Fyp

Velocity, Bearing Estimation from GPS Measurements

BSc (Hons.) in Surveying and Geo-Informatics Department of Land Surveying and Geo-Informatics The Hong Kong Polytechnic University

Yeung Chun Yiu May 2006

Precise Velocity Estimation from GPS Measurements

Abstract Abstract of dissertation entitled: PRECISE VELOCITY ESTIMATION FROM GPS MEASUREMENT submitted by Yeung Chun Yiu for the degree of Bachelor of Science (Hons.) in Surveying and Geo-Informatics at the Hong Kong Polytechnic University in May 2006. A lot of research has been conducted on the feasibility of using GPS as a vehicle velocity meter. In particular, the precision of velocity is one of the interests. In this paper, there would be different kinds of velocity measurement techniques to evaluate the precision of GPS velocity. Investigation was performed on comparing and analyzing different velocities obtained so as to discover the best solution for deriving velocity and the suggestions for maximizing the performance of GPS. The project was performed in static and kinematic environments using both the carrier phase derived Doppler and raw receiver Doppler methods to collect the velocity raw data. Different environments for velocity measurement such as multipath and high dynamics were assessed.

2

Precise Velocity Estimation from GPS Measurements

Acknowledgements I would like to express my gratitude to my project supervisor, Dr. Wu Chen, Associate Professor of the Department of Land Surveying and Geo-Informatics, for furnishing me with valuable opinions and guidance on my work. I am also grateful to thank Mr. Sydney Cheng, teaching assistant in the department of Land Surveying and Geo-Informatics, for his useful opinions and guidance on my field works as well as data analysis. Moreover, I would like to thank my classmate CHENG Shui Lun, TAI Po Lok, Yu Tsz Kin for their assistance in the field work with me so that my burden is greatly reduced. Finally, I would like to thank to my families for their support.

3

Precise Velocity Estimation from GPS Measurements

Contents ABSTRACT……………………………………………………………...…………….. i ABKNOWLEDGEMENT…………………………………………………………... ii CONTENTS…….…………………………………………………………………..… iii LIST OF FIGURES………………………………………………………………….. iv LIST OF TABLES…………………………………………………………………..... v CHAPTER 1 INTRODUCTION 1.1 Background………………………………………………………………..... 1 1.2 Objectives…………………………………………………………….……... 1

CHAPTER 2 LITERATURE REVIEW 2.1 GPS Velocity Interpretation…………………………………………………. 2.2 Doppler’s shift in GPS……………………………………………….……..… 2.3 Carrier Phase Derived Doppler and Receiver Generated Doppler………. 2.4 Kalman Filter…………………………...…………………………………….. 2.5 Velocity Measurement Procedure………...……………………………….… 2.6 Error in GPS Velocity …………………………...……………………….….. 2.7 How to Improve GPS Velocity………………………………………….…….

CHAPTER 3 METHODOLOGY 3.1 Observations Modes for GPS Velocity…………………………………….. 3.1.1 Static Observation ………………………………...………..………. 3.1.2 Kinematic Observation……………...……………………………… 3.1.3 GPS Velocity Accuracy Assessment….……………………………. 3.2 Data Output………….………………………………………………………...

CHAPTER 4 FIELD WORKS 4.1 Site Reconnaissance…………….…………………………………………….. 4.2 Preparation before Field Works…………………………………………… 4.3 Static Observation……………………….……………………………………. 4.4 Kinematic observation……………………………………………………....

CHAPTER 5 DATA ANALYSIS 5.1 Static Observation result……….………………………….…………………. 5.2 Kinematic Observation result....………….……...…………………………... 5.2.1 Pseudorange Derived Velocity……..………………………………. 5.2.2 Kalman Filtering……………………………………………………. 5.2.2.1 Algorithm Design…………………………………………. 5.2.2.2 Result after adjustment with Kalman Filtering………....

4

Precise Velocity Estimation from GPS Measurements 5.2.3 RTK result………...…………………………………………………

CHAPTER 6 RECOMMENDATIONS AND CONCLUSION REFERENCE…………………………………………………………………………

5

Precise Velocity Estimation from GPS Measurements

List of Figures Figure 2.2.1 Doppler’s Effect………..…………………………………………………… Figure 3.2.1 Structure of a NMEA-0183 sentence……………………………………… Figure 4.1.1 Map of GPS Static observation……………………………………………. Figure 4.1.2 Map for Route of GPS Kinematic Observation (Manual)......…..……….. Figure 4.1.3 Photos for Route of GPS Kinematic Observation (Manual)...….……….. Figure 4.3.1 Resolving for Two Horizontal Velocity Vectors…………….……………. Figure 4.4.1 Route for Kinematic Observation (Manual)………...……………………. Figure 5.1.1 Speed over Ground in Static Mode (North)………..……...……………… Figure 5.1.2 Speed over Ground in Static Mode (East)………………..………...……... Figure 5.1.3 Static Velocity Data at the Beginning……...……………………………… Figure 5.2.1 Sample of NMEA 0183 Output Data……………………………………… Figure 5.2.2 Position Variation along a 100m Track using Velocity Data (Trial 1)….. Figure 5.2.3 Using Pseudorange to Generate the Position Data (Trial 1)……………... Figure 5.2.4 Position Variation along a 100m Track using Velocity Data (Trial 2)….. Figure 5.2.5 Using Pseudorange to Generate the Position Data (Trial 2)……………... Figure 5.2.6 Position Variation along a 100m Track using Velocity Data (Trial 3)….. Figure 5.2.7 Using Pseudorange to Generate the Position Data (Trial 3)……………... Figure 5.2.8 GPS Velocity (compared with pseudorange) (North) (Trial 1)………….. Figure 5.2.9 GPS Velocity (compared with pseudorange) (East) (Trial 1)……………. Figure 5.2.10 Velocity North Changes after Running up the Whole Path (Trial 1)….. Figure 5.2.11 Velocity East Changes after Running up the Whole Path (Trial 1)……. Figure 5.2.12 Pseudorange-derived Velocity (North) (Trial 1)………………………… Figure 5.2.13 Pseudorange-derived Velocity (East) (Trial 1)……………………..…… Figure 5.2.14 RTK-derived Velocity (North) (Trial 1)…………………………………. Figure 5.2.15 RTK-derived Velocity (East) (Trial 1)…………………………………... Figure 5.2.16 GPS Velocity (compared with RTK) (North) (Trial 1)…………….…… Figure 5.2.17 GPS Velocity (compared with RTK) (East) (Trial 1)…………………… …

6

Precise Velocity Estimation from GPS Measurements

List of Tables Table 3.2.1 VTG Sentence Output from Leica GPS System 500………………………. Table 3.2.2 VTG Sentence Output from Trimble DSM 212H…………………………. Table 5.1.1 Statistical Result Showing the Static Observation Result………………… Table 5.2.1 Position Shifts Generated from Velocity and Pseudorange Position Data. Table 5.2.2 Difference between RTK and GPS Velocity (North and East) in Three Trials (Mean and Standard Deviation of Total Time Elapsed)………………………...

