authorities, causing their eyes to focus even further away from the road ahead. Land Surveyors Are Already In Danger In this Newsletter https://goo.gl/7yn61C, I included an article about a driver involved in a hit and run in Houston, Texas. In that case, the land surveyor wasn't even in the road, he was on the sidewalk. Unfortunately, the surveyor died from the accident and the details have not come to light about the exact cause. Nevertheless, I would not be sur-prised if a cell phone played a part in the surveyor's death. Even if a cell phone was not involved in this instance, it brings to light the fact that, had the surveyor not been working alone, he may have had warning from another party member that a recklessly driven car was approaching. In that instance, there were witnesses around that reported the event. What would happen if a surveyor was working alone, without bystanders nearby, and was hit by a car and then the driver decided to run? This is another reason why it is so important to have a two party crew whenever working in streets. Another instance involved a lone surveyor in Orlando kneeling to mark a spot on the street. The surveyor was subse-quently hit by a utility truck. http://goo.gl/Mc3wd5 The Majority of Fatal Work Injuries Were Caused By Transportation Incidents. In a news release from February 2015, the Bureau of Labor Statistics ("BLS") released data on fatal work injuries in California for 2013. By far, the most fatalities were caused by "transportation incidents". The 2013 number increased by 10% from 2012. Transportation accidents were the most frequent fatal events in the United States in 2013. Fortunately, California is below the national trend. Death is not the only thing to be considered. Injuries, from transportation incidents, have steadily risen over the past three (3) years as reported by the BLS. Nationwide, there have been: • 41,140 injuries in 2011 • 42,610 in 2012 • 44,410 in 2013 Even though nonfatal, these cases undoubtedly led to loss time and OSHA violations the damage done to the worker cannot be discounted. Time away from work can lead to financial stress and, certainly, the health of the worker after the incident could lead to them being unable to return to work at all.

One Man Crews, cont. from page 6

Continued on page 11

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Just For Laughs KENKEN Solution to last puzzle. Directions: Each row and each column must con-tain the numbers 1 through 6 without repeating. The numbers within the heavily outlined boxes, called cages, must combine using the given opera-tion (In any order) to produce the target numbers in the top-left corners. Freebies: Fill in the single-box cages with the number in the top-left corner.

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Have equipment to sell? Looking for a great deal?

Check out the CLSA Forums!

PAGE 9 THE PRISM

Classifieds Mid Valley Engineers seeks Licensed Land Surveyor or L.S.I.T. Full Service Engineering & Surveying firm located in California's Central Valley, is looking for a Qualified Licensed Land Surveyor (California required, Nevada also preferred) or is an LSIT looking to become a Licensed Land Surveyor. Applicant must have expertise in directing and performing all aspects of acquiring, processing, analyzing and compiling data to prepare maps, documents and deliverables for boundary surveys, topographic surveys, control and design sur-veys, subdivisions, records of survey, ALTA/ACSM surveys, lot-line adjustments/easement acquisitions, and be able to perform outside field survey work. Email your resume to [email protected] along with a list of 5 - 7 Business References. O’Dell Engineering has Openings O’Dell Engineering has openings for several survey positions in their Modesto, Fresno, and Pleasanton Offices. Go to: www.odellengineering.com/profile/employment/ for more information, online application, and submittal instructions. Surveying Instructor needed ASAP Evergreen Valley College has an imme-diate need for a surveying instructor. If the position is not filled in the next few days the surveying program will be cancelled. The minimum qualifications are: any Bachelor's degree and two years of professional experience, or any Associate's Degree AND six years of professional experience. The open classes, with schedules, can be viewed here: EVC Surveying Classes In order to apply, first... Go to www.sjeccd.edu Click on the "Employment" tab at the top right of the page Follow the https://sjeccd.hiretouch.com/ link on the "How to Apply" section. You will need to create an account, then follow all instructions The potential candidate should also send an email to [email protected] 

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If you have a historic or interesting photo you would like to see in a future edition of The Prism, please submit to: [email protected]

PAGE 10 THE PRISM

Monument Obituary A Land Surveying Dilemma By Mike Quartaroli, L.S.

Mike Quartaroli is on location in Canada and will be back next edition with more reports of Survey Monuments whose lives have been cut short.

