analysis of parameters influencing weak gnss signal processing · 2018-10-01 · rapid temporal...

ION GNSS+ 2018, Session F1, Miami, FL, September 24-28, 2018 of 14

Analysis of Parameters Influencing Weak GNSS

Signal Processing

Thyagaraja Marathe, Ali Broumandan, Gérard Lachapelle

PLAN Group,

Department of Geomatics Engineering, Schulich School of Engineering,

University of Calgary, Canada

BIOGRAPHIES

Thyagaraja Marathe received his doctoral degree from the University of Calgary. During 2016-17 he was a post-doctoral

scholar in the PLAN Group. He currently works at Rx Networks Inc. as research engineer. His areas of interest include GNSS

receiver design, antenna array processing, high accuracy positioning and embedded system design.

Ali Broumandan received his Ph.D. degree in Geomatics Engineering from the University of Calgary. During 2013-18, he

worked in the PLAN Group as senior research associate where his research focussed on GNSS signal processing.

Gérard Lachapelle, Professor Emeritus, has been involved in a multitude of GNSS R&D projects since 1980, ranging from

RTK positioning to indoor location and signal processing enhancements, first in industry and since 1988, at the University of

Calgary where he initiated the PLAN Group in the early 2000s.

ABSTRACT

Indoor navigation and positioning methods are continuously evolving as a result of the diversity of applications. In some

wireless high channel traffic areas, indoor navigation is facilitated by various wireless technologies such as Wi-Fi hotspots,

Bluetooth beacons and other special signal transmitters. In addition to the use of these technologies, significant performance

improvements can be achieved by integrating these systems with data obtained with GNSS receivers. Furthermore,

standalone GNSS based indoor positioning is essential for low channel traffic areas like isolated residential complexes and

houses where deploying dedicated infrastructure might not be viable. Therefore, regardless of the recent evolution of non-

GNSS approaches, there is a need to exploit weak GNSS signals and characterize their behavior in indoor environments. The

research presented in this paper focuses on assessing different factors that contribute towards GNSS weak signal detection.

There are three main factors that have a major impact on weak signal processing using long term integration, namely short

term stability of the receiver clock, accuracy of the estimated trajectory used during integration, and changes in the channel

model during integration. Individual contributions due to each one of these are analyzed. Indoor GPS data was collected in

different indoor environments, namely commercial concrete building and townhouse with brick walls for the characterization

process. Effect of the indoor channel behavior is characterized for a static user and for a moving antenna placed on a linear

motion table. Additionally, spatial domain characteristics for two closely placed antennas are analyzed. Finally, data samples

are collected for a short period every 30 minutes over a seven-hour window and position estimates are compared to study

time domain dependencies. Analyses are supported with measurement and position domain results.

INTRODUCTION

Using a small hand held GNSS receiver, one can estimate position, velocity and time. GNSS receivers form the integral part

of navigation, traffic management, military operations and emergency services. Standard receivers are able to locate

themselves with an accuracy of a few metres outdoors. This accuracy level is achievable with clear view of the sky with a

typical signal level of -130 dBm(Kaplan & Hegarty, 2006). The signal levels observed in indoor conditions are lower due to

additional attenuation caused by the building structure. An attenuation of tens of dB may be introduced depending upon the

material used for construction (Seco-Granados, López-Salcedo, Jiménez-Baños, & López-Risueño, 2012; Puricer & Kovar,

2007). Typical attenuation factors are 5-15 dB for residential houses, 20-30 dB for office buildings and above 30 dB [hence

mostly undetectable] for underground facilities (Mautz, Overview of current indoor positioning systems, 2009). A report

from the National Institute of Standards and Technology (NIST) provides details about the signal attenuations for different

building materials (Stone, 1997). Indoor environments are particularly challenging for several reasons. In many scenarios,


line-of-sight (LOS) signals might not be observable by the receiver and instead, many non-LOS (NLOS) signals might be

present. Sometimes, LOS and NLOS signals can be present simultaneously, leading to severe multipath distortions. Indoor

signals are highly attenuated and susceptible to scattering due to indoor artifacts. Indoor environments are also subject to

rapid temporal changes due to the movement of people and objects like doors (Mautz, Indoor Positioning Technologies,

2012).

