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 ±Ëµµ: ÁöÇ¥¸é°ú 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 ¡æ 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

2)

P_s = -130dBm

kT₀ = -171dBm/Hz

I₀ = power density of the interfering signal per Hz

C/N₀ = ´ÜÀ§ dB-Hz. open sky 40-50dB-Hz, µµ½ÉÁö 15-40dB-Hz, ½Ç³» 25dB-Hz ÀÌÇÏ.

System noise temperature:

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

T_a = 130 K, ¥á = 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.

¥á: antenna cable loss (fractional)

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

3)

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 ¡æ Calibrate the receiver oscillator ¡æ 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 N^1/2. 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), ¼Ò¿ä½Ã°£¿¡ °ü°è¾øÀÌ À§¼ºÀ» Æ÷ÂøÇÒ ¼ö ÀÖ´Â ÃÖ¼Ò ½ÅÈ£ ·¹º§

• 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

À§¼ºÁ¾·ù: GPS L1, Glonass, Galileo(w/ firmware upgrade), Beidou(w/ firmware upgrade)

ä³Î¼ö: 99(Ž»ö), 33(track)

Å©±â: 9.6*9.6*1.85mm

Àü·Â¼Ò¸ð: Ç×¹ý 57mW(3.0-4.3V), ¹é¾÷»óÅ = 30mW(2-4.3V)

TTFF(-130dBm ¼ö½ÅÀü·Â ½Ã): cold/warm start = 23s, hot start = 1s, Self-assisted ephemeris data¸¦ »ý¼ºÇÏ¿© ÃÖÃÊ ephemeris data ÀÔ·Â ÈÄ 3ÀÏ ÀÌÀü±îÁö 3ÃÊ À̳»¿¡ À§¼º Æ÷Âø °¡´É.

°¨µµ: acquisition = -148dBm, re-acquisition = -160dBm, tracking/navigation = -165dBm

Á¤È®µµ(-130dBm ½ÅÈ£ ÀԷ½Ã): À§Ä¡ 3.0m, ¼Óµµ 0.02m/s, ½Ã°£ 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: ¼ö½Å±â¿¡¼ »ý¼ºÇÑ gps ½ÅÈ£ÀÇ FFT¿Í ¼ö½ÅµÈ GPS ½ÅÈ£ÀÇ FFTÀÇ °ø¾×º¹¼Ò¼ö¸¦ °öÇÑ ÈÄ À̸¦ IFFT·Î ½Ã°£¿µ¿ªÀ¸·Î º¯È¯.

3) Correlator-based acquisition = parallel frequency space search: ¼ö½Å±â¿¡¼ »ý¼ºÇÑ gps C/A ÄÚµå¿Í ¼ö½ÅµÈ GPS ½ÅÈ£ÀÇ convolutionÀ» ½Ã°£Ãà¿¡¼ ¼öÇà(time shift of 50us and multiplication)

4) Carrier freqeuncy acquisition: À§¼º½ÅÈ£¿Í GPS¿¡¼ »ý¼ºÇÑ RF ½ÅÈ£ÀÇ ÁÖÆļö¿Í À§»óÀÌ C/A ÄÚµåÀÇ 1°³ ÆÞ½º(ÃÑ 1024°³ ÆÞ½ºÀÇ Gold code ÆÞ½º ÁßÀÇ Çϳª) Áֱ⠾à 1ms º¸´Ù ÈξÀ ÀÛ¾Æ¾ß ÇÑ´Ù(¡¾10ms)

ÁÖÆļö search: ¡¾10kHz 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: ¡¾5kHz

GPS receiver oscillator's frequency offset: 1.575kHz/1ppm. Typical oscillator = ¡¾1 to ¡¾3ppm. A value of ¡¾5kHz is a safe choice.

GPS receiver velocity: ¡¾5.25kHz 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 ¡æ –103 dBm

Anti-jamming techniques:

Navigation signals of opportunity: INS, Loran. Àǵµ/ºñÀǵµÀû RFI, ½Ç³»/µµ½ÉÁö

Null-steering: GPS Àç¹Ö½ÅÈ£ ¹æÇâÀ¸·Î ¾ÈÅ׳ª null Çü¼º

CRPAs(controlled radiation pattern antennas):

IM(inertional measurement): IMÀ» »ç¿ëÇÏ¿© GPS Ž»ö´ë¿ªÆøÀ» ÁÙÀÓ. ÀÌ °æ¿ì RFIÀÇ ¿µÇâÀ» ÁÙÀÏ ¼ö ÀÖÀ½.

