GPS Fundamentals

[GNSS(global navigation satellite system)]

agilent-gps fundamentals.pdf

GPS(USA)=1575MHz, Glonass(Russia)=1602MHz, Galileo(EU)=1575MHz, Compass(China)=1590MHz, QZSS(Japan)

[GPS Signal Format]

[GPS Signal Mathematics]

lu-GPS signal level.pdf

GPS 궤도: 지표면과 20,200km

Received power at the Earth's surface: –130dBm with 0dBic antenna

SV EIRP 13.4dBW

Free-space loss (25,092km) -184.4dB

Attmospheric attenuation -2.0dB

User antenna gain(hemispherical) 3.0dB

Depolarizatio loss -3.4dB

-----------------------------------------------------------

User receiver power -160dBW = -130dBm

Thermal noise power per Hz -174dBm/Hz

User receiver C/N₀ ratio 44dBHz without receiver noise

Typical average received power -125dBm

High-sensitivity receiver -158 to -152dBm

(bilich-gps receiver SNR.pdf)

(maccougan-hsgps.pdf)

GPS receiver sensivity:

langley-gps receiver noise.pdf

Shannon-Hartley theorem: in Gaussian noise environment

C: channel capacity = data rate = bps

B: channel's passband bandwidth

N: total noise power in the bandwidth B

Example: spread-spectrum communication. C = 12.2kbps, B = 5MHz → S/N = –27.7 dB, S/N << 1, (N₀: white noise)

Nyquist rate: (number of pulses per second)

CNR: at pre-detection in the RF stage. Used to check the health of the RF channel

SNR: at pre-modulation or post-detection

Signal-to-noise ratio unit: C/N (or S/N) depend on the bandwidth of the receiver's tracking loop, which is not necessarily constant nor publicly available. Thus, the C/N or S/N is scaled by the receiver to the standard bandwidth of 1Hz, which results in bandwidth-independent C/N₀ or S/N₀ measured in dBHz units.

GPS receiver sensitivity:

Acquisition sensitivity: -140 to -150dBm

Tracking sensitivity: -150 to -160dBm

Sensitivity formulas:

1) (simple estimator)

C/N₀ = 174-130-2 = 42dB

P_s = -130dBm

kT₀ = -171dBm/Hz

I₀ = power density of the interfering signal per Hz

C/N₀ = 단위 dB-Hz. open sky 40-50dB-Hz, 도심지 15-40dB-Hz, 실내 25dB-Hz 이하.

System noise temperature:

(receiver thermal noise), k = 1.38×10^-38 W/(K·Hz) (Boltzman's constant)

T_a = 130 K, α = 0.91, NF = 1.5 dB, T_sys = 263 K

N (at the antenna input) = –174 dBm/Hz

C/N₀ = –130–(–174) = 44 dB

GPS antenna noise:

T_ant = antenna noise temp.

α: antenna cable loss (fractional)

T_a: antenna noise temperature w/o cable loss. 130 K (typ.)

Received power at the Earth's surface: –130dBm with 0dBic antenna

C/N₀ = 44dBHz with a 0 dBc gain antenna. A common commercial GPS receiver can acquire the GPS signal above 38 dBHz.

C/A code band width: 4MHz, N = -108dBm

S/N = –22dB

Indoor attenuation: 15-30dB. Low SNR requires a longer acquisition time.

Processing gain = 10 log (chip rate/data rate) = 43 dB, chip rate = 1.023 Mcps, data rate = 50 bps

Post-correlator E_b/N₀ = 9.5 dB for BPSK with BER = 10^‑5 (AWGN dominated). E_b = energy per bit

Post-correlator E_b/N₀ = processing gain × SNR

Pre-correlator SNR = post-correlator E_b/N₀ – processing gain (dB) = –33.5 dB

Software GPS implementation loss = 3.5 dB

SV Acquisition time vs signal level:

[GPS Receiver Architecture]

GPS signals are acquired and tracked by hardware and software techniques that vary considerably from receiver to receiver.

Modern receivers are largely digital in design and used software-based digital signal processing techniques often with 12 or more parallel channel receivers.

Almanac: used in a receiver to determine SVs visible and the Doppler shift for each SV. Valid for 3 months.

Ephemeris: used to calculate the precise position of each SV. Valid for 4 hours.

Ionospheric model: transmitted every 12.5 min.

GPS-UTC time correction parameters: transmitted every 12.5 min.

First SV acquired → Calibrate the receiver oscillator → Reduce search space for subsequent SV searches.

• Front-end

	LNA	SAW	Coax	RF	Mixer	IF	NF(total)
G(dB)	28	-1.5	-3.9	19	-6	19
NF(dB)	0.8	1.5	3.9	3.3	6	7	1

High-sensitivity receiver:

maccougan-hsgps.pdf

In high-sensitivity receivers, massive parallel correlation is necessary to facilitate the complex task of searching for weak GPS signals while using long coherent integration periods and further non-coherent accumulation.