Some GNSS receivers can estimate position indoors. However, accuracy is not sufficient for many applications. To enable

accurate indoor positioning, several alternatives exist such as

beacons that send out signals that cover large areas (e.g. using signals of opportunity like Wi-Fi signals, Bluetooth

signals, signals from cell towers or TV transmissions)

flickering light patterns from LED light fixtures

radio frequency identification tags (RFID) and inertial sensors.

Each of the above techniques works in specific scenarios. Therefore, hybrid systems that encompass two or more of the

above are generally used to provide effective positioning solutions for different indoor scenarios. In many cases, high

sensitivity GNSS receivers are used with the above techniques to further improve performance.

High sensitivity receivers work in different indoor scenarios by extending signal detection capability. The receiver should

then ideally be provided with additional information such as navigation data bits, satellite broadcast ephemeris, coarse user

position and time. If this information is available, coherent integration time can be extended, which will eventually enable

weak signal detection. To integrate beyond the navigation data bit period, navigation data bit transition epochs should also be

known. The following factors have a major impact on long term integration:

short term stability of the user clock

accuracy of the estimated trajectory occurring during integration

changes in the channel model during integration.

During the integration interval, the receiver clock should be stable as oscillator instability results in reduced effective

coherent integration time. Therefore, having a clock with good short term stability is important to achieve the expected gain

(Gowdayyanadoddi N. S., 2015). Similarly, if the user is in motion, signal changes should be compensated during integration

as errors in the estimated trajectory will also lead to reduction of integration gain. As discussed previously, studies have

characterized the signal attenuations as they pass though different building materials. However, an indoor signal model is not

merely dependent on attenuation. Because of the different building structures and materials used for the interior, each indoor

scenario is unique. Therefore, signals consist of different reflections, hence different signal characteristics. Even if the user is

static, due to the satellite motion and relative proximity of the reflecting surfaces, observed SNR values vary; if the user is in

motion, there will be different effects compared to the static case. Consequently, signals collected indoors continuously varies

over time. Similarly, signals received at two closely placed indoor antennas also differ. Therefore, it is important to

characterize channel model variation effects over space and time.

The effects of the above three factors on the coherent integration gain are studied in the sequel. Coherent integration

performance is characterized for three oscillators with different short term stabilities. Four different user trajectory error

profiles are simulated and coherent gain for each case is assessed. The effect of the indoor channel behavior is characterized

for static and moving antennas placed on a linear motion table. Spatial domain characteristics for two closely placed antennas

are then analyzed. Finally, intermediate frequency (IF) sample data is collected for a short duration every 30 minutes over a

seven-hour window and position estimates are compared to study time domain dependencies.

METHODOLOGY

Performance enhancement can be achieved with high sensitivity receivers by providing a priori information about

ephemerides, coarse user position and time. While extending the coherent integration time in such receivers, the processing

gain is affected by various metrics including contributions from the user clock drift and satellite motion. Assuming a high

sensitivity receiver that has access to ephemeris, coarse user position and time, a wider search grid is required to acquire all

available satellites; this results to an increase in the required processing power. As an alternative to the stand-alone receiver

architecture, the reference-rover based receiver architecture shown in Figure 1 is used herein to assess long coherent

integration performance. This is a modified form of the GSNRxTM

(Petovello, O'Driscoll, Lachapelle, Borio, & Murtaza,

2008) software receiver for high sensitivity signal detection. The receiver contains a reference and rover processing section;

the reference section processes the IF data collected from the open sky antenna and the rover section processes IF data


collected from an indoor antenna, shown in Figure 1. By having access to open sky data continuously, effects due to the

satellite motion on the processing gain are removed and the search grid is centered on the actual code-delay and Doppler tiles.

The code delay, Doppler frequency, time and navigation data bits extracted from the open sky signals are used to reduce the

search space while processing the indoor data for each PRN. Ephemerides available from the open sky data and estimates of

the open sky user position are used to select the mid-point of the cross-ambiguity function (CAF) search grid. The correlation

is performed for the incoming signal with a locally generated signal corresponding to each delay-Doppler pair and differential

measurements are formed based on the maximum value of the CAF. With this approach, the CAF function corresponding to

the indoor signal captures the effects due to satellite motion, user clock drift and at the same time makes the correlation

values free from the navigation data bit transitions that pose a limitation on extending the integration time. As a result, the

CAF contains effects that are mainly due to the indoor signal characteristics.