7

Precise Velocity Estimation from GPS Measurements

Chapter 1: Introduction 1.1 Background Traditionally, measuring velocity can be done externally by speedometers. Nowadays, with the growing popularity and accuracy of the Global Positioning System (GPS), GPS is becoming one of the possible solutions to determine velocity with an accuracy of a few meters depending on the specification and methods. In this case, a number of researches have been done to achieve a cheaper and more accurate velocity measurement using GPS by adopting specific approaches and controls. To determine more precise GPS velocity, the Doppler’s frequency shift measurement is one of the approaches. This approach has been researched for a few years and their results appear that the development should attain a desirable accuracy in the future. In this situation, the GPS will soon be a major solution in precise velocity determination. 1.2 Objectives Apart from the trend of GPS velocity development, some interests are drawn on the accuracy of the velocity and its ability of accuracy achievement in stand-alone mode. Therefore, I would emphasize on two main ways of position determination, pseudorange and carrier phase position, to find the velocity with computation of time. Furthermore, based on velocity accuracy achieved, the accuracy position output from pseudorange should be raised by the adjusting with velocity. The ultimate achievement is to: -investigate how the GPS provides precise velocity by experiments and thereby proposes the potential application in navigation; -examine the factors and errors which will affect the velocity measurement; -express the accuracy on using the GPS to measure velocity as compared to the method by position determination; -state the advantages and disadvantages of using the GPS to measure velocity; -provide bearing assessment.

8

Precise Velocity Estimation from GPS Measurements

Chapter 2 Literature Review 2.1 GPS Velocity Interpretation Velocity measured by GPS is divided into three dimensions: X, Y and Z. This reflects how the GPS receiver determines the change in velocity in three dimensions. For navigation, X and Y (Northing and Easting) components are very useful which gives an account of velocity in horizontal motion. Z (Up) component is to derive the vertical velocity and motion of the receiver. The application of Z component is particularly important for hydrographic field to determine the wave motion. There is also a three dimensional velocity (3D velocity) which is equal to square root of the sum of square of three velocity components: V3D = (VX2+VY2+VZ2)1/2. This quantity reflects the total amount of velocity measured in three dimensions. 2.2 Doppler’s shift in GPS Doppler’s shift describes the relative motion between the satellite and the receiver in GPS system. When the source of wave approaches the observer, the wavelength is stretched and decreases. Since the velocity of wave is constant, the frequency will increase. The opposite results when the source of wave is away from the observer. The figure below illustrates the phenomenon: Figure 2.2.1 Doppler’s Effect

λ1

λ2

When a satellite transmits signal (in wave) to the receiver, the signal will be received on the ground receiver with a change in frequency and wavelength since both the receiver

9

Precise Velocity Estimation from GPS Measurements and satellite are in motion. This small change in frequency is the Doppler’s shift and the GPS receiver has to continually track it to determine the velocity. The basic equation for Doppler’s shift is as follow: V  Fd = Fs   C  where, Fd is the Doppler shift frequency Fs is source frequency V is the relative speed between source and observer C is the speed of sound Many reviews on achieving precise GPS velocity measurements usually adopt the Doppler’s shift frequency to determine a more stable and smooth velocity. The Doppler’s shift can not be measured directly by a single receiver. The velocity is derived by the Kalman filter inside the GPS receiver. 2.3 Carrier Phase Derived Doppler and Receiver Generated Doppler Most modern GPS systems use the Doppler’s shift signal received and so the output velocity is smoothed. There are two common ways for GPS receiver to compute the velocity. One is to use receiver generated Doppler which provides measurement of instantaneous velocity. Another is to use carrier phase-derived Doppler to obtain mean velocity between epochs. The noise from receiver generated Doppler is usually larger than the carrier phase derived Doppler since the measurement time for receiver generated one is short. On the other hand, the carrier phase derived Doppler provides a smooth velocity output with a long period of measurement between observation epochs and the noise is much lesser. By differencing carrier phase observation equation, the carrier phase derived Doppler can be computed.

10

Precise Velocity Estimation from GPS Measurements The frequency of carrier on receiver is constant while the received carrier frequency is changing because of the Doppler’s shift by the relative motion between the satellite and receiver. The phases for receiver and satellite are related by the time elapsed for the signal to transmit from the satellite to the receiver. The carrier phase measurement is then the integral number of carrier cycles plus the fractional cycles. However, GPS receiver has no ability to determine the integer number of cycles and therefore the initial number of cycles becomes ambiguous. The GPS receiver will assume the number of cycles arbitrary when it first locks on the satellite. To solve the integer ambiguity N, the coordinates of the receiver are required. Here is the carrier phase observable equation:

Ф = ρ + c(dt-dT) + λN - dion + dtrop + ε where Ф is the carrier phase observable, ρ is the geometric range between satellite and receiver, c is the speed of light, dt-dT are the GPS time offsets of satellite and receiver clocks, λ is the wavelength of carrier. dion and dtrop are the ionospheric and tropospheric delays and ε is the receiver noise. The GPS receiver continuously locks on the satellite signal. The time rate of change of carrier phase is free from the integer ambiguity and is related to the Doppler’s shift which is used for determining velocity. The above equation can be transferred as the observation equation for velocity determination. Serrano et al[2004] demonstrated the algorithm as below:

 us = hus ⋅ (v u − V s ) + B u − ε us Φ  Φ with

S ε usΦ = −b s + I us + Tus + ∂V + ξ

where

 us is the velocity, hus is the directional cosine vector between the receiver and Φ

satellite,

v u is the receiver velocity vector, V s is the satellite velocity vector, B u is the

receiver clock drift, and

ε us

 Φ

is the error component consists of several components( b s is

11

Precise Velocity Estimation from GPS Measurements

the satellite clock drift, rate,

I us is the ionospheric delay rate, Tus is the tropospheric delay

∂V is the error in satellite velocity derivation and ξ is the receiver system noise.) S

εs

The components inside u were modeled out as random errors and the remaining Φ parameters became unknowns. The satellite velocities and satellites clock drift can be estimated from Earth-Centered-Earth-Fixed (ECEF) satellite coordinates from broadcast ephemerides by differencing epoch-by-epoch satellite positions. Each epoch of velocity solution can be achieved. The first order central difference approximation of the carrier phase to generate the Doppler measurements was demonstrated by Cannon and Szarmes et al [1997]. They performed experiments on finding velocity errors with two types of receivers using the raw Doppler measurement from the receivers and carrier phase-derived Doppler measurements by the first order central difference approximation in both static, low dynamics and high dynamics. The advantage of it is the easy implementation and provision of appropriate velocity estimates in low dynamics environments. The velocity errors are minimized a lot after applying the approximation.