(diggelen-a-gps.pdf)

(maccougan-hsgps.pdf)

(diggelen-a-gps.pdf)

High-sensitivity GPS receiver architecture

(diggelen-a-gps.pdf)

Coherent and non-coherent integration:

(diggelen-a-gps.pdf)

Coherent integration: sequential correlation of multiple 1ms sequences (N times). Signal voltage increase by a factor of N while the noise (uncorrelated and not band-limited) voltage increases by a factor of N¹^/2. The gain by a coherent integration is given by

Every 20ms there is a possible navigation bit transition that can change the phase of the correlation peak. This 20ms period limits coherent integration of the GPS signal unless the navigation bits are known a-priori. In addition, any residual frequency error after Doppler removal can cause the power in the in-phase component to increase such that there is no point in further integration. In other words, coherent integration is very sensitive to frequency error.

Non-coherent integration uses the square root of the sum of squares of the in-phase and quadrature phase signal components after coherent correlation of some interval.

I₃, Q₃ = the accumulated in-phase/quadrature-phase coherent signal after correlation.

M = number of incoherent accumulations

Navigation bits become irrelevant in the non-coherent integration and some residual frequency errors during non-coherent accumulation that are within the carrier tracking bandwidth of the receiver can be tolerated. However, squaring of the signal in non-coherent accumulation also results in squaring of the noise and results in squaring loss.

The squaring loss is significant if the post coherent correlation SNR is low. Thus, maximal coherent integration prior to non-coherent integration results in less squaring loss.

The total processing gain is given by

The limitations of coherent accumulation are data bit transitions and residual frequency errors. Predicting the data bit transitions and limiting residual frequency errors during coherent correlation is necessary to obtain optimal gain prior to non-coherent accumulation. This is because reduction of the resulting squaring loss is paramount to beneficial non-coherent accumulation. The limitations of coherent correlation are highly dependent on the receiver operating mode. If the receiver is already tracking the GPS signals, the task of maintaining signal tracking under weak signal conditions is much easier than acquisition of weak GPS signals.

For weak signal acquisition

- Maximize the coherent integration interval prior to non-coherent accumulation.

- Minimize residual frequency errors during coherent integration: oscillator instability, user-motion induced Doppler effects, thermal noise inducing frequency error jitter. Thermal noise can often be a dominant source of carrier tracking error, especially for weak GPS signal tracking.

- Minimize the impact of the thermal noise.

The amount of tolerable frequency error during the total dwell time depends on the length of coherent integration and the type of carrier tracking performed. A frequency lock loop and/or a phase lock loop are used to perform Doppler removal.

- Minimize the signal loss in the signal chain.

(maccougan-hsgps.pdf)

Receiver architectures:

[Commercial GPS Receivers]

• Common: update rate 1-20Hz, dynamic = 4g, 515m/s, 18km altitude; 55mW power tracking. 0.9dB NF 20dB gain LNA, 1.2dB Rx chip NF, SBAS(WAAS/EGNOS) support, 7-day extended ephemeris AGPS, multipath detection and mitigation, Jamming detection and mitigation

• Sensitivity = -148dBm(cold start), -165dBm (tracking), 소요시간에 관계없이 위성을 포착할 수 있는 최소 신호 레벨

• TTFF spec.: with 0dBic antenna.

• SkyTraQ(US) Venus628LP: single-chip 7x7mm, 65-ch., 8M time-freq search/sec (8MIPS), 2.5m CEP, TTFF(open sky) = 29s(cold), 1s(hot), 3.5s AGPS; Re-acq. < 1s

• Falcom(Germany) USB-GPS-Stick: u-blox UBX-G5010 single chip (u-blox 5 engine), 50-ch., high sen. for indoor fix., extremely fast TTFF at low signal levels, Galileo capable, A-GPS support, integrated TCXO, CMC antenna, 1M effective correlator, TTFF less than 1s with long correlation/dwell times, 4Hz update; TTFF= 29s(cold), 29s(warm), <1s(hot); sensitivity = -144dBm(acq.), -160dBm(track), antenna peak gain -1dBic

• US Technology UST-SNR-GPS: 18x18mm ceramic antenna w/o larger ground plane, -1dBic max. gain, MTK MT3318 chipset, 50-ch.; DPGS RTCM protocol WAAS, EGNOS, MSAS; 3m CEP; TTFF = 36s(cold), 33s(warm), 1s(hot), <1s(reacq.); sensitivity = -146dBm(cold), -158dBm(track), -158dBm(reacq.)