Indoor data was collected using a Maxtena helical antenna and a Novatel 702 GG antenna was used for open sky data

collection. IF samples were collected at the rate of 10.125 M samples/s with a phase-coherent multi-channel

Fraunhofer/TeleOrbit RF front-end using calibrated cabling; in this context ‘calibrated’ means that the bias contribution due

to each cable was determined in advance. The IF samples were processed using the reference-rover receiver configuration

described above.

Figure 1: Reference-rover based strategy to aid weak signal acquisition

The differenced pseudorange obtained using the maximum value of the CAF is given by

,i i i

peak geo cc MPDR b (1)

where i

peakDR is the relative pseudorange corresponding to the ith

satellite, i

geo is the geometric range difference between

the open sky antenna and indoor antenna for the ith

satellite, ccb is the bias added due to the difference in cable lengths and

connectors between open sky and indoor antennas, i

MP is the multipath component due to all reflections for the ith

satellite,

and is the pseudorange error contribution due to noise.

The pseudorange corresponding to the indoor antenna is given by

,i i i

rov ref peakPR PR DR (2)

where i

rovPR is the pseudorange for the ith

satellite corresponding to the indoor antenna and i

refPR is the pseudorange for ith

satellite corresponding to the open sky antenna.

Acquisition, Tracking & Positioning

Open sky antenna

Indoor antenna Position of the open sky antenna,

Code phase, Carrier Doppler, Navigation data

Post-processing

(Measurement generation, position computation,

pseudorange error analysis)

Acquire & obtain the Cross Ambiguity Function (CAF)

REFERENCE

ROVER


The pseudorange (PR) error for the ith

satellite is expressed as

.i i i

PR peak geo ccDR b (3)

Another metric used during characterization is the SNR given in decibels as (Gowdayyanadoddi N. S., 2015; Kaplan &

Hegarty, 2006)

( ) 10 ( )

0

10log ,dB CI dB

CSNR G

N

(4)

where C is the recovered desired signal level, 0N is the noise density and( )CI dBG is the coherent integration gain. Coherent

integration gain is obtained as

( ) 1010log ( ),CI dB CG T (5)

where CT is the coherent integration time in seconds.

Based on the cases considered for analysis in this work, different data collection setups were used. Details of the setup used

for each test are provided below.

RESULTS AND ANALYSIS

The results are divided into three sub-sections. Firstly, the effects of clock stability and trajectory errors on the long-term

integration gain are assessed. Also, channel model variations are compared for static and slowly moving antenna. Secondly,

IF data collected with two closely placed static antennas is analyzed. Thirdly, corresponding to a static indoor site, two-

minute data segments were collected every thirty minutes for about seven hours; the time variations of position errors are

studied for the segments. GPS L1 C/A signals are used for the analyses. The IF datasets required were collected at two sites;

one in a concrete building and the other is a town house with brick walls.

The GPS satellite spatial distributions during the data collection campaigns are shown in Figure 2 (Trimble, 2017).

Using cables of different lengths during data collection introduces different biases in pseudorange characterization. Even

though this bias component is common for all satellites and is removed during position estimation, it is crucial to know its

magnitude for pseudorange error analysis. Therefore, biases occurring in the cables are individually measured. IF data

corresponding to all test cases that involved pseudorange error analysis was collected at a pre-surveyed site to enable this

error analysis. The acquisition search was performed in the code domain from -1 chip to +1 chip at a resolution of 0.02 chips

and in carrier Doppler domain from -1 Hz to +1 Hz with a step size of 0.25 Hz.

(a) (b) (c) (d)

Figure 2: Sky plot corresponding to (a) Clock effect comparison test: concrete building (b) Clock effect comparison

test: Townhouse (c) Channel model effects test and spatial diversity test in concrete building (d) Temporal diversity

test in concrete building


Assessing contributions from parameters affecting long term integration

As previously discussed, the three main factors that have a major impact on the long term integration are the short term

stability of the user clock, the accuracy of the estimated trajectory used during integration, and changes in the channel model

during integration. Individual contributions due to each one of these are analyzed below.