Picture of the Issue

Pictured: Monument Preservation,Alberta Providence, Canada “Seven Year Imprisonment For Removal” Picture provided by Mike Quartaroli

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One Man Crews, cont. from page 7

Reprinted with Permission from The American Surveyor Magazine,

Vol. 13, No. 7

What Can Be Done? The most important thing to do is always be aware of your surroundings. You may have surveyed a million streets and been on the very street you are surveying plenty of times, but the behavior of drivers cannot be predicted. Dis-tracted driving can lead to very dangerous situations. Using a two man crew to warn the other members of the survey party is necessary to help abate some of the dangers presented by distracted drivers. • Effective use of radios is also necessary when working in the street. Be sure that your radios are properly charged and that all crew members are on the correct channel. • Hand signals are good but they cannot warn someone while their head is down looking at a data collector. Some-times the sounds of traffic can become background noise lulling the surveyor into a false sense of security. Remain vigilant and be aware of your surroundings at all times.

• Safety vests, cones and signs should all be used in conjunction while per-forming survey work in the roadway. It is imperative to use these safety measures, especially when working on hills, around curves or other obstacles to warn drivers of the surveyor's pres-ence in the road. • A job walk before starting each job should be conducted to identify poten-tial hazards in the areas that work will be performed. • Finding safe places to park survey vehicles and set up sites should be decided based on both safety and effec-tive usage. Considering how to safely get into and out of vehicles with equip-ment should also be a factor. • Consider the weather as well. Is there fog rolling in? Was there rain in the forecast? These factors can be ex-tremely dangerous. Update: Since publishing this article in Janu-ary, 2016, I have found three other instances of surveyors being struck and killed in roadways: • Samuel Pagano, 22, of South Wales, NY, was hit and killed by a car that crossed the center line. http://goo.gl/aN2ve4 • Russell Scott Atchinson, 58, of Mod-esto was alone and on his hands and knees over a manhole in Stanislaus, CA when he was hit by a GMC Sierra pickup. http://goo.gl/Wlw27Z • 59-year-old Enrique Diaz, was wear-ing a reflective vest and was in a striped area just on the highway which separates the inside lane from the traffic merging onto 95 when he was struck and killed. http://goo.gl/g9uOxy

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In Equation (4):

• the J is a matrix of coefficients determined from the linearized equations; that is for a distance, it is the parenthetical values in Equation (3) evaluated at some approximate coordinate values for the stations I and J;

• W a matrix of weights for each observation; • K a vector of the differences between the observed and computed values for each measurement; and • X a matrix of corrections to be applied to the approximate coordinates for the stations. Because in a horizontal adjustment the equations are nonlinear, this solution process must be iterated until the correc-

tions to the approximate coordinates become negligibly small. This is also true for a geodetic adjustment. However, the equa-tions for a differential leveling network and a GNSS baseline vector adjustment are linear and thus can be solved without iterating.

So What Is the Least Squares Method? It is simply a method where equations are written for each observation in terms of the unknown parameters. These

equations are weighted according to the precisions of the observations in order to return the errors back to their sources.

The weighted equations are then solved using Equation (4), which minimizes the sum of the weighted, squared residuals and yields the most probable solution for any set of data. It is a method of solving an over-determined system of equations that yields the most probable values for the unknown parameters. During this process all geometric constraints are satisfied.

In essence, the least squares method is nothing more than what many of us did in an algebra class when the instructor asked us to solve a system of equations for the unknown parameters x and y. Back then, we solved these equations by the process of elimination.

However, for each station, we have two unknown x and y’s. For a survey with 10 stations, we could have 20 unknowns. Thus, the process would be difficult to perform by hand as we did in algebra class, but the fact that we use matrices and com-puters does not make it any more foreign than using some other method such as the compass-rule adjustment.

It is simply a process of solving a system of equations for unknown parameters. This process results in a minimum for the sum of the weighted, squared residuals when we follow Equation (4) and the most probable solution for the given set of data.

The least squares method does not guarantee that the solution is always a good one. Just like other methods of adjust-ment, the basic principle of garbage in, garbage out still applies. However, if care is taken in collecting our observations and all systematic errors are removed from the observations, it will always yield the most-probable solution for any given set of data.

It additionally provides post-adjustment statistics such as standard deviations on the adjusted coordinates and observa-tions, as well as error ellipses for the stations that allow the user to analyze the results and determine if the results are within the tolerances of the project.

It also provides advanced statistical methods that allow the user to analyze the observations for blunders, but that is for my next series of articles.

Until then, happy surveying.

Veiw Equations and Exhibits at : http://cdn.coverstand.com/36207/321808/01558cc03e7055082438314d72c99a39555f76c2.1.pdf

Reprinted with Permission from xyHt Magazine, August 2016

Least Squares... cont. from page 3

California Land Surveyors

Association Education Foundation

Or another Charity of your choice.