JPALS(Joint Precision Approach and Landing System): IM°ú beam steering Àû¿ë.

Adptive filter method

[GPS ÀÚ°¡°£¼·]

ÀÚ°¡°£¼·(self jamming)ÀÇ Á¤ÀÇ: GPS ȸ·Î¿Í Àü¿øÀ» °øÀ¯ÇÏ´Â ´Ù¸¥ ȸ·Î·ÎºÎÅÍÀÇ ÀâÀ½°£¼·

ÀÚ°¡°£¼·ÀÇ ÃøÁ¤:

1) ½ºÆåÆ®·³ºÐ¼®±â: ÃÖ¼Ò½ÅÈ£·¹º§ ÃøÁ¤ÇÒ ¼ö ÀÖµµ·Ï ¼³Á¤ (½ÅÈ£ ¹ÌÀΰ¡½Ã Ç¥½ÃµÇ´Â ½ºÆåÆ®·³Àº ¿ÀâÀ½°ú ½ºÆåÆ®·³ºÐ¼®±â ÀâÀ½ÀÇ ÇÕ)

2) GPS ¼ö½Å±â ÀԷ´ÜÀ¸·Î À¯ÀԵǴ ÀâÀ½À» ÃøÁ¤: ÀÌ ¶§ ÀâÀ½ÃøÁ¤À» À§ÇØ »ç¿ëÇÏ´Â ¿¬°á¼±ÀÌ ÀâÀ½ À¯ÀÔ°æ·Î·Î µ¿ÀÛÇÏ¸é ¾ÈµÊ.

3) ÀâÀ½À¯ÀÔ°æ·Î È®ÀÎ:

¤· ȸ·Î¿¡¼ ¹æ»çµÈ ÀâÀ½ÀÌ ¾ÈÅ׳ª¿¡ ¼ö½ÅµÇ¾î GPS ¼ö½Å±â ÀԷ´ÜÀ¸·Î À¯ÀÔ: ¾ÈÅ׳ª¸¦ 1m ÀÌ»ó ȸ·Î·ÎºÎÅÍ ¶³¾î¶ß¸®°í ÃøÁ¤. ¾ÈÅ׳ª ´ë½Å Á¤ÇÕºÎÇϸ¦ ¿¬°áÇÏ°í ÃøÁ¤

¤· ȸ·Î¿¡¼ ¹æ»çµÈ ÀâÀ½ÀÌ È¸·Î¼±·Î¿¡ ¼ö½ÅµÇ¾î À¯ÀÔ: ´Ù¸¥ ȸ·Î µ¿ÀÛ ÁßÁöÇÒ °æ¿ì º¯È °üÃø.

¤· Ÿȸ·Î·ÎºÎÅÍ Àü¿øÁ¢Áö¼±À» Ÿ°í GPS ¼ö½Å±â·Î À¯ÀÔ: ´Ù¸¥ ȸ·Î µ¿ÀÛ ÁßÁöÇÒ °æ¿ì º¯È °üÃø. GPS ¼ö½Å±â¿¡ ´Ù¸¥ Àü¿ø(ÀüÁö) »ç¿ëÇÏ¿© ½ÇÇè.

¤· Ÿȸ·ÎÀÇ Àü¿øÁ¢Áö¼±ÀÌ ¾ÈÅ׳ª Á¢Áö¿Í ¿¬°áµÇ¾î ¾ÈÅ׳ª¸¦ ÅëÇØ À¯ÀÔ: ´Ù¸¥ ȸ·Î µ¿ÀÛ ÁßÁöÇÒ °æ¿ì ¾ÈÅ׳ª/¾ÈÅ׳ª ´ë½Å Á¤ÇÕºÎÇÏ ¿¬°áÇÏ¿© Â÷ÀÌÁ¡ °üÃø.