• SiRF star III: Digital and RF in a single chip, 200,000+ effective correlator, 12-ch, L1 C/A code, 10Hz update,

- Reference signal level: open sky = all SV > -144dBm, indoor = 7 SV's at -155dBm, 1 SV at -147dBm

- AGPS by CDMA: open sky < 1s, indoor < 18s

- Hot start: open sky < 1s, indoor <15s

- Cold start: open sky < 35s

- Tracking sensitivity -159dBm

- Position accuracy: <10m autonomous, <5m SBAS

SiRF III with 21*13*4 chip antenna (sirf iii-GP-635T-121130.pdf): CEP < 2.5m (-130dBm), acquisition -147dBm, tracking -161dBm, hot start 1s, warm and cold starts 27s; 20 ch,, 200k correlators

• ublox-5(ublox-5 with sarantel qha.pdf, gps_bee-ublox.pdf): NEO-5G, 50ch, 1M correlators, -3.5dBic antenna gain, hot start < 1s, cold and warm starts 29s, cold start -144dBm, reacquisition -160dBm, tracking & navigation -160dBm

• Fastrax UP501(fastrax-UP601.pdf, fastrx_product_leaflet_11-2011.pdf): high-sensitivity GPS, 66 chs for acq., 22 chs for tracking, cold start -148dBm, navigation -165dBm, hot start 1s, cold start 33s

• Fastrax IT530M: fastrax-IT530M.pdf

위성종류: GPS L1, Glonass, Galileo(w/ firmware upgrade), Beidou(w/ firmware upgrade)

채널수: 99(탐색), 33(track)

크기: 9.6*9.6*1.85mm

전력소모: 항법 57mW(3.0-4.3V), 백업상태 = 30mW(2-4.3V)

TTFF(-130dBm 수신전력 시): cold/warm start = 23s, hot start = 1s, Self-assisted ephemeris data를 생성하여 최초 ephemeris data 입력 후 3일 이전까지 3초 이내에 위성 포착 가능.

감도: acquisition = -148dBm, re-acquisition = -160dBm, tracking/navigation = -165dBm

정확도(-130dBm 신호 입력시): 위치 3.0m, 속도 0.02m/s, 시간 1ms

Anti-jamming: AIC(active interference cancellation)

[Causes of the GPS Signal Variation]

kirchner-gps multipath.pdf

Multipath interference

Satellite transmitting antenna gain pattern

Path length variation due to SV movements

Receiving antenna gain pattern

[GPS Signal Multipath Interference]

kos-gps mutipath effect.pdf

yedukondalu-gps multipath mitigation by adaptive filtering.pdf

byun-gps multipath.pdf

Types: carrier phase multipath, code multipath

Effects: 1) signal strength reduction, 2) increased positioning error

Pseudorange is the time shift required to correlate a replica of the code generated in the receiver with the received code from the satellite, multiplied by the speed of the light (the inaccuracy of the receiver clock's absolute time is not calibrated). The alignment (correlation peak) is done by a correlation detector. In the presence of a multipath signal, the resulting cross-correlation function is distorted, and the peak of the function is displaced from its correct position. This shift of the correlation peak introduces a pseudorange error.

As different receivers deal with the signals on a different way, multipath error can be dependent on the architecture of the receiver.

Due to the much shorter chip length, P-code ranging signals are much less sensitive to the multipath reflections.

Multipath effect may cause an error up to 150m for C/A code measurements, and up to 15m for P-code.

Multipath mitigation by antenna: 1) antenna placement (as high as possible from roof surface, away from nearby structures), 2) the use of RHCP antenna, 3) the suppression of ground reflections using a specially designed antenna such as the choke ring antenna.

Multipath mitigation by signal processing: use a larger bandwidth combined with much closer spacing of the early and late reference codes ( < 1/2 chip). Narrow bandwidth causes rounding of the cross-correlation function peak. The direct and reflected signal component peaks are rounded, and the sloping side of the reflected signal can shift the position of the resultant correlation peak. 1 C/A chip = 293.3m.

To reduce multipath effect on the positioning performance, receiver manufacturers have developed specific correlation configurations. Typical values of pseudorange error for so-called narrow correlators are 10-15m. Modern technology GPS receivers have multipath detection firmware.

Another signal processing technique for multipath mitigation is the delay lock loop developed by Novatel.

Multipath effects are greater on pseudorange measurements than on carrier phase measurements. Multipath errors of up to 3cm are commonly encountered in carrier phase measurements.

[GPS Signal Decoding]

GPS Acquisition:

• Simultaneous (2D) search Doppler frequency shift and code offset (delay)

• Correlation: multiplying GPS signal with a locally generated version of the satellites CDMA code with a given delay.

• Integration: search of the exact delay producing the maximum correlator output. 1ms(=C/A code repetition time) for strong signal. For weak signals, the integration time increased to enhance S/N.

• Time for Doppler frequency fix: proportionally increased as integration time increased.

• Acquisition time: proportional to the square of integration time. N²

• World record: -183dBW using 265ms integration period

• Cross correlation: correlation between SV codes. less than autocorrelation by 24dB.