 (t ) ≈ Φ(t + ∆t ) − Φ(t − ∆t ) where Φ (t ) is the derivatives of input signal Ф(t) at Φ 2∆t time t 2.4 Kalman Filter Kalman filter, in mathematical and statistical sense, is a constraint to the observations. For navigation application in GPS, it is used to integrate with measurements from other systems such as INS and AHRS. Two processes are modeled by a Kalman filter [NAVSTAR GPS USER EQUIPMENT INTRODUCTION, 1996]. The first model is the system dynamics model and describes how the error state vector changes in time. The second model is the measurement model and describes the relationship between the error state vector and any measurements

12

Precise Velocity Estimation from GPS Measurements processed by the filter. The principle of the Kalman filter is to determine the accuracy of measurements and apply larger weighing to those measurements which are accurate and reversely smaller for inaccurate measurements. The system dynamics process continuously tracks the error state vector of the total navigation state. The total navigation state can be defined as the mean position and velocity in accordance with different applications. The system can predict the error state vector for next epoch. At particular time t, the error in the estimated total navigation state is x(t) with y(t) denotes the navigation state and ŷ(t) its estimate. x(t)= ŷ(t)-y(t). This differential equation is non-linear and expanded in a Taylor’s series. Then the equation is differenced with the true state and higher order terms are eliminated. At discrete time tk, the linear differential equation for the time rate of change of the navigation error state is: x(tk)=Фk-1x(tk-1)+Gk-1(tk-1)w(tk-1) where Gk-1 is the state transition matrix which indicates the change of error state vector with time w(tk-1) is the white, zero mean Gaussian noise sequence The measurement process is to relate the error state vector with measurements provided by other sensors. Forming the measurement equation is similar to system dynamic process. The non-linear total navigation state differential equation is expanded and the higher order forms are ignored. The equation at particular time tk is: z(tk)=Hkx(tk)+v(tk) where z(tk) is the measurement at time tk Hk is the measurement matrix v(tk) is the white, zero mean Gaussian sequence. 2.5 Velocity Measurement Procedure Most studies for velocity measurement of vehicles using GPS were conducted into two parts. The first part requires a static measurement of GPS. The place for static measurement of GPS varies with the goals of studies. Usually, the measurement is

13

Precise Velocity Estimation from GPS Measurements performed for 30 to 45 minutes of rate of 1 Hz [Szarmes et al]. The purpose of the static measurement is to derive how the GPS velocity agrees with the zero velocity and thus determine the velocity estimates as well as the precision and errors. The second part is the kinematic observation. The first procedure of all is the static initialization. For kinematic measurement, it is required to stay on a platform for about 15 minutes for static initialization to derive GPS velocity performance under the real situation. After static initialization, the GPS receiver is moved along the predetermined path from the starting point to the ending point. The visibility to the sky is essential. The receiver should be moved at constant velocity according to different demands of the measurement procedure. The result produced by Szarmes et al [1997] indicated the performance of two types of receivers. In terms of static test, the result shows a millimeter deviation of 3D velocity errors for two receivers. In aircraft static initialization, there are a number of approaches to assess the measurements. With [a] raw Doppler measurements of two receivers, [b] the first order central difference approximation of carrier phase measurement for one particular receiver and [c] the two receiver raw Doppler measurements differenced with the previous carrier phase derived Doppler velocities, the tests try to find the best solution for velocity estimates for two receivers and the result of one receiver is prior to another one. The kinematic test adopts the approach [c] in the static initialization to assess the accuracy in velocity. It shows a very small increase in velocity error from static to kinematic.

14

Precise Velocity Estimation from GPS Measurements 2.6 Error in GPS Velocity Velocity Noise It is the unmannered attenuation and amplification due to undesirable disturbance of signals. Noise is common in all measuring system. The cause of noise principally comes from the receiver. Multi-path Environment Multipath environment is always the main error source of GPS. High multipath condition causes the satellite signal reflection from the building and obstacles to the receiver so that inaccurate signals arrive the receiver. A good receiver usually establishes an algorithm to certify that only the earliest signal is considered. Dynamics Dynamics refer directly to the acceleration such that high dynamic is in a larger acceleration condition and low dynamic is in a smaller acceleration and even in a static condition. Low dynamic is easier for GPS to derive an accurate velocity with its estimates whilst high dynamic requires an accurate velocity estimates from satellite signal. 2.7 How to Improve GPS Velocity Before understanding how to achieve a precise velocity, a number of factors should be considered which directly affects velocity output. Receiver Quality Receiver manufacturers should have a satisfactory quality on positioning ability. Good receiver should produce desired Doppler’s measurement and minimum clock bias. Doppler-aided Velocity/Position Algorithms Application of Kalman filter in GPS precise velocity is revealed in some researches. The Doppler-aided velocity/position algorithm is to combine the code range with Doppler measurements and process them with Kalman filter [Simpsky et al]. Simpsky provided driving tests which adopts Doppler measurement and provide velocity solution with proper modeling of tropospheric delay.

15

Precise Velocity Estimation from GPS Measurements

Chapter 3 Methodology 3.1 Observations Modes for GPS Velocity One of the requirements in this dissertation is to set up a GPS receiver in static mode to determine how the receiver velocity varies with zero velocity. Leica GPS system 500 (SR 530) provides Static, Rapid-Static, Kinematic (static initialization), Kinematic on-the-fly, Real Time RTK observation modes which will be required in the dissertation. 3.1.1 Static observation In static observation, a stand-alone GPS receiver is placed on a point to obtain the velocity. This point should be located properly such that a desirable visibility can be obtained. The receiver is placed statically for 45 minutes and the real time velocity data are transmitted from the RS232 port to the serial port of laptop through the data communication cable. These data are converted into digital format and they are drawn into graphs to show the variation of the GPS velocity. 3.1.2 Kinematic observation For kinematic observation, the receiver is moved manually around a predefined track. The track is a square path setting up by a steel tape. Kinematic observation requires a static initialization of receiver for about 15 minutes which also provides horizontal coordinates of the starting point. A laptop is connected with the receiver to collect NMEA messages. Then the receiver starts to move and the starting time is counted. The observation rate in kinematic observation is usually larger than that in static mode to obtain a faster rate of changing in position. After the receiver is travelled along the whole path, it ends at the starting point and the stoppage time is counted. The receiver is put back on the tripod and stayed for a while. 3.1.3 GPS velocity accuracy assessment In this dissertation, there will be several methods to assess the accuracy of GPS velocity. They are pseudorange approach, carrier phase-derived velocity approach, RTK approach

16

Precise Velocity Estimation from GPS Measurements Pseudorange approach Pseudorange is the collection of horizontal position data through $GPLLK of NMEA 0183 message output. This message provides pseudorange local grid coordinates data. These data are collected to determine the position changes and thus determine the velocity in kinematic observation. The data are adjusted together with the position data processed by GPS velocity and time using Kalman filter. Carrier phase-derived velocity approach This method requires the determination of velocity vectors both from receiver and satellites as well as the receiver clock drift. The velocity vectors of receiver are determined from carrier phase-derived position changes in receiver during field works while the satellites velocity vectors are calculated from the position changes in satellite from the data of broadcast ephemerides. The Real time kinematic approach Real time kinematic method adopts the similar approach as carrier-phase but difference in an additional one control point providing adjustment of position data. 3.2 Data Output The message received from GPS receiver is in NMEA 0183 standard format. NMEA 0183 standard is developed by the National Marine Electronics Association which provides a standard interface for definition of electrical signal requirements and data transmission protocol, through different means of transmission ports such as serial port. NMEA 0183 standard has developed for several years and the mostly updated version is 3.01. Each GPS manufacturers develop their own versions of NMEA message output but most messages are similar to the standard format. According to different functions available in the receiver, the receiver provides different messages. The figure below shows the structure of a standard NMEA-0183 sentence.