User clock stability

Setup used to compare clocks:

Four different clocks, namely a BVA, OCXO, TCXO and MEMS are used. The BVA unit is a 10 MHz ultra-stable oscillator

exhibiting excellent short term stability which uses BVA (Boîtier à Vieillissement Amélioré) technology(Gaggero, 2008;

Oscilloquartz, 2005). The OCXO is the internal oven controlled crystal oscillator (OCXO) clock output from the National

Instruments (NI) RF front-end. The TCXO is a temperature compensated crystal oscillator (TCXO) from Fordahl (part

number: DFA S1-LHZ10 MHz). The MEMS is a resonator based on micro electro mechanical systems (MEMS) technology,

from Sand 9 Inc. The frequency of all clocks is 10 MHz and their stability comparison is given in Table 1.

Table 1: Comparison of clock stability parameters

Clock Short term stability Deviation (ppm or ppb) Allan deviation

BVA Very good/excellent 2.5x10-13

(1-30s)

OCXO Good ±20 ppb

TCXO Moderate <10-10

MEMS Low 150 ppm

The BVA clock was used to collect the open sky data with the 702 GG antenna in all cases and indoor static data was

collected using each of the other three clocks separately. Indoor data was collected at the following three sites:

Indoor: Site-1 – Navigation lab in the 3rd

floor of a concrete building on the University of Calgary campus. Room

includes concrete structure with some openings for glass windows on two sides of the room.

Indoor: Site-2 – Main floor of a townhouse with brick walls

Indoor: Site-3 – Basement of above townhouse

The data collection setup is shown in Figure 3 and pictures of the sites are shown in Figure 4.


Figure 3: Test setup for static tests Figure 4: Data collection environment showing the site

location for each case: (a) Concrete building (b) Townhouse

In this section, SNR values are used as a metric to evaluate the processing gain degradation or detection performance.

Description of results:

The coherent integration time was set to different values in increasing order from 20 ms to 5 s. The BVA clock was used for

collecting the reference data (open sky data) and OCXO, TCXO and MEMS units were used for indoor data collection. The

SNR profiles for the OCXO, TCXO and MEMS units at Site-1 are given in Figure 5 (a), Figure 5 (b) and Figure 5 (c),

respectively. At this site, PRN23 had a high signal level for all the oscillators as the signal was coming through the window

and PRN7 had a low SNR as the signal was coming through multiple reflections. For the OCXO, the processing gain

continues to increase with an increase in integration time. The SNR trend indicates increase in gain even beyond 5s of

integration, providing an indication that integration might be further extended to increase gain. OCXO long term coherent

integration beyond several seconds was possible due to its good short term stability. By doubling the coherent integration

time, up to 3 dB gain in signal power can be achieved (Kay, 1998). Based on this proposition, for PRN7 one would expect a

gain of approximately 24 dB, as the integration time is increased from 20 ms to 5 s. However, gain was observed to be 20 dB,

4 dB lower than the expected value. During the initial integration time increase, the gain was found to be a function of the

latter. However, only a small increase in gain or in other words gain saturation was observed while increasing the integration

time beyond 3 s. Indoors, signals are attenuated and signal levels are low and are affected by higher indoor noise levels.

Exponential increase in the SNR profile for initial increase in the coherent integration time is mainly due to the reduction in

noise levels and coherent signal gain. As the integration time is increased, a slight increase in signal gain is still observed,

however SNR improvement due to noise reduction is insignificant as the majority of the noise effects would have already

been reduced by averaging.

Figure 5: SNR Comparison for different clocks in concrete building (a) OCXO (b) TCXO (c) MEMS

TeleOrbit front-

end

MEMS

clock

IF data recorder

BVA

clock

External TCXO

Open sky

antenna

(Novatel 702

GG)

Indoor

antenna

(Maxtena) OCXO output

from

NI front-end

Indoor

Maxtena antenna

Townhouse with

brick wall

Mainfloor

Basement

(a)

(b)


Coherent integration performance was evaluated for only TCXO and MEMS clock in the townhouse scenario. SNR

variations obtained by varying the integration times for the data collected in the basement and main floor are given in Figure