¤· ÁÖº¯È¸·Î°¡ ¿©·¯ °³ ÀÖÀ» °æ¿ì ¼øÂ÷ÀûÀ¸·Î µ¿ÀÛÀ» ÁßÁö½ÃÄÑ °£¼·¿øÀ» ã¾Æ ³¿. ÁÖº¯È¸·Î°¡ Ưº°ÇÑ µ¿ÀÛÀ» ÇÒ ¶§ (¿¹: ¸¶ÀÌÅ©·ÎÇÁ·Î¼¼¼ ºÎÆýÃ) ´õ ¸¹Àº ÀâÀ½ÀÌ À¯ÀԵǴÂÁö È®ÀÎ.

ÀÚ°¡°£¼· ¹æÁö/Á¦°Å:

1) ¸¹Àº °æ¿ì ÁÖº¯È¸·Î¿¡¼ ¹ß»ýµÈ ÀâÀ½À» ¿ÏÀüÈ÷ Á¦°ÅÇϱâ´Â °ï¶õ. GPS µ¿ÀÛ¿¡ ¿µÇâÀ» ÁÖÁö ¾ÊÀº ·¹º§·Î °¨¼Ò½ÃÅ°´Â °ÍÀÌ Áß¿ä.

2) ÁÖº¯È¸·Î¿¡¼ ¹ß»ýÇÏ´Â ÀâÀ½ÀÇ ÁÖÆļö ºÐ¼®. ºñ¼±Çü¼ÒÀÚ¿¡ ÀÇÇÑ °íÁ¶ÆÄ(harmonics), È¥Çձ⿡ ÀÇÇÑ Â÷ÁÖÆļö ¼ººÐ Æ÷ÇÔ.

3) Ŭ·Ï½ÅÈ£¿¡ ÀÇÇÑ °£¼·ÀÌ °¡Àå ÈçÈ÷ ¹ß»ý: squared clock signals

4) ´Ù¾çÇÑ °£¼·Á¦°Å ´ëÃ¥:

¤· Decoupling capacitor: 15 pF for 0402 packages.

¤· 10–100 W resistor: to remove high frequency transients

¤· ŬŽð½ÅÈ£ ÀâÀ½¾ïÁ¦¿ë metal shield

¤· µ¿ÀϱâÆÇ¿¡ Ÿȸ·Î ½ÇÀå½Ã ÀÚ°¡°£¼·À» °í·ÁÇÏ¿© ±âÆÇ ·¹À̾ƿô ¼³°è

¾ÈÅ׳ª¸¦ ÅëÇÑ ÀÚ°¡°£¼·:

¾ÈÅ׳ª¸¦ ÅëÇÑ Àüµµ¼º °øÅë¸ðµå ÀâÀ½ (CCMN)ÀÌ ÀâÀ½°£¼·ÀÇ ÁÖ¿äÇÑ ¿øÀÎÀÌ µÉ ¼ö ÀÖÀ½. ´ÜÀÏÁ¾´Ü(single-ended) ¾ÈÅ׳ª(¿¹: ¸ð³ëÆú)´Â CCMNÀ» ¼ö½Å±âÀÇ ÀÔ·ÂÀ¸·Î Àüµµ½ÃÅ´. ÆòÇü ¾ÈÅ׳ª(¿¹: ´ëĪ±¸Á¶ ´ÙÀÌÆú, quadrifilar helix)Àº CCMNÀ» ¼ö½Å±â·Î Àüµµ½ÃÅ°Áö ¾ÊÀ½

ÀÚ°¡°£¼·ÀÌ ÀÖÀ» °æ¿ì GPS ¼º´É:

GPS´Â CDMA ¹æ½ÄÀ» »ç¿ëÇϱ⠶§¹®¿¡ ÀÚ°¡ÀâÀ½ÀÌ ÀÖ´õ¶óµµ ¼º´ÉÀÌ ¼¼È÷ ÀúÇϵÊ. µû¶ó¼ GPS ¼º´É(ÃʱâÃøÀ§½Ã°£ µî) ÃøÁ¤¸¸À¸·Î´Â ÀÚ°¡°£¼·À» Á¤È®ÇÏ°Ô Æò°¡ÇÒ ¼ö ¾øÀ½.