• Doppler processing: sequential method (slower, overall acquisition time N²), non-sequential FFT method (faster, overall acq. time, N^1.5)

Code and carrier PLL: to track time delay, carrier phase, frequency

Code Tracking Loop:

Equivalent code loop noise bandwidth. If the code loop operates independently of the carrier-tracking loop, then the code loop bandwidth needs to be wide enough to accommodate receiver dynamics.

Predetection integration time = post-correlator IF bandwidth

Wavelength of the PRN code: 29.305 m for P-code, 293.05 m for C/A-code

DLL discriminator correlator factor

Code tracking loop jitter: positioning random error due to code tracking loop noise

Correlator:

Using the dedicated baseband processor

By SW residing in an application processor of a handheld device (such as the Philip's software GPS technology "Spot"): drastic reduction of the size of the GPS solution.

Number of correlators: directly affect TTFF and SNR, a few hundred correlators per channel are not adequate.

Large number of correlators: fast fix with low signal level.

NavSync CW25 chip: 12,288 correlators per channel. massively parallel search is possible. signal sensitivity as low as -155dBm can be tracked - tracking sensitivity (27dB down from normal level). Correlation gain 20-30dB.

Code search resolution cell (code phase search): 1/2 PN chip. In the worst case, all the resolution cells in the entire uncertainty region must be tested before the signal is detected. Statistically half of the total number of resolutions cells must be tested. 511 resolution cells in time are tested in parallel. Code phase search is same as shifting the phase of the replica PRN code generated by the receiver until it correlates with the received satellite PRN code.

Frequency search resolution cell (carrier phase search): reciprocal of the coherent integration period, use FFT to extend 511-time resolution cells to 64-frequency resolution cells. 511x64 = 32704 time-frequency resolution cells. Carrier phase search is same as changing the receiver frequency until it correlates with the received satellite carrier frequency plus Doppler.

The FFT search method is extremely efficient and effectively accomplishes massive parallel correlation comparable to the tens of thousands of correlators needed to acquire weak signals using serial search techniques. Since acquisition does not need to be a real-time continuous operation, it can be performed using a snap-shot technique to search for signals only when needed, saving both cost and circuit real-estate compared to a dedicated massive correlator chip.

The hardware search is a sequential serial search in the time domain using correlation techniques; whereas, the software search involves buffering samples to facilitate a Fourier transform. This operation is accomplished in the frequency domain by making use of the fundamental mathematical relationship that multiplication in the frequency domain is equivalent to convolution in the time domain (and vice versa). Acquisition techniques in software also complement assisted GPS (A-GPS) information as an SDR is easily tuned depending on the quality of the aiding information.

GPS signal acquisition:

1) Serial search

2) FFT-based acquisition = parallel code phase search: 수신기에서 생성한 gps 신호의 FFT와 수신된 GPS 신호의 FFT의 공액복소수를 곱한 후 이를 IFFT로 시간영역으로 변환.

3) Correlator-based acquisition = parallel frequency space search: 수신기에서 생성한 gps C/A 코드와 수신된 GPS 신호의 convolution을 시간축에서 수행(time shift of 50us and multiplication)

4) Carrier freqeuncy acquisition: 위성신호와 GPS에서 생성한 RF 신호의 주파수와 위상이 C/A 코드의 1개 펄스(총 1024개 펄스의 Gold code 펄스 중의 하나) 주기 약 1ms 보다 훨씬 작아야 한다(±10ms)

주파수 search: ±10kHz Doppler search, 100Hz frequency bin spacing

- Frequency search bin width: 1000/(correlation shifting time/code chip period)

Depends on the desired integration time and the desired maximum SNR loss due to frequency mismatch.

Commonly used bin size = 500Hz

- Frequency search width:

Doppler shift due to satellite velocity: ±5kHz

GPS receiver oscillator's frequency offset: 1.575kHz/1ppm. Typical oscillator = ±1 to ±3ppm. A value of ±5kHz is a safe choice.

GPS receiver velocity: ±5.25kHz at 1000m/s

- Number of frequency search bins = Search width/bin width = 20kHz/100Hz = 200

5) Time (code) space search

- Time step: depends on desired correlation (SNR) loss due to misaligned spreading code phases. Typical value is 1/2 of a chip.

[L2 Codeless Reception]

dunn-codeless gps.pdf

spectracom-codeless gps.pdf

leyssens-commercial dual-freq gps receivers.pdf

trimble-sps855-datasheet.pdf

Method: carrier phase or codeless receiver (some commercial receivers)

Commercial receivers:

iGage: X90-OPUS, $2450, L1/L2/L2C

Trimble SPS855 GNSS modular receiver, with antenna option GA810

Septentrio PolarRx2, 48-channel dual-frequency, L1/P1/P2

[GPS Jamming]

gerden-gps jamming.pdf

astech-z-12 gps receiver.pdf

GPS filter:

70 dB rejection of the out-of-band signal

Maximum out-of-band jamming level = –47 dBm; Telemetry transmitter = 27 dBm, Tel-GPS antenna isolation = 60 dB, GPS filter out-of-band rejection = 70 dB → –103 dBm

Anti-jamming techniques:

Navigation signals of opportunity: INS, Loran. 의도/비의도적 RFI, 실내/도심지

Null-steering: GPS 재밍신호 방향으로 안테나 null 형성

CRPAs(controlled radiation pattern antennas):

IM(inertional measurement): IM을 사용하여 GPS 탐색대역폭을 줄임. 이 경우 RFI의 영향을 줄일 수 있음.