6. Comparing the SNR variations for all scenarios by using the TCXO, the integration gain increases as integration time

increases up to 1s and then starts decreasing beyond that time. Signals being received at a receiver antenna are generated by a

stable onboard clock at the satellite. In order to wipe off carrier and code components in the incoming signals, local replicas

of carrier and code are generated using the reference clock available in the receiver. Due to different clock characteristics at

transmitter and receiver, generating a perfect replica that matches incoming signals is challenging. Signal loss over the

integration period depends on the stability of the clock present in user receiver. As seen from the results, based on the short-

term stability characteristics of TCXO, integrating beyond some interval (about 1 s) leads to gain degradation. This behavior

further worsens for the MEMS clock where the integration gain starts dropping beyond 200 to 300 ms. The OCXO provides

best long term coherent integration performance, then the TCXO and lower performance occurred with the MEMS clock.

This observation is also in accordance with the stability metrics provided in Table 1.

Average signal attenuations of 17.3 dB, 9.2 dB and 18 dB were observed in the concrete building, townhouse main floor and

townhouse basement respectively.

(a) (b)

(c) (d)

Figure 6: SNR Comparison for different clocks in townhouse (a) TCXO-main floor (b) TCXO- basement (c) MEMS-

main floor (d) MEMS-basement


Processing gain performance as a function of user trajectory drift

For moving users, the coherent integration gain depends on the accuracy of the estimated trajectory of the user. To evaluate

this degradation, user trajectory drifts were simulated.

Setup used to simulate trajectory errors:

The GPS signals required for this test were generated with an IF software simulator; satellite and user data and other signal

parameters were taken from the Spirent simulator’s scenario files and signals were regenerated in software considering actual

code delays, carrier Doppler and navigation data corresponding to each satellite. A user moving in a straight line in the North

direction (in East-North horizontal plane) was simulated. To undertake the analysis, errors in this trajectory were simulated

and four profiles were considered with different final errors values ranging from 0.25 m to 1.5 m in 500 ms. The

corresponding placements of the satellites above the user and error trajectories used in integration are given in Figure 7(a)

and Figure 7(b), respectively.

(a) (b)

Figure 7: Simulation of trajectory errors: (a) GPS satellite visibility corresponding to simulated data (b) Error

trajectories considered


Signals corresponding to different PRNs were integrated from 20 to 500 ms and SNR values obtained for each case are

provided in Table 2. Each cell entry in the table contains SNR for error profile-1, 2, 3 and 4 respectively, and PRNs are

arranged in the increasing order of their elevation angles from left to right in the table. The SNR values observed for all PRNs

for error (0.25 m) profile-1 and error (1.5 m) profile-4 is given in Figure 8 and Figure 9.

Table 2: SNR for four error profiles for different integration times

SNR (dB)

Satellite identifier

PRN18 PRN7 PRN17 PRN15 PRN28 PRN27

Inte

gra

tio

n t

ime

(ms)

20 34 / 34 / 34 / 34 34 / 34 / 34 / 34 33 / 33 / 34 / 33 33 / 33 / 33 / 33 33 / 33 / 33 / 33 34 / 34 / 34 / 34

50 37 / 36 / 36 / 35 37 / 37 / 37 / 37 36 / 35 / 35 / 35 36 / 36 / 36 / 36 36 / 36 / 36 / 36 36 / 36 / 36 / 36

100 38 / 37 / 35 / 31 38 / 38 / 38 / 38 37 / 36 / 35 / 32 38 / 38 / 38 / 37 38 / 38 / 38 / 38 38 / 38 / 38 / 38

150 39 / 35 / 30 / 25 39 / 39 / 39 / 39 37 / 35 / 30 / 20 39 / 39 / 38 / 37 39 / 38 / 38 / 38 39 / 39 / 39 / 39

200 38 / 28 / 26 / 27 39 / 39 / 39 / 39 37 / 30 / 20 / 27 39 / 39 / 38 / 35 39 / 39 / 39 / 38 39 / 39 / 39 / 39

300 35 / 30 / 20 / 18 40 / 40 / 40 / 39 35 / 26 / 24 / 23 39 / 38 / 34 / 25 39 / 39 / 38 / 37 39 / 39 / 39 / 39

400 21 / 17 / 20 / 21 40 / 40 / 39 / 38 29 / 25 / 24 / 19 39 / 34 / 26 / 30 39 / 39 / 37 / 32 40 / 39 / 39 / 38