17

Precise Velocity Estimation from GPS Measurements

Asterisk Delimiter Comma Delimiter

$GPVTG,153.5313,T,153.5313,M,0.011,N,0.021,K,A*33 Message Identifier

Field 1 Field 2 Field 3 Field 4 Field 5 Field 6

Checksum Field 9 Field 8 Field 7

Figure 3.2.1 Structure of a NMEA-0183 sentence NMEA-0183 sentences are strings of comma-delimited text. There are several fields and a checksum for each message sentence. These sentences will vary slightly in different systems and some message outputs may not be provided in some systems. Two GPS systems, Leica GPS system 500(SR 530) and Trimble DSM 212H are assessed and they respectively provide slightly different NMEA messages of velocity outputs. They both adopt message identifier VTG as velocity message output and provide nearly the same VTG format. However, the Trimble GPS is mainly used for marine application and it uses “track over ground” as the direction from true north. The Leica GPS is used mainly in land application and the velocity information output is “course over ground”. The speed output has two kinds of units: knots and km/hr with 3 decimal places. 1 Knot is equal to 1.8532 km/hr. The VTG formats of two types of receiver are displayed as below: Leica GPS system 500 VTG - Course Over Ground and Ground Speed $GPVTG, x.x, T, x.x, M, x.x, N, x.x, K, A*hh

18

Precise Velocity Estimation from GPS Measurements Field 1 2 3 4 5 6 7 8 9 10

Format $GPVTG

Content Header, incl. Talker ID,message sent from Receiver x.x Course over ground, degrees (0.0° to 359.9°) T True (fixed text “T”) x.x Course over ground, degrees (0.0° to 359.9°) M Magnetic (fixed text “M”) x.x Speed over ground N Knots (fixed text “N”) x.x Speed over ground K Km/h (fixed text “K”) A Mode Indicator A = Autonomous mode D = Differential mode N = Data not valid *hh Checksum Carriage Return Line Feed Table 3.2.1 VTG Sentence Output from Leica GPS System 500

Trimble DSM 212H VTG - Course Over Ground and Ground Speed $GPVTG,0,T,,,0.000,N,0.000,K*33 Field 1

Format $GPVTG

Content Header, incl. Talker ID,message sent from Receiver Course over ground, degrees (0.0° to 359.9°) True (fixed text “T”) shows that track made good is relative to true north Not Used Not Used Speed over ground in knots (0-3 decimal places) Knots (fixed text “N”) shows that speed over ground is in knots Speed over ground in kilometers/hour (0-3 decimal places) Km/h (fixed text “K”) shows that speed over ground is in kilometers/hour

2 3

x.x T

4 5 6 7

x.xxx N

8

x.xxx

9

K

Checksum

*hh Table 3.2.2 VTG Sentence Output from Trimble DSM 212H

Besides, GPVTG, there are two other NMEA-0183 messages GPGGA and GPLLK which are also necessary to determine the UTC time of position and local grid coordinates.

19

Precise Velocity Estimation from GPS Measurements

Chapter 4 Field Works 4.1 Site Reconnaissance One of the major problems of using GPS is the visibility as mentioned in the previous chapter. Therefore, the choice of location for field works must be thoughtfully considered. A suitable location would be a plain area with few high-rise buildings and structures. After consideration, I choose the plain area at podium level at core A inside the campus for static observation. This place provides a satisfactory visibility with considerable multipath environment.

Figure 4.1.1 Map of GPS Static Observation For kinematic observation, I choose Ho Man Tin for field measurement. This place provides adequate visibility for GPS. This area is a football court with good sky visibility and thus providing a desirable situation for GPS. The area is also plain and large enough for field works.

20

Precise Velocity Estimation from GPS Measurements

Figure 4.1.2 Map for Route of GPS Kinematic Observation (Manual)

Figure 4.1.3 Photos for Route of GPS Kinematic Observation (Manual) 4.2 Preparation before Field Works The basic equipments used in the dissertation require two Leica GPS 500 systems with radios, tripods, external batteries and a laptop with NMEA data acquisition software. Before GPS field work, it is necessary to calibrate the GPS for static and kinematic modes. The update rate is set to 5 seconds for static and 1 second for kinematic. Faster observation rate would be required for kinematic mode to obtain faster data change in

21

Precise Velocity Estimation from GPS Measurements measurement. Finally, proper transformation parameters from WGS84 coordinates to HK80 grid coordinates should be inputted into the receiver before field works. 4.3 Static Observation The data are collected on 27th February, 2006, using the Leica GPS system 500. Standalone GPS receiver is put in a static environment to collect velocity data and these data are transferred to the laptop in real time for 45 minutes. There is quite a large variation of velocity when the receiver starts to operate. Therefore, the receiver is stayed for some times to wait for a more static performance of velocity output. The data will be collected until they become stable. It is necessary to convert the unit (km/hr) into unit (m/s) for post-processed interpretation. The resulting velocity vector will then be resolved into two horizontal velocity vectors by the course angle from true north (Ө). vx = v cosӨ

N

vy = v sinӨ

Ө vy

E

vx Figure 4.3.1 Resolving for Two Horizontal Velocity Vectors

22

Precise Velocity Estimation from GPS Measurements 4.4 Kinematic Observation In kinematic observation, the receiver is moved manually within an area starting and ending at the same position. A laptop is connected with the receiver to acquire the LLK, VTG and GGA messages so that the pseudorange position, time and velocity data can be determined. The following figure illustrates the phenomenon: Start & End (x0,y0)

25 m

Figure 4.4.1 Route for Kinematic Observation (Manual) A route of approximate 100 meters with each side equals to 25 meters is set up by a steel tape. A GPS receiver is stayed on the starting point for 15 minutes to determine the coordinates (xo, yo) and perform initialization. Then the receiver is moved manually along the route as shown above from the starting point and the starting time is recorded. It travels along a square path and ends at the starting point. The receiver will be put back on the tripod to attain the same ending position and the ending time is recorded. The test is performed for three times to assess and compare the accuracy of three tests. The advantage of a square path is its easy route design. The receiver should be held as vertical as possible during movement to minimize errors such as cycle clips. The update rate of data is fixed at 1 second interval. The principle behind the experiment is to discover the velocity performance for standalone GPS in kinematic environment. The formula below explains the phenomenon: x = xo + vxΔt

23

Precise Velocity Estimation from GPS Measurements y = yo + vyΔt where xo and yo are the initial coordinates, x and y are the coordinates of the next epoch. Δt is the time elapsed, vx is the easting velocity vector and vy is the northing velocity vector. The coordinates of the next location can be computed by using the velocity data and time. The relevant data are loaded from the LLK, VTG and GGA messages. The position of next epoch is computed by using the formula above. After running up the whole path and coming back to the starting point, the pseudorange position calculated from the GPS velocity and time as well as the position of the initial coordinates can be compared. There are three attempts in the experiment. It is necessary to collect three sets of data and to compare their respective accuracy. Some interpretations are focused on the pseudorange and carrier phase observation. Pseudorange observation is equal to the difference between the receiver time tr and satellite time tk at signal transmission

24

Precise Velocity Estimation from GPS Measurements

Chapter 5 Data Analysis 5.1 Static Observation Result The static velocity data is compiled and two graphs for each vector are drawn below.