JPALS(Joint Precision Approach and Landing System): IM과 beam steering 적용.

Adptive filter method

[GPS 자가간섭]

자가간섭(self jamming)의 정의: GPS 회로와 전원을 공유하는 다른 회로로부터의 잡음간섭

자가간섭의 측정:

1) 스펙트럼분석기: 최소신호레벨 측정할 수 있도록 설정 (신호 미인가시 표시되는 스펙트럼은 열잡음과 스펙트럼분석기 잡음의 합)

2) GPS 수신기 입력단으로 유입되는 잡음을 측정: 이 때 잡음측정을 위해 사용하는 연결선이 잡음 유입경로로 동작하면 안됨.

3) 잡음유입경로 확인:

ㅇ 회로에서 방사된 잡음이 안테나에 수신되어 GPS 수신기 입력단으로 유입: 안테나를 1m 이상 회로로부터 떨어뜨리고 측정. 안테나 대신 정합부하를 연결하고 측정

ㅇ 회로에서 방사된 잡음이 회로선로에 수신되어 유입: 다른 회로 동작 중지할 경우 변화 관측.

ㅇ 타회로로부터 전원접지선을 타고 GPS 수신기로 유입: 다른 회로 동작 중지할 경우 변화 관측. GPS 수신기에 다른 전원(전지) 사용하여 실험.

ㅇ 타회로의 전원접지선이 안테나 접지와 연결되어 안테나를 통해 유입: 다른 회로 동작 중지할 경우 안테나/안테나 대신 정합부하 연결하여 차이점 관측.

ㅇ 주변회로가 여러 개 있을 경우 순차적으로 동작을 중지시켜 간섭원을 찾아 냄. 주변회로가 특별한 동작을 할 때 (예: 마이크로프로세서 부팅시) 더 많은 잡음이 유입되는지 확인.

자가간섭 방지/제거:

1) 많은 경우 주변회로에서 발생된 잡음을 완전히 제거하기는 곤란. GPS 동작에 영향을 주지 않은 레벨로 감소시키는 것이 중요.

2) 주변회로에서 발생하는 잡음의 주파수 분석. 비선형소자에 의한 고조파(harmonics), 혼합기에 의한 차주파수 성분 포함.

3) 클록신호에 의한 간섭이 가장 흔히 발생: squared clock signals

4) 다양한 간섭제거 대책:

ㅇ Decoupling capacitor: 15 pF for 0402 packages.

ㅇ 10–100 W resistor: to remove high frequency transients

ㅇ 클롴신호 잡음억제용 metal shield

ㅇ 동일기판에 타회로 실장시 자가간섭을 고려하여 기판 레이아웃 설계

안테나를 통한 자가간섭:

안테나를 통한 전도성 공통모드 잡음 (CCMN)이 잡음간섭의 주요한 원인이 될 수 있음. 단일종단(single-ended) 안테나(예: 모노폴)는 CCMN을 수신기의 입력으로 전도시킴. 평형 안테나(예: 대칭구조 다이폴, quadrifilar helix)은 CCMN을 수신기로 전도시키지 않음

자가간섭이 있을 경우 GPS 성능:

GPS는 CDMA 방식을 사용하기 때문에 자가잡음이 있더라도 성능이 서서히 저하됨. 따라서 GPS 성능(초기측위시간 등) 측정만으로는 자가간섭을 정확하게 평가할 수 없음.

텔레메트리 송신기에 의한 GPS 수신기 간섭:

L-대역 TM 송신기: 1435.5/1535.5MHz, +34dBm

GPS L1 대역 간섭: L-대역 TM 안테나와 GPS L1 안테나의 분리도가 30dB 이상 되어야 GPS 수신기 동작 [Richen et al.]