480 28 / 26 / 21 / 20 40 / 40 / 39 / 37 21 / 25 / 24 / 19 39 / 28 / 31 / 26 40 / 38 / 35 / 30 40 / 39 / 39 / 35

Note:

1) Each cell entry contains SNR for error profile-1, 2, 3 and 4 respectively

2) PRNs are arranged in the increasing order of their elevation angles from left to right in the table


Figure 8: SNR at different integration times for different

PRNs arranged in increasing order of their elevation

from left to right for error profile-1 (0.25 m)

Figure 9: SNR at different integration times for different

PRNs arranged in increasing order of their elevation

from left to right for error profile-4(1.5 m)

The relative motion between satellites and the user gives rise to carrier and code Doppler effects. Since GNSS satellites are in

motion Doppler effects occur even for stationary receivers. For a kinematic user, additional effects occur. Doppler effects

caused by satellite motion are calculated using coarse time, user position and known satellite ephemeris. Doppler changes due

to user motion also need to be considered. The reference user trajectory is used to calculate Doppler frequencies caused by

user motion which has to be considered in performing long coherent integration.

As the signals are generated in a controlled signal environment, signal levels are set to 40 dB-Hz in an AWGN channel.

Under ideal conditions, by increasing the coherent integration time one should expect to see improvement in the SNR. The

results show that, when performing integration when trajectory errors are present, SNR initially improves and then drops as

integration time increases. This is the result of trajectory errors. Lower elevation satellites experience a larger effect because

the user motion is in the horizontal plane. SNR degradations for various integration times are listed in Table 2. As previously

mentioned, signals used for this test were generated using software simulations assuming a perfect oscillator. Therefore, the

SNR degradations do not have any contributions due to user clock instability. PRN7 is a low elevation satellite; since it is

orthogonal to the user motion, it is less affected. Even though different satellites get affected differently based on their

position with respect to the user motion, integration gain can be significantly compromised due to user trajectory errors.

Channel model variations

The main goal in this section is to characterize the temporal and spatial variations of the indoor channel. For this, data was

collected using two antennas, one static and another moving.

Setup used to analyze channel variations:

As shown in Figure 10, two indoor helical antennas were used for this analysis and IF data corresponding to actual GNSS

signals was collected at indoor Site-1. One of the antennas (Antenna-1 in Figure 10) was stationary and another (Antenna-2

in Figure 10) was subjected to slow linear motion. To perform the linear motion, an Anorad table was programmed to move a

distance of 40 cm back and forth in the North-South direction at the rate of 1cm/s. One of the indoor antennas was placed on

the motion table. The static antenna was placed at a distance of roughly 40 cm from the moving antenna. Due to its high short

term stability, the BVA clock was used as the source for all data channels of the front-end. A coherent integration of 1 s was

used.

18 7 17 19 10 8 15 26 28 2715

20

25

30

35

40

PRN

SN

R (

dB

)

No error

20ms

50ms

100ms

150ms

200ms

300ms

400ms

480ms

18 7 17 19 10 8 15 26 28 2715

20

25

30

35

40

PRN

SN

R (

dB

)

No error

20ms

50ms

100ms

150ms

200ms

300ms

400ms

480ms


(a) (b)

Figure 10: Data collection environment for static and motion tests: (a) Facing North (b) Facing South


SNR variations for static and slow linear motion cases are shown in Figure 11 and Figure 12. For the static data case, a slow

varying pattern can be seen in the SNR indicating the constructive and destructive nature of indoor multipath signals. As

shown by Gowdayyanadoddi et al (2015), in the presence of multipath, a slow linear motion leads to faster decorrelation of

the multipath, which is also evident in Figure 12. Linear constant motion brings in only an offset in the carrier Doppler;

therefore, user trajectory is not considered in the coherent integration process.

There are higher SNR variations and an increase in the SNR mean when the antenna is moving. The signal levels and the

SNR statistics for all PRNs for static and moving cases are given in Table 3. The pseudorange (PR) errors corresponding to

the static and linear cases are also provided in Table 3.