Speed Over Ground (North) (m/s) versus time Velocity (North) (m/s) 0 0

500

1000

1500

2000

2500

3000

-0.001 -0.002 -0.003 -0.004 -0.005 -0.006 Time Elapsed (second)

Clips

Figure 5.1.1 Speed over Ground in Static Mode (North)

Speed Over Ground (East) (m/s) versus time

Velocity (East) (m/s) 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0 0

500

1000

1500

2000

Time elapsed (second)

Figure 5.1.2 Speed over Ground in Static Mode (East)

25

2500

3000

Precise Velocity Estimation from GPS Measurements It can be seen from the above graphs that the velocities for north and east vectors are not real “zero” and there are some errors for the GPS receiver. The velocity output is around 5 millimeters per second for northing vector and 1.75 to 3 millimeters per second for easting vector. The velocity error is quite small for both velocity vectors. The variation is not large for northing vector and less than 2 millimeters per second for easting vector. This small variation indicates the small static velocity errors. The table below shows the data collected during the beginning. It shows the variation of velocity is quite high and there are some outliers. Large velocity variation during the start of survey

Outlier

Figure 5.1.3 Static Velocity Data at the Beginning I reject the beginning section of data and start recording data until they become static. The velocity data only contains three decimal places and therefore there are some “clips” shown in figures 5.1.1 and 5.1.2 above when there is a 0.001km/hr change of velocity. Speed Over Ground (North) Speed Over Ground (East) (m/s) (m/s) Mean -0.00492866 0.00233564 standard deviation 0.00018725 0.000459 RMS 0.00493222 0.00238032 Table 5.1.1 Statistical Result Showing the Static Observation Result

26

Precise Velocity Estimation from GPS Measurements 5.2 Kinematic Observation Result 5.2.1 Pseudorange derived velocity The data produced in the kinematic is quite different from the static observation. This time the observation should include the velocity, time and pseudorange position data from NMEA 0183 output and carrier phase position data. These data are collected and post-processed.

Figure 5.2.1 Sample of NMEA 0183 Output Data After data processing, respective velocity generated position and pseudorange position variations are figured out. Figures 5.2.2-5.2.7 show the position variations and using pseudorange and velocity data in three trials. Figures 5.2.8 and 5.2.9 show the velocity variation from GPS.

27

Precise Velocity Estimation from GPS Measurements

Position variation along a 100m track using velocity data (Trial 1) 5

0 -30

-25

-20

-15

-10

-5

0

5

Start & End

-5

y (m)

-10

-15

-20

-25

-30 x (m)

Figure 5.2.2 Position Variation along a 100m Track using Velocity Data (Trial 1) GPS pseudorange position data (Trial 1) 819055 819050

Start & End

Northing (m)

819045 819040 819035 819030 819025 819020 836685

836690

836695

836700

836705

Easting (m)

28

836710

836715

836720

836725

Precise Velocity Estimation from GPS Measurements Figure 5.2.3 Using Pseudorange to Generate the Position Data (Trial 1) Position variation along a 100m track using velocity data (Trial 2) 5 0 -30

-25

-20

-15

-10

-5

0

5

-5

Start & End

y (m)

-10 -15 -20 -25 -30 x (m)

Figure 5.2.4 Position Variation along a 100m Track using Velocity Data (Trial 2)

819055

GPS Pseudorange position data (Trial 2) End

819050

Start

Grid Northing

819045 819040 819035 819030 819025 819020 836685 836690 836695 836700 836705 836710 836715 836720 836725

Grid Easting

29

Precise Velocity Estimation from GPS Measurements Figure 5.2.5 Using Pseudorange to Generate the Position Data (Trial 2) Position variation along a 100m track using velocity data (Trial 3) 5 0 -30

-25

-20

-15

-10

-5

0

5

-5

Start & End

y (m)

-10 -15 -20 -25 -30 x (m)

Figure 5.2.6 Position Variation along a 100m Track using Velocity Data (Trial 3)

GPS Pseudorange position data (Trial 3) 819055

Start & End

819050

Grid Northing

819045 819040 819035 819030 819025 819020 836685 836690 836695 836700 836705 836710 836715 836720 836725

Grid Easting

30

Precise Velocity Estimation from GPS Measurements Figure 5.2.7 Using Pseudorange to Generate the Position Data (Trial 3) Speed Over Ground (North) (m/s) versus time Trial 1 (Manual)

1.5

Velocity North (m/s)

1 0.5 0 15:33:24

15:33:42

15:33:59

15:34:16

15:34:34

15:34:51

15:35:08

15:35:25

15:35:43

15:36:00

15:36:17

-0.5 -1 -1.5 Time elapsed(hh:mm:ss)

Figure 5.2.8 GPS Velocity (compared with pseudorange) (North) (Trial 1) Speed Over Ground (East) (m/s) versus time Trial 1 (Manual) 1.5

Velocity East (m/s)

1 0.5 0 15:33:24

15:33:42

15:33:59

15:34:16

15:34:34

15:34:51

15:35:08

15:35:25

15:35:43

15:36:00

-0.5 -1 -1.5

Time elapsed(hh:mm:ss)

Figure 5.2.9 GPS Velocity (compared with pseudorange) (East) (Trial 1)

31

15:36:17

Precise Velocity Estimation from GPS Measurements

Position shifts generated from velocity data (m) Trial

Shifts in Northing (m) (End –Start) (N1) -0.083 0.167 0.187 Abs(N1-N2)

Shifts in Easting (m) (End –Start) (E1) 0.373 0.411 0.412 Abs(E1-E2)

Position shifts generated from pseudorange data (m)