참고문헌

Sarantel Inc., "Detecting and prevention of self-jamming signals", Application Note AN-09 v2 Iss 4-06, 2009.: 안테나에 의한 자가간섭

H. W. Ott, Electromagnetic Compatibility Engineering, Wiley, 2009.: 간섭제거 기술

A. Richen et al., "Improving interoperability of GPS and L-band telemetry with shaped-pattern antennas": L-대역 텔레메트리 송신기에 의한 GPS 수신기 간섭 제거 방안

[AGPS, A-GPS]

tester-fast hot start.pdf

lamance-agps.pdf

diggelen-a-gps.pdf

A-GPS 데이터:

위성궤도(ephemeris): 위성에서 수신하여 지상 통신망(이동전화, DMB, FM/AM 방송 주파수)으로 GPS 수신기에 제공

위성 clock 정보: 위성에서 수신하여 지상 통신망(이동전화, DMB, FM/AM 방송 주파수)으로 GPS 수신기에 제공

GPS time calibration: 이동전화망에서 기본으로 제공. 기지국 장비는 이상적인 reference oscillator(원자시계) 주파수의 ±50ppb (= 5´10^-8statiblity) 이내로 정확한 발진기 보유. 이동전화는 cell tower oscillator와 locking된 VCO 보유함으로써 GPS 위성발진기 주파수의 ±100ppb(= 10^-7 stability) 보유.

GPS frequency locking: 이동전화망에서 기본으로 제공

GPS 수신기 위치정보: 이동전화망의 Wi-Fi cell ID 이용. 정확도 300m 이내

통신망으로 clock timing을 전송할 때의 오차:

1m of clock accuracy = 3ns time accuracy

SV clock with relativistic correction: relative motion + gravitational force → special relativity and general relativity theory → A clock on an SV run faster by 38ms per day than one on the Earth surface.

Fine-time acquisition sensitivity:

Coarse-time acquisition sensitivity:

SV atomic clock accuracy: ±1ns

GPS timing signal accuracy

GPS Positioning Error (1 sigma):

(참고문헌)

langley-dop.pdf

http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/ModernSurveyingTech/objectives/B_11_Objectives.htm : Module 2: Global Positioning System, Lecture 11: Satellite geometry and accuracy measures

http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System

위성오차는 자료원마다 편차가 있음. 다음은 Wikipedia에서 인용한 수치.

Signal arrival: ±3m

Ionosphere: ±5m

Ephemeris: ±2.5m

Satellite clock: ±2m

Troposhere: ±0.5m

Multipath: ±1m (상황에 따라 다름)

Receiver noise: ±0.0m (수신기와 상황에 따라 다름),

3s_R = ±6.7m

Satellite clock errors: Coeffients of the behavior of the satellite clocks are included in the broadcast navigation message. The correction is generally less than 1ms and the broadcast correction has a typical accuracy of about 5 to 10ns or equivalent 1.5 to 3m. As the satellite clock error is common to all receivers simultaneously tracking the same satellite, the effect can be removed by single differencing measurements between receivers.

Ephemeris errors (orbital errors): Obital errors are due to errors in the broadcast ephemerides and typically range from 2 to 10m. Can be removed by single differencing measurements between two receivers with remaining error being 0.5ppm of the distance between two receivers.

Ionosphere-induced errors: a few meters at the zenith and many tens of meters at the horizon. Single frequency GPS receivers use a set of broadcast ionospheric correction coefficients included in the GPS navigation message. Can be significantly reduced by single differencing measurements between two receivers.

Tropospheric effects: 0.4dB attenuation at horizon, 0.04dB at zenith. 2m at zenith and 25m at horizon. Trophospheric models can typically correct for about 90% of the delay.

Multipath errors: much more probable and significant in HSGPS receivers. Most multipath mitigation techonologies are based on the design of suitable architectures in receivers that can minimize multipath and there are also special antenna designs such as choke rings and other multipath-limiting antennas. The standard correlator has a spacing of 1.0 chip between the early and the late correlators and precorrelation bandwidth of 2MHz. In contrast, the Narrow Correlator^TM has a precorrelation bandwidth of 8MHz and a correlator spacing of 0.1 chip between the early and the late correlators.

(maccougan-hsgps.pdf)

MET(multipath estimation technique)

MEDLL(multipath estimation delay lock loop)

Error components are all independent that the total error is the root-sum-square(RSS) of individual errors.

$3\sigma_R= \sqrt{3^2+5^2+2.5^2+2^2+1^2+0.5^2} \, \mathrm{m} \,=\,6.7 \, \mathrm{m}$

: UERE(user equivalent range error)

$\ \sigma_{rc} = \sqrt{PDOP^2 \times \sigma_R^2 + \sigma_{num}^2} = \sqrt{PDOP^2 \times 2.2^2 + 1^2} \, \mathrm{m}$ (error in estimated receiver position)

PDOP: 0-4 = excellent positioning, 5-8 = acceptable, 9-99 = poor

PDOP calculation:

(x, y, z): receiver position

(x_i, y_i, z_i): SV position

$R_i\,=\,\sqrt{(x_i- x)^2 + (y_i-y)^2 + (z_i-z)^2}$

$A = \begin{bmatrix} \frac {(x_1- x)} {R_1} & \frac {(y_1-y)} {R_1} & \frac {(z_1-z)} {R_1} & c \\ \frac {(x_2- x)} {R_2} & \frac {(y_2-y)} {R_2} & \frac {(z_2-z)} {R_2} & c \\ \frac {(x_3- x)} {R_3} & \frac {(y_3-y)} {R_3} & \frac {(z_3-z)} {R_3} & c \\ \frac {(x_4- x)} {R_4} & \frac {(y_4-y)} {R_4} & \frac {(z_4-z)} {R_4} & c \end{bmatrix}$