ÅÚ·¹¸ÞÆ®¸® ¼Û½Å±â¿¡ ÀÇÇÑ GPS ¼ö½Å±â °£¼·:

L-´ë¿ª TM ¼Û½Å±â: 1435.5/1535.5MHz, +34dBm

GPS L1 ´ë¿ª °£¼·: L-´ë¿ª TM ¾ÈÅ׳ª¿Í GPS L1 ¾ÈÅ׳ªÀÇ ºÐ¸®µµ°¡ 30dB ÀÌ»ó µÇ¾î¾ß GPS ¼ö½Å±â µ¿ÀÛ [Richen et al.]

Âü°í¹®Çå

Sarantel Inc., "Detecting and prevention of self-jamming signals", Application Note AN-09 v2 Iss 4-06, 2009.: ¾ÈÅ׳ª¿¡ ÀÇÇÑ ÀÚ°¡°£¼·

H. W. Ott, Electromagnetic Compatibility Engineering, Wiley, 2009.: °£¼·Á¦°Å ±â¼ú

A. Richen et al., "Improving interoperability of GPS and L-band telemetry with shaped-pattern antennas": L-´ë¿ª ÅÚ·¹¸ÞÆ®¸® ¼Û½Å±â¿¡ ÀÇÇÑ GPS ¼ö½Å±â °£¼· Á¦°Å ¹æ¾È

[AGPS, A-GPS]

tester-fast hot start.pdf

lamance-agps.pdf

diggelen-a-gps.pdf

A-GPS µ¥ÀÌÅÍ:

À§¼º±Ëµµ(ephemeris): À§¼º¿¡¼ ¼ö½ÅÇÏ¿© Áö»ó Åë½Å¸Á(À̵¿ÀüÈ, DMB, FM/AM ¹æ¼Û ÁÖÆļö)À¸·Î GPS ¼ö½Å±â¿¡ Á¦°ø

À§¼º clock Á¤º¸: À§¼º¿¡¼ ¼ö½ÅÇÏ¿© Áö»ó Åë½Å¸Á(À̵¿ÀüÈ, DMB, FM/AM ¹æ¼Û ÁÖÆļö)À¸·Î GPS ¼ö½Å±â¿¡ Á¦°ø

GPS time calibration: À̵¿ÀüȸÁ¿¡¼ ±âº»À¸·Î Á¦°ø. ±âÁö±¹ Àåºñ´Â ÀÌ»óÀûÀÎ reference oscillator(¿øÀڽðè) ÁÖÆļöÀÇ ¡¾50ppb (= 5¢¥10^-8 statiblity) À̳»·Î Á¤È®ÇÑ ¹ßÁø±â º¸À¯. À̵¿ÀüÈ´Â cell tower oscillator¿Í lockingµÈ VCO º¸À¯ÇÔÀ¸·Î½á GPS À§¼º¹ßÁø±â ÁÖÆļöÀÇ ¡¾100ppb(= 10^-7 stability) º¸À¯.

GPS frequency locking: À̵¿ÀüȸÁ¿¡¼ ±âº»À¸·Î Á¦°ø

GPS ¼ö½Å±â À§Ä¡Á¤º¸: À̵¿ÀüȸÁÀÇ Wi-Fi cell ID ÀÌ¿ë. Á¤È®µµ 300m À̳»

Åë½Å¸ÁÀ¸·Î clock timingÀ» Àü¼ÛÇÒ ¶§ÀÇ ¿ÀÂ÷:

1m of clock accuracy = 3ns time accuracy

SV clock with relativistic correction: relative motion + gravitational force ¡æ special relativity and general relativity theory ¡æ 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: ¡¾1ns

GPS timing signal accuracy

GPS Positioning Error (1 sigma):

(Âü°í¹®Çå)

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

À§¼º¿ÀÂ÷´Â ÀÚ·á¿ø¸¶´Ù ÆíÂ÷°¡ ÀÖÀ½. ´ÙÀ½Àº Wikipedia¿¡¼ ÀοëÇÑ ¼öÄ¡.