Figure 11: SNR variation for all PRNs: static Figure 12: SNR variation for all PRNs: slow linear motion

Table 3: PR errors and SNR statistics for different PRNs for static and slow linear motion


PRN7 PRN9 PRN16 PRN23 PRN26 PRN27

Sta

tic

PR error mean (m) /

PR error RMS (m)

-19.4 / 21.0 -18.4 / 20.7 -2.4 / 8.4 2.7 / 14.4 -4.3 / 15.3 -5.6 / 12.7

SNR mean (dB) / SNR

RMS (dB)

14.7 / 3.4 16.3 / 4.4 24.2 / 2.2 23.4 / 6.2 17.9 / 3.2 14.1 / 3.4

Lin

ear PR error mean (m) /

PR error RMS (m)

-60.3 / 13.5 -32.5 / 27.2 -6.3 / 19.5 -3.6 / 16.5 -14.3 / 20.2 -21.3 /

23..1

SNR mean (dB) / SNR

RMS (dB)

19.6 / 3.7 22.8 / 4.6 26.9 / 4.2 28.1 / 5.4 21.6 / 4.6 15.6 / 4.2

Antenna-1

Antenna-2


Since the reference-rover based strategy is used during differential pseudorange generation, the pseudorange errors given in

Table 3 have contributions only from indoor multipath and noise. Due to the slow linear motion, one would expect to see an

error reduction due to multipath decorrelation. However, during that time, the standard deviation of the SNR increases in the

moving case compared to the static case. Since it is difficult to segregate the error contributions due to multipath and noise,

these two error contributions are lumped together. Measurements seem to have less benefitted from motion; instead, errors

during linear motion increase compared to the static case.

Spatial diversity

Similar to the setup used to characterize channel model variations, two indoor antennas were used to analyze the channel

variations in the spatial domain. Both antennas were kept static with a separation of roughly 40 cm. A coherent integration of

1 s was used.

This section explores potential advantages of using data over closely placed antennas indoors. The SNR profiles observed at

static antennas placed at a distance roughly 40 cm from each other are given in Figure 13 and Figure 14. Figure 13 shows the

SNR variations of antenna 1 while Figure 14 shows relative SNR of antenna 2 with respect to antenna 1. Clearly, for various

PRNs the instantaneous received signals at two antennas differs. PR errors corresponding to each antenna are given in Table

4.

Figure 13: SNR variation for all PRNs: Static antenna-1 Figure 14: Ant2-Ant1 SNR variations for all PRNs

Table 4: PR error and SNR statistics for two nearby static antennas


PRN3 PRN7 PRN9 PRN16 PRN23 PRN26 PRN29

Sta

tic-1

PR error mean (m) -10.4 -59.7 -25.7 1.6 -27.1 -2.8 -19.7

SNR mean (dB) 17.1 16.6 22.5 27.1 24.6 26.5 17.0

Sta

tic-2

PR error mean (m) -5.2 -45.0 -1.1 2.6 3.9 -0.1 -9.0

SNR mean (dB) 15.8 11.6 19.4 30.0 25.9 23.8 16.5

For most PRNs, the average PR errors for static antenna-2 were observed to be lower than those at antenna-1. One would

expect that with better signal levels the PR errors should be lower. However, the average SNR values for most of the antenna-

1 PRNs were relatively higher than those of antenna-2. In an attempt to combine the measurements from two antennas,

selection combining of measurements was done based on the SNR. Considering all PRNs, combining the measurements from

multiple closely placed antennas will definitely lead to performance enhancements; however, as indoor environments are


subjected to constructive and destructive multipath, the use of the instantaneous SNR as a metric for combining might not be

sufficient.

Measurements surpassing the SNR threshold of 15 dB were used for position estimation for antenna-1 and antenna-2 and the

position errors obtained in east, north and up (ENU) coordinates are given in Table 5. Similar to the analysis of PR errors,

average 3D position errors for antenna-2 (30 m) were found to be lower than the errors for antenna-1 (45 m).

Table 5: Position errors obtained for two nearby static antennas

Average position error (m)

East North Up C

ase

Static-1 19.7 -6.4 -40.2

Static-2 -2.2 25.7 -15.9

Temporal diversity

Another important factor to be evaluated is performance over time. As observed from the previous analysis of spatial

diversity data, pseudorange measurements corresponding to different satellites were affected in different manner as a function

of indoor multipath. Changing multipath characteristics will result in different pseudorange errors. Consider the case of static

indoor positioning where the final objective is to provide accurate solutions. For many such applications, obtaining an

accurate position is important compared to the time required to obtain it. Therefore, this case provides the flexibility to collect

data over a longer time window.