$Q = \left (A^T A \right )^{-1}$

$Q = \begin{bmatrix} d_x^2 & d_{xy}^2 & d_{xz}^2 & d_{xt}^2 \\ d_{xy}^2 & d_{y}^2 & d_{yz}^2 & d_{yt}^2 \\ d_{xz}^2 & d_{yz}^2 & d_{z}^2 & d_{zt}^2 \\ d_{xt}^2 & d_{yt}^2 & d_{zt}^2 & d_{t}^2 \end{bmatrix}$

$PDOP = \sqrt{d_x^2 + d_y^2 + d_z^2}$

$\ TDOP = \sqrt{d_{t}^2} = |d_{t}|\$

$PDOP = \sqrt{d_x^2 + d_y^2 + d_z^2}$

wieser-positioning error due to noise and multipath.pdf

Information supplied to the receiver: receiver location (approximate), UTC (approximate), almanac, ephemeris

UTC time aiding: fine aiding ±10us, coarse aiding = ±2s

With no external aiding: typical GPS time drifts at a rate of around 0.06ms/min resulting in the loss of the 1ms epoch within 15 min.

Lack of time aiding and knowledge of variation in reference frequency limits the aided hot-start TTFF. Provision of accurate time aiding allows the code-phase search space to be minimized.

The exponential increase in frequency-code phase search space results from the loss of accurate time and the uncertainty around local receiver reference frequency.

As received GPS signal strength decreases from -130dBm to -160dBm the resulting coherent integration time required to maintain target SNR increases with corresponding decrease in bandwidth of each search bin from 500Hz to 10Hz.

Stability of the local reference frequency translates to error in conversion of the RF signal to IF due to difference between the locally generated LO and the target mixing frequency. Mixing RF to IF results in additional pre-correlation frequency error, which will depend on reference conditions. 0.5ppm reference stability leads to frequency error of 788Hz.

Cell phone GPS assistance data: 이동전화 신호를 통해 GPS 보정신호를 받음. 해당 기지국 내에 있는 이동전화에 replacement navigation message를 송신(satellite Doppler shift 정보를 제공함으로서 보다 긴 적분시간 적용(대역폭 감소)하여 S/N비를 증가). 이동전화 주파수를 이용하여 cell phone 발진기의 주파수를 locking하여 Doppler search 공간을 줄임.

Assisted GPS(AGPS):

• IF the time of day is given with an accuracy of X microseconds, then the complexity is reduced from C(with no time aid) to ceil(1.023X)/1023*C, where ceil(y) is the smallest integer greater than y. If X = 10 ms, then complexity is reduced by roughly 99%.

• Receiver always being powered and assistance data always received.

• Relay information (= assistance data) to GPS receiver to help shorten acquisition time.

- SV ephemeris (orbit parameters): mandatory

- SV clock corrections: mandatory

- Other error corrections: ionospheric, tropospheric

- Accurate local time: produces 3dB sensitivity improvement

- GPS receiver (UE=user equipment) location

- Visible satellites

- Relative code delay offsets

- Doppler frequencies

- DGPS corrections (optional)

- Navigation message bits: produces 3dB SNR improvement

• GPS receiver maximum distance from server station: 150km

• Benefits:

- Search space is drastically reduced. 100-1000 times faster in all SNR conditions

- SNR (code phase tracking) improvement: 25dB, operation in low signal and heavy multipath

environments (foliage, indoors, urban canyons).

- TTFF almost independent of SNR.

- Indoor operation of GPS is possible.

- Accuracy: 4m open sky, 20-50m(indoors, urban canyons)

[Self-assisted GPS]

tester-fast hot start.pdf

When tracking the GPS transmission, the receiver is locked directly to GPS time and whilst not tracking, the receiver local time will drift compared to satellite time. The rate of drift depends on the relative performance of the receiver's ability to either predict reference variations or maintain the frequency reference with known performance.

Maintaining an accurate local estimate of system GPS time enables self-assistance. The receiver has no absolute time or frequency reference and must make time hypothesis which are validated against the GPS signal itself to ensure local receiver time predictions remain within suitable tolerances. This requires the receiver to periodically activate and re-lock to the GPS transmission. Existence of accurate local time enables used of minimum size search windows for re-detection of the GPS satellite signals.

The fine-time self-assistance approach forms the basis of a recent GPS receiver development. Unfiltered CEP50 position accuracy (over 12 hours) for the receiver operating without a Kalman filter is 2.8m and the self-assisted hot-start TTF is 2.5s over signal power -130dBm to -150dBm. Alternate approaches require 200,000+ correlators and network aiding information to deliver comparable TTF.