Shifts in Northing (m) (End –Start) (N2) -0.636 2.003 0.331

Shifts in Easting (m) (End –Start) (E2) 0.227 -1.541 1.702

Trial 1 Trial 1 Trial 2 Trial 2 Trial 3 Trial 3 Difference between two methods of data Trial 1 0.553 0.146 Trial 2 1.836 1.952 Trial 3 0.144 1.29 Table 5.2.1 Position Shifts Generated from Velocity and Pseudorange Position Data Assuming the starting point starts at (0, 0), the velocity and time data are processed together to generate the relative position variation along the track. At the same time, the

pseudorange position data are also recorded. After processing out three sets of data in two approaches, we find out the shifts in easting and northing and compare their error values for these two approaches. The main interpretation should focus on the starting and ending position. In the above three trials, the shift in velocity generated position data are in reasonable amount which is not larger than 0.5 meters. The pseudorange position data are erroneous with unexpected large errors in trials 2 and 3. The position shifts are very large in compare with trial 1. When comparing the velocity generated position data with pseudorange position data, there are obviously large differences. The main cause is due to the large errors in pseudorange position data. Trial 1 has the least difference compared with other two trials. Another thing is examined is the pattern of two methods of position outputs. The velocity

32

Precise Velocity Estimation from GPS Measurements generated position has a nearly square pattern along the whole track. However, the pseudorange position pattern is not in a “square” pattern. The error generated should be composed of both random errors and less accurate position performance. Based on the above information, both the pseudorange and velocity data should contain errors but pseudorange would have larger errors. The shifts in the three trials are larger and more unexpected for pseudorange data since stand-alone pseudorange positions usually have large errors in meters level. After each trial, the receiver is put back to the tripod. The static position keeps changing since the velocity is not absolutely zero. However, the position does not really shift after the receiver stops and the static velocity implies the velocity error generated by the

Velocity North (m/s)

receiver as it is not zero. Speed over ground (North) changes with time (After running up the whole path) (trial 1) 0.1 0.08 0.06 0.04 0.02 0 -0.02 0

5

10

15

20

25

30

Time (second)

Figure 5.2.10 Velocity North Changes after Running up the Whole Path (Trial 1) Speed over ground (East) changes with time (After running up the whole path) (trial 1) Velocity East (m/s)

0.02 0 -0.02 0

5

10

15

-0.04 -0.06 -0.08 Time (second)

33

20

25

30

Precise Velocity Estimation from GPS Measurements

Figure 5.2.11 Velocity East Changes after Running up the Whole Path (Trial 1) Velocity derived from pseudorange (North) (Trial 1)

Velocity North (m/s)

2 1.5 1 0.5 0 15:33:07 -0.5

15:33:50

15:34:34

15:35:17

15:36:00

15:36:43

-1 -1.5 -2 Time (hh:mm:ss)

Figure 5.2.12 Pseudorange-derived Velocity (North) (Trial 1) Velocity derived from pseudorange (East) (Trial 1)

Velocity East (m/s)

2 1 0 15:33:07 -1

15:33:50

15:34:34

15:35:17

15:36:00

15:36:43

-2 -3 -4 Time (hh:mm:ss)

Figure 5.2.13 Pseudorange-derived Velocity (East) (Trial 1) The velocity data derived from pseudorange are also assessed to find its accuracy. The data contain errors and outliers and cannot be used as the velocity determination or comparison with the GPS velocity. From the results above, we know the pseudorange position data contains errors. It would

34

Precise Velocity Estimation from GPS Measurements be a good way to adjust it by using the velocity data. 5.2.2 Kalman Filtering 5.2.2.1 Algorithm Design I adopt the method of Kalman filtering from two sets of equations models. Dynamic equation  x E = x E 0 + v x ∆t + n1   y N = y N 0 + v y ∆t + n 2 where xE, yN are the easting and northing derived from velocity and xEo, yEo are the initial easting and northing derived from velocity vx and vy are the velocities easting and northing n1 and n2 are the errors. Observation equation  x k = x E + n3   y k = y N + n4 where xk, yk are the pseudorange easting and northing n3 and n4 are the errors. We can see the relationship from the above two sets of equations. The position derived from the velocity should have the same position derived from pseudorange if there are no errors. As the field works done, we assume the initial position (xEo, yEo) as (0, 0) and generate the position solution at next epoch by GPS velocity and time. The velocity generated position difference should have similar position difference that provided by pseudorange. Time is set at 1 second interval and the receiver time is modeled out as random error. Therefore, the remaining components pseudorange position and velocity are combined together and adjusted by Kalman filter. There are four components pseudorange easting (xk), northing (yk) and velocity easting (vx), northing (vy) to be adjusted.

35

Precise Velocity Estimation from GPS Measurements

 xk   n1  y  n  k 2  The state vector is then created as x ( k ) = and v k =   V x   n3       n4  V y  Observation model The observation model includes the measurement and state vector. The equations are as follow: At particular epoch k, the estimated state vector equals to x(k). By using least square adjustment, the observation at time = tk will become  xk  y  k y( k ) = A( k ) x ( k ) + V ( k ) where y( k ) =   and A( k ) = I V x    V y  where A(k) is the design matrix, x(k) is the state vector matrix, y(k) is the matrix of observation and V(k) is the error vector of observation matrix Dynamic model The dynamic model shows the relationship of two state vectors between the two different epochs. In this model, the state vector at time t = k-1 is used to relate the observation at time t = k by transition matrix where Δt = 1 second. x ( k ) = Φ( k , k − 1) x ( k − 1) + U ( k ) where x(k-1), x(k) are state vectors at epochs k-1 and k, U(k) is the error vector of state vector matrix and Φ(k,k-1) is the transition matrix and

1 0 Φ( k , k − 1) =  0  0

0 ∆t 1 0 0 1 0 0

0 ∆t  = 0  1

1 0  0  0

0 1 0 0

1 0 1 0

0 1 0  1

The first procedure of Kalman filter is the prediction model. The estimated state vector  between two adjacent epochs x ( k , k − 1) is computed from the estimated state vector in

36

Precise Velocity Estimation from GPS Measurements the previous epoch and transition matrix.

37

Precise Velocity Estimation from GPS Measurements Prediction The prediction model is as follow:   x ( k , k − 1) = Φ( k , k − 1) x ( k − 1, k − 1)   P ( k , k − 1) = Φ( k , k − 1) P ( k − 1, k − 1)Φ( k , k − 1) + Q   where P ( k , k − 1) and P ( k − 1, k − 1) are the predicted covariance matrices of the   estimated state vector x ( k , k − 1) and x ( k − 1, k − 1) Q is the covariance matrix of error vectors U(k) Estimation   K ( k ) = P ( k , k − 1) AT ( k ) A( k ) P ( k , k − 1) AT ( k ) + R( k )   x ( k , k ) = x ( k , k − 1) + K ( k )[ y( k ) − A( k ) x( k , k − 1)]  P ( k , k ) = [ I − K ( k ) A( k )] P ( k , k − 1)

[

]

−1

where K(k)is the gain matrix x(k,k)is the state vector at epoch k using prediction model P(k,k)is the covariance matrix of state vector at epoch k using prediction model R(k) is the covariance matrix of error vectors V(k)

5.2.2.2 Result after Adjustment with Kalman Filtering The above algorithms are matched into the observations dataset and the pseudorange coordinates are adjusted by varying the covariance matrix of state vector and error vectors of state vector and observation vectors. Different settings of the above covariance matrices would produce different results and the pattern of pseudorange coordinates which is best-fit with the pattern in velocity-derived positions estimation would be the best setting for the Kalman Filter. The choices of covariance matrix are based on… For the covariance matrices of error vectors Q and R, the choice is based on two directions. R is computed based on the receiver ability in evaluating the positions and velocity. The values inside the R matrix are usually set in a constant value and the values

38

Precise Velocity Estimation from GPS Measurements in Q matrix are varied. The variation is based on the accuracy of the observation data that should be achieved and the values should start from small values and enlarge it until the pattern match best with the data in velocity-derived position (the dynamic model).