It was observed during previous analyses of SNR variations in Figure 13 and Figure 14 that the SNR profile varies over time,

indicating related changes in the indoor channel characteristics. Pseudorange error behavior changes based on the SNR and

position errors directly depends on the pseudorange errors.

For this time domain analysis, IF data was collected from only one indoor antenna. Two minutes of IF data was collected

every thirty minutes over a time window of seven hours. Coherent integration of 1 s was used. The satellite sky-plot during

data collection is given in Figure 2(d). As the data was collected at a pre-surveyed point, the true position was known and the

errors were computed with respect to this position; these are given in Figure 15 and tabulated in Table 6.

Figure 15: Position error bar plot for 15 datasets collected every 30 minutes

Position errors for different data sets were found to differ. This is due to the changes in geometry and in measurement errors

as function of time. By averaging dataset position estimates, the position accuracy has improved. The position errors in the

9 9:30 10 10:30 11 11:30 12 12:30 1 1:30 2 2:30 3 3:30 4 Mean

-10

0

10

20

30

40

50

Data set identifier

Po

sitio

n E

rro

r (m

)

East

NorthUp


vertical direction were found to be higher in all cases due to satellite geometry. The two-dimensional position spread of all

datasets is given in Figure 16 and the corresponding 3D position errors are given in Figure 17.

Table 6: Position errors obtained for 15 data sets collected every 30 minutes spanning 7 hours

Average position error (m)

East North Up

Da

ta s

et i

den

tifi

er

9am 0.48 4.67 17.4

9:30am -5.45 0.18 12.41

10am -1.03 -5.72 -5.13

10:30am -3.5 0.4 17.61

11am 0.89 6.73 6.03

11:30am -5.56 0.99 16.07

12pm -3.94 -9.7 8.38

12:30pm 32.4 4.49 51.85

1pm -4.61 -3.81 5.27

1:30pm -5.89 -0.69 16.81

2pm -2.42 -5.73 11.56

2:30pm 1.02 1.01 3.78

3pm -14.50 5.57 50.51

3:30pm -3.65 -1.40 33.31

4pm 4.71 -1.98 45.33

mean position (considering all above samples) -0.74 -0.33 19.4

Figure 16: 2D position spread for 15 datasets collected

every 30 minutes

Figure 17: Time series of 3D position error for 15 datasets

collected every 30 minutes

-60 -40 -20 0 20 40 60-60

-40

-20

0

20

40

60

East error (m)

Nort

h e

rror(

m)

9am

9:30am

10am

10:30am

11am

11:30am

12pm

12:30pm

1pm

1:30pm

2pm

2:30pm

3pm

3:30pm

4pm

0 20 40 60 800

50

100

150

200

250

Time (s)

3D

err

or

(m)

9am

9:30am

10am

10:30am

11am

11:30am

12pm

12:30pm

1pm

1:30pm

2pm

2:30pm

3pm

3:30pm

4pm


CONCLUSIONS

Different factors that contribute towards GNSS weak signal detection, measurement generation and position solutions were

assessed. A comparison of SNR values for different coherent integration times using different clocks showed the coherent

integration limits occurring with three clock types. OCXO based oscillators improved extended coherent integration

performance as compared to the use of MEMS clocks in which case integration time was limited to a few hundred

milliseconds. By analyzing coherent integration for different user trajectory error profiles, it was found that a few metres of

trajectory error can compromise signal detection performance depending on the relative motion between receiver antenna and

satellite. Indoor channel characterization showed that signal level variations due to multipath fading can reach 20 dB in the

environment tested. Spatial antenna diversity using two static indoor antennas demonstrated good independence of signals

received at each antenna, which can be used to improve signal level in fading environments. It was also found that position

accuracy in indoor scenarios can be significantly improved (horizontal accuracy better than 1 m for the scenario considered)

by collecting short intermittent samples over a long duration. This can be particularly useful for the case of determining

positions of static cell transmitters in the indoors.

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