Adjustment Computations Adjustment Computations: Spatial Data Analysis

CHAPTER 17

GNSS Baseline Processing


Conversions between Geodetic and Geocentric Coordinates

GNSS Baseline Vector Processing

As discussed in Chapter 17 of Adjustment Computations several methods can be used to check GPS baselines before a network is processed. This worksheet explores some of these methods.

Length of Sessions

Static survey methods are the most precise form of GNSS surveys. These methods can be used for baselines of any length. However, rapid static survey methods can be used for shorter baselines typically found in surveys. The maximum length of a baseline for a rapid static survey is dependent on ionospheric conditions. Typically, the maximum length is between 10 km to 20 km. Beyond these distances, a static survey should always be performed. No matter the type of survey used, session lengths should be long enough to ensure good results. While the appropriate length of a session is dependent on several factors including number of visible satellites, ionospheric conditions, type of receiver, processing software, and so on, Table 17-1 recommends session lengths as a guide for both dual- and single-frequency receivers using both static and rapid static methods. Due to ionospheric refraction, single frequency receivers should only be used on baselines that are less than 20 km in length. The following example demonstrates the use of this table to determine minimum recommended session lengths for various baseline lengths.

The time interval between observations in a GNSS survey is known as the epoch rate. Rapid static surveys typically collect data every 5 seconds. The epoch rate for static surveys is dependent on the length of the session. For shorter sessions, a 15-sec epoch rate is typically used. For sessions over 2 hours in length, the epoch rate is generally decreased to 30 seconds or more. Typically the longer the session, the slower the epoch rate.

Table 17.1

Method of survey Single Frequency Dual Frequency

Static

Rapid Static

Example 1

Using a dual-frequency receiver, what is the recommended session length for a baseline that is 32 km in length? What is the recommended epoch rate?


Since the baseline is greater than 20 km, a static survey should be used.

Example 2

Using a singlel-frequency receiver, what is the recommended session length for a baseline that is 6 km in length? What is the recommended epoch rate?


Example 3

Using a single-frequency receiver, what is the recommended session length for a baseline that is 13 km in length? What is it for a dual-frequency receiver?


Part 1

Part 2

Nontrivial baselines

When using more than two GNSS receivers in a survey, trivial baselines will be computed. That is, baselines whose values are dependent on other baselines observed during the session will be computed. An equivalent example of this would be observing all the angles about a point except for the last. The last angle can be computed as 360° - (sum of the observed angles). However when this is done, the last angle is mathematically dependent on the other observed angles. If the last angle is independently observed in the field, a true horizon closure can be computed, and angular misclosure be determined. This same thing happens with GPS receivers. There are only n - 1 nontrivial baselines in any observing session where n is the number of receivers. Thus when using four receivers, six baselines will be computed by the software. However only three of these six are mathematically independent. The other three baselines are mathematically determined from the three nontrivial lines. Which baselines a surveyor calls trivial and/or nontrivial is a matter of choice. A basic rule of thumb is that no triangle should ever be formed in a single observation session when selecting baselines. A triangle in a single session always represents one trivial baseline. The following example demonstrates the computation of nontrivial baselines for various numbers of receivers. Simply change the number of receivers to see the number of nontrivial baselines.

Analysis of Baseline Observations

Fixed Baselines

Baselines between fixed control points are measured to verify the accuracy of both the GNSS measurement system and the control being fixed. If large discrepancies do occur, then the source of the control should be determined to see if it meets the project standards. If the control is determined to be valid, then the hardware and processing software should be checked.

Each XYZ component of the observed, fixed baseline is compared against the length of the baseline. The results of this comparison is generally expressed in parts-per-million (ppm). This process is demonstrated below using the example in Section 17.7 of the book.

Control station coordinates

Observed baseline components

Computed baseline components

Parts-per-million

Analysis of Repeat Baselines

Repeat baselines are observed to check the consistency of the observations and field procedures. For example, if the tripod is out of adjustment, this problem may be observed when a baseline is occupied a second time. Thus repeat baselines should be performed with independent setups. The results of the checks is expressed in terms of parts-per-million, where each XYZ component is compared against the length of the baseline.

Parts-per-million

Loop Closures

Similiar to leveling, GNSS loops can be checked for closure by checking each XYZ component of the loop. Each component should sum to zero for each loop. The loop misclosure is typically expressed in terms of the parts-per-million where the linear misclosure is compared against the overall loop length. The example below is taken from Section 17.7.3 of the book.

Function to compute perimeter distance around loop.

Function to compute misclosure of each XYZ component. X: c = 0, Y: c = 1, Z: c =2.


Section 17.8 - Least Squares Adjustment of GNSS Networks

In this section, the least squares adjustment of GNSS baseline vectors is explored. This section reads the data in Table 17.1 of Adjustment Computations from the file "C17.txt". It then parses the data into individual matrices solves the system of matrices using the least squares procedures outlined in Chapter 17.

Parse data

Parse control station data

Parse unknown station ids

findsta is used to match the station identifier to its storage location in the sta input table or add it to the table.

Parse GNSS baseline vector data

Function to build A, W, and L matrices

Least squares solution

Store results in station matrix

Compute statistics and adjusted observations

Adjusted observations

Adjusted observations

Residuals

Standard Deviations for baseline vector components

Compute baseline vector parts-per-million

Convert XYZ geocentric coordinates to geodetic coordinates using functions from XYZ.mcd

 

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