819055

0 0 0  1000   1000 0 0   0 P= 0 0 1000 0     0 0 0 1000  

Adjusted Result with P = 1000, R = 25,25,0.0001,0.0001 Q = 25,25,0.0001,0.0001

Adjusted Northing (m)

819050 819045 819040 819035 819030 819025 819020 836685

836690

836695

836700

836705

836710

836715

836720

836725

836720

836725

Adjusted Easting (m)

P= 0 0 1000 0     0  0 0 1000   819050  52 0  0 0   819045  0 52 0 0  R=  2 0  819040  0 0 0.01 0 0 0 0.012   819055

Adjusted Northing (m)

0 0with P0= 1000, 1000  Adjusted Result R = 25,25,0.0001,0.0001   0 1000 0 0   Q = 100,100,0.01,0.01

819035

10 2 0   0 10 2 819030 Q= 0  0 819025  0 0  819020 836685

836690

0 0 0.12 0 836695

0  0   0  0.12  836700

836705

836710

836715

Adjusted Easting (m)

39

 52  0 R= 0 0 

0 52 0 0

0 0 0.012 0

0  0   0  0.012 

52  0 Q= 0 0 

0 52 0 0

0 0 0.012 0

0  0   0  0.012 

Precise Velocity Estimation from GPS Measurements

819055

Adjusted Result with P = 1000, R = 25,25,0.0001,0.0001 Q = 10000,10000,1,1

Adjusted Northing (m)

819050 819045 819040 819035

0 0 0  1000   0 1000 0 0   P= 0 0 1000 0     0 0 0 1000    52 0 0 0   2 0 5 0 0  R=  2 0   0 0 0.01 0 0 0 0.012   1002 0 0 0   2  0 100 0 0 Q=  2 0 0 1 0   0 0 0 12  

819030 819025 819020 836685 836690 836695 836700 836705 836710 836715 836720 836725 Adjusted Easting (m)

The above three graphs tell the position variation after the adjustment by fixing the R matrix and varying the Q matrix. The graphs above are started from the smallest value “5m” for position coordinates and “0.01m/s” for velocity inside the Q matrix. The values are increased as “10m / 0.1m/s” and “100m / 1m/s” for graphs 2 and 3. The result from the second graph shows the best result among the three and provides the smoothest solution. It is found that when the values inside the Q matrix increase, the resulting graph will be more “straight”. The Q matrix is large in compared with the R matrix and the information is mainly based on the dynamic model (i.e. The velocity-derived position). The decision of the amount of values inside the Q matrix is based on the resulting graph. The choice of values inside the Q matrix is that the increment of values should undertake a significant change in patterns. After several trials, the best change in values with the pattern would be as above shown. Now, the next procedure is to perform another test to deduce the values for other R matrices varying with Q matrix.

40

Precise Velocity Estimation from GPS Measurements 0 0 0  1000   0 1000 0 0   P= 0 0 1000 0     0 0 0 1000   10 2 0 0 0   2  0 10 0 0  R=  2 0 0.1 0   0  0 0 0 0.12  

Adjusted Result with P = 1000, R = 100,100,0.01,0.01 Q = 100,100,0.01,0.01

819055

Adjusted Northing (m)

819050 819045 819040 819035

10 2 0   0 10 2 Q= 0  0  0 0 

819030 819025 819020 836685

836690

836695

836700

836705

836710

836715

836720

0 0 0.12 0

0  0   0  0.12 

836725

Adjusted Easting (m)

0 0 0  1000   1000 0 0   0 P= 0 0 1000 0     0 0 0 1000   10 2 0 0 0   2  0 10 0 0  R=  2 0 0.1 0   0  0 0 0 0.12  

Adjusted Result with P = 1000, R = 100,100,0.01,0.01 Q = 10000,10000,1,1

819055

Adjusted Northing (m)

819050 819045 819040 819035

100 2 0 0 0   2  0 100 0 0 Q=  0 12 0   0  0 0 0 12  

819030 819025 819020 836685

836690

836695

836700

836705

836710

Adjusted Easting (m)

836715

836720

836725

The two graphs above show the variation based on fixing another R matrix. The approach is similar to previous set of R matrix. This time the R matrix is larger and the Q matrix is varied from the smallest value. The smallest value should not be larger than the R matrix since the receiver ability should not overtake the measurement error. Graph 2 shows similar pattern as the previous third graph. It illustrates that the dynamic model overtakes the measurement model. These two graphs do not show a great difference with the

41

Precise Velocity Estimation from GPS Measurements previous set of graphs and therefore it is needed to adjust the values of P matrix to outline more suitable solutions. This time the values inside P matrix are increased to “10000” to see any significant change for the graph.

819055

0 0 0  10000   0 10000 0 0   P= 0 0 10000 0     0 0 0 10000   52 0 0 0   2 0 5 0 0  R=  2 0 0.01 0  0 0 0 0 0.012  

Adjusted Result with P = 10000, R = 25,25,0.0001,0.0001 Q = 25,25,0.0001,0.0001

Adjusted Northing (m)

819050 819045 819040 819035

52  0 Q= 0 0 

819030 819025 819020 836685

836690

836695

836700

836705

836710

836715

836720

0 52 0 0

0 0 0.012 0

0  0   0  0.012 

836725

Adjusted Easting (m)

819055

0 0 0  10000   10000 0 0   0 P= 0 0 10000 0     0 0 0 10000   52 0 0 0   2 0 5 0 0  R=  2 0 0.01 0  0 0 0 0 0.012  

Adjusted Result with P = 10000, R = 25,25,0.0001,0.0001 Q = 100,100,0.01,0.01

Adjusted Northing (m)

819050 819045 819040 819035

10 2 0   0 10 2 Q= 0  0  0 0 

819030 819025 819020 836685

836690

836695

836700

836705

836710

836715

Adjusted Easting (m)

42

836720

836725

0 0 0.12 0

0  0   0  0.12 

Precise Velocity Estimation from GPS Measurements

819055

0 0 0  10000   0 10000 0 0   P= 0 0 10000 0     0 0 0 10000   52 0 0 0   2 0 5 0 0  R=  2 0 0.01 0  0 0 0 0 0.012  

Adjusted Result with P = 10000, R = 25,25,0.0001,0.0001 Q = 10000,10000,1,1

Adjusted Northing (m)

819050 819045 819040 819035

100 2 0 0 0   2  0 100 0 0 Q=  2 0 0 1 0   0 0 0 12  

819030 819025 819020 836685

836690

836695

836700

836705

836710

836715

836720

836725

Adjusted Easting (m)

From the results above, it is possible to adjust the position from velocity information under suitable adjustment model, parameters and constraints, etc. The resultant positions would be smoother, as compared with unadjusted information.