[HSGPS(High Sensivity GPS)]

hide-hsgps.pdf

[GPS Receiver Startup Modes]

surveylab-gps startup modes.pdf

agilent-gps fundamentals.pdf (추가작업 필요)

Factors affecting TTFF:

SV almanac: determine which satellite is overhead. Data valid for 3 months.

SV ephemeris: precise orbital information. Data valid for 4 hours.

Received signal levels

Receiver location

Clock accuracy relative to UTC

Cold start

Warm start: almanac, receiver location within 60 miles, time (less than 3 days passed since the receiver was synchronized with UTC)

Hot start: position fix within the last 2 hours, ephemeris data for at least 5 satellites

Factory start:

• Receiver never used since fabrication

• Receiver not powered for more than a year.

• No information at all on GPS satellite. The GPS receiver chip has never been fully operated after its semiconductor fabrication.

• Almanac download alone takes 12.5 minutes.

• TTFF = 13.5 min.

Cold start:

• Receiver not powered for 8-12 hours.

• Almanac in non-volatile memory is valid.

• Invalid ephemeris (older than 4 hours): ephemeris data is broadcast every 30 seconds.

• Receiver position not valid: away from previous fix by more than 100km

• Receiver time: unknown

• Receiver works through an internal list of all satellites acquiring each SV in view in turn. Acquisition time is the longest among all start-up modes.

• TTFF = 30-40s @ 2011

• Forced cold start: wrong information (very old almanac) on SV will make receiver spend more time than in the total cold start mode. In this case, a forced cold start is necessary.

Warm start:

• Receiver not powered for 30 minutes.

• Valid almanac

• Invalid ephemeris (older than 4 hours)

• Receiver position: approximately known (within 100km of the last fix)

• Receiver time: approximately known (GPS has been active in the last three days or RTC has been on by backup power).

• Receiver immediately detects overhead SVs but needs to download current ephemeris data.

• TTFF = 30-40s @ 2011 (not much different from cold-stat time)

Hot start:

• Receiver not powered for 15 minutes.

• Valid almanac

• Valid ephemeris data for at least 5 SVs (less than 4 hours old)

• Receiver position: not changed (exactly known)

• Receiver time: exactly known

• Receiver rapidly tracks overhead SVs and needs to download a minimum of data.

• TTFF = 1s @ 2011

Reacquisition:

• Receiver always being powered. After blockage for up to 10s while tracking SV signals.

• TTFF < 1s @ 2011

(참고)

- 보통의 GPS 수신 chip 규격; hot start = 1s, cold and warm start = 27s

- Cold start는 출고시 저장된 almanac data 사용. 출고 3개월이 경과되지 않으면 유효함.

- Warm start는 새로이 획득한 almanac data 사용. 이에 따라 cold start 시간과 warm start 시간에는 차이가 없음.

- Cold start와 warm start의 경우 시간과 주파수 정보가 없으므로 부팅 및 소프트웨어 구동시작 시간 0.5초 이하, time/frequency search에 약 2.4초, 위성측위 데이터 수신에 24초가, 위치계산에 0.1초 이하 등 총 27초 소요.

- Hot start의 경우 부팅 및 소트웨어 구동시작 시간 0.5초 이하, time/frequency search에 0.1초 이하, 위치계산에 0.1초 이하 등 총 1초 이하 시간 소요.

Carrier phase measurements:

For correct tracking of arrival times

The number of carrier wavelengths and fractions of carrier wavelengths between the receiver and the transmitter.

GPS-based phase interferometer: differential carrier phase GPS (항공분야), RTK(real time kinetic)(측위분야). 기준수신기로부터 1000bps 이상의 속도로 GPS 위상신호를 받아서 이동수신기의 위상과 비교. 기준국과 이동국 거리가 10km일 경우 1-cm 급 정확도, 100km일 경우 10-cm급 정확도. RTK는 carrier phase 이용(at the expense of ambiguity) 0.5cm 분해능. Code phase measurement는 1m 분해능.

Carrier phase 차이의 2πN ambiuity를 해결하기 위해 다양한 알고리즘이 개발되었다. 위성이 궤도를 상당히 비행할 때까지 기다려서 N 결정. L1과 L2를 사용하여 wide-lane을 형성하여 수십초 안에 N을 결정할 수 있다. L1/L2/L5 신호를 이용하여 N을 쉽게 결정할 수 있다.

Non-dispersive 지연(비이온층 지연): L1/L2/L5 신호를 이용하면 총 지연중 이온층지연과 비이온층지연(대기유전율지연)을 구분.

Carrier-tracking loop:

- Costas-type phase locked loop

- Carrier loop noise bandwidth. Must be wide enough to follow the receiver dynamics.

- Carrier tracking loop jitter:

[High-End Professional GPS Receivers]

Novatel

Septentrio