43

Precise Velocity Estimation from GPS Measurements 5.2.3 RTK Result Another comparison method used is the RTK derived velocity. The result is shown as follow: RTK velocity (North) (Trial 1) 1.5

RTK velocity North (m/s)

1 0.5 0 15:55:26

15:56:10

15:56:53

15:57:36

15:58:19

15:59:02

-0.5 -1 -1.5 elasped time (hh:mm:ss)

Figure 5.2.14 RTK-derived Velocity (North) (Trial 1)

RTK velocity (East) (Trial 1) 1.5

RTK velocity East (m/s)

1 0.5 0 15:55:26

15:56:10

15:56:53

15:57:36

15:58:19

-0.5 -1 -1.5 elapsed time (hh:mm:ss)

Figure 5.2.15 RTK-derived Velocity (East) (Trial 1)

44

15:59:02

Precise Velocity Estimation from GPS Measurements

Speed Over Ground (North) (m/s) versus time Trial 1 (GPS velocity) (Manual) 1.5

Velocity North (m/s)

1 0.5 0 15:55:35

15:57:19

15:59:02

-0.5 -1 -1.5

Time elapsed(hh:mm:ss)

Figure 5.2.16 GPS Velocity (North) (Trial 1) Speed Over Ground (East) (m/s) versus time Trial 1 (GPS velocity) (Manual) 1.5

Velocity East (m/s)

1 0.5 0 15:55:35

15:57:19

15:59:02

-0.5 -1 -1.5

Time elapsed(hh:mm:ss)

Figure 5.2.17 GPS Velocity (East) (Trial 1) In the above figures, it shows the variation of velocity over the time by two methods. The patterns are nearly the same and the difference of using two approaches was not really large. This tells the velocity derived from RTK does not have large impact in improving the velocity. The velocity primarily output from the GPS is already desirable.

45

Precise Velocity Estimation from GPS Measurements Trial 1

Trial 2

Trial 3

Difference between RTK and GPS velocity -0.000139692 -0.000196162 -0.000013979 (North) (m/s) [RTK-GPS] Difference between RTK and GPS velocity 0.000047683 -0.000009129 -0.000054974 (East) (m/s) [RTK-GPS] Difference between RTK and GPS velocity 0.001817727 0.002582316 0.002954699 (North) (m/s) Standard deviation Difference between RTK and GPS velocity 0.002557648 0.002925877 0.002734525 (East) (m/s) Standard deviation Table 5.2.2 Difference between RTK and GPS Velocity (North and East) in Three Trials (Mean and Standard Deviation of Total Time Elapsed) From the table above, we can see the differences between RTK and GPS velocity in three trials are very small. The standard deviation indicates the differences compared between two velocity determination approaches are not very large. In compare with the pseudorange position coordinates and RTK carrier phase position coordinates, the difference is obvious. Their large accuracy difference furthermore describes good position coordinates are not essential in determining good velocity solution. GPS velocity should itself provide quite an accurate solution from receiverderived Doppler.

46

Precise Velocity Estimation from GPS Measurements

Chapter 6 Recommendations and Conclusion 6.1 There are totally two methods to be done as the methodology planned and the pseudorange and RTK carrier phase data are assessed. 6.3 The planned schedule requires me to do the velocity comparison with vehicles but I can’t finish the measurement on time. This is good for vehicle planning Conclusion Inside the three methods on deriving the velocity, the RTK approach should be the most accurate but the fact is that it makes a very small amount of difference with the velocities outputted from the GPS. This difference should also include some errors but they shouldn’t do a very large amount of disturbance to real values. Pseudorange provides quite a large data discrepancy but it is quite reasonable since the data accuracy is not high. Although I haven’t done the carrier phase velocity estimation, the velocity measurement shouldn’t have larger data errors with that provided by RTK. Since RTK determined the position based on carrier-phase platform, the The two with velocity are performed and the result tells that the GPS velocity contains small extent of errors of around 0.002 to 0.005 m/s. This amount is very small and the velocity is good enough for velocity determination. For future development, there should be similar measurements using vehicles for more realistic environment. The vehicle can provide higher speed and the data can be further determined. It also provides high dynamic solution (large acceleration).

47

Precise Velocity Estimation from GPS Measurements

Reference Papers and Reference Books P.J.G. Teunissen and A. Kleusberg (Eds.) (1998), GPS for Geodesy, Springer-Verlag, Berlin-Heidelberg-New York; pp. 165-166. Luis Serrano, Donghyan Kim and Richard B. Langley (2004), A GPS Velocity Sensor: How Accurate Can It Be? – A First Look, Proceedings of ION NTM 2004 San Diego, California, 26-28 January, 2004; pp 875-885. Andrew Simsky and Frank Boon, Carrier Phase & Doppler-based Algorithms for Realtime Standalone Positioning, Septentrio NV, Belgium S. Ryan, G Laceapelle and M.E. Cannon (1997), DGPS Kinematc Carrier Phase Signal Simulation Analysis in the Velocity Domain, Proceedings of ION GPS 1997, Kansas City, Missouri, September 16-19, 1997. M. Szarmes, S. Ryan and G Lachapelle (1997), DGPS High Accuracy Aircraft Velocity Determination Using Doppler Measurements, Proceedings of the International Symposium on Kinematic Systems (KIS), Banff, AB. Canada, June 3-6, 1997. Luis Serrano, Don Kim and Richard B. Langley (2004), A Single GPS receiver as a RealTime, Accurate Velocity and Acceleration Sensor, Proceedings of ION GNSS 2004, Long Beach, California, 21-24 September, 2004; pp 2021-2034. Capt. J. Hebert and J. Keith (1997), DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination, Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June – 2 July, 1997. A.M. Bruton, C.L. Giennie and K.P. Schwarz (1999), Differentiation for High-Precision GPS Velocity and Acceleration Determination, GPS Solutions, Vol.2, No. 4; pp. 7-21 User Manuals and Internet Resources NAVASTAR GPS USER EQUIPMENT INTRODUCTION, SEPTEMBER 1996 PUBLIC RELEASE VERSION http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf Appendix C, DSM 12/212 Operation Manual, Part No. 34520-00, Revision A (1998), Trimble Navigation Ltd., Surveying and Mapping Division, May 1998.

48

Precise Velocity Estimation from GPS Measurements Appendix E, Leica GPS System 500 Technical Reference Manual Version 4.0 (2002), Leica Geosystems AG, Heerbrugg, Switzerland, 2002 NMEA 0183 Standard, National Marine Electronics Association http://www.nmea.org/pub/0183/

49