Signal arrival: ¡¾3m

Ionosphere: ¡¾5m

Ephemeris: ¡¾2.5m

Satellite clock: ¡¾2m

Troposhere: ¡¾0.5m

Multipath: ¡¾1m (»óȲ¿¡ µû¶ó ´Ù¸§)

Receiver noise: ¡¾0.0m (¼ö½Å±â¿Í »óȲ¿¡ µû¶ó ´Ù¸§),

3s_R = ¡¾6.7m

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.

: UERE(user equivalent range error)

(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

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 ¡¾10us, coarse aiding = ¡¾2s

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: À̵¿ÀüÈ ½ÅÈ£¸¦ ÅëÇØ GPS º¸Á¤½ÅÈ£¸¦ ¹ÞÀ½. ÇØ´ç ±âÁö±¹ ³»¿¡ ÀÖ´Â À̵¿ÀüÈ¿¡ replacement navigation message¸¦ ¼Û½Å(satellite Doppler shift Á¤º¸¸¦ Á¦°øÇÔÀ¸·Î¼ º¸´Ù ±ä ÀûºÐ½Ã°£ Àû¿ë(´ë¿ªÆø °¨¼Ò)ÇÏ¿© S/Nºñ¸¦ Áõ°¡). À̵¿ÀüÈ ÁÖÆļö¸¦ ÀÌ¿ëÇÏ¿© cell phone ¹ßÁø±âÀÇ ÁÖÆļö¸¦ lockingÇÏ¿© Doppler search °ø°£À» ÁÙÀÓ.

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 (Ãß°¡ÀÛ¾÷ ÇÊ¿ä)

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

(Âü°í)

- º¸ÅëÀÇ GPS ¼ö½Å chip ±Ô°Ý; hot start = 1s, cold and warm start = 27s

- Cold start´Â Ãâ°í½Ã ÀúÀåµÈ almanac data »ç¿ë. Ãâ°í 3°³¿ùÀÌ °æ°úµÇÁö ¾ÊÀ¸¸é À¯È¿ÇÔ.

- Warm start´Â »õ·ÎÀÌ È¹µæÇÑ almanac data »ç¿ë. ÀÌ¿¡ µû¶ó cold start ½Ã°£°ú warm start ½Ã°£¿¡´Â Â÷ÀÌ°¡ ¾øÀ½.

- Cold start¿Í warm startÀÇ °æ¿ì ½Ã°£°ú ÁÖÆļö Á¤º¸°¡ ¾øÀ¸¹Ç·Î ºÎÆà ¹× ¼ÒÇÁÆ®¿þ¾î ±¸µ¿½ÃÀÛ ½Ã°£ 0.5ÃÊ ÀÌÇÏ, time/frequency search¿¡ ¾à 2.4ÃÊ, À§¼ºÃøÀ§ µ¥ÀÌÅÍ ¼ö½Å¿¡ 24ÃÊ°¡, À§Ä¡°è»ê¿¡ 0.1ÃÊ ÀÌÇÏ µî ÃÑ 27ÃÊ ¼Ò¿ä.

- Hot startÀÇ °æ¿ì ºÎÆà ¹× ¼ÒÆ®¿þ¾î ±¸µ¿½ÃÀÛ ½Ã°£ 0.5ÃÊ ÀÌÇÏ, time/frequency search¿¡ 0.1ÃÊ ÀÌÇÏ, À§Ä¡°è»ê¿¡ 0.1ÃÊ ÀÌÇÏ µî ÃÑ 1ÃÊ ÀÌÇÏ ½Ã°£ ¼Ò¿ä.

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 (Ç×°øºÐ¾ß), RTK(real time kinetic)(ÃøÀ§ºÐ¾ß). ±âÁؼö½Å±â·ÎºÎÅÍ 1000bps ÀÌ»óÀÇ ¼Óµµ·Î GPS À§»ó½ÅÈ£¸¦ ¹Þ¾Æ¼ À̵¿¼ö½Å±âÀÇ À§»ó°ú ºñ±³. ±âÁر¹°ú À̵¿±¹ °Å¸®°¡ 10kmÀÏ °æ¿ì 1-cm ±Þ Á¤È®µµ, 100kmÀÏ °æ¿ì 10-cm±Þ Á¤È®µµ. RTK´Â carrier phase ÀÌ¿ë(at the expense of ambiguity) 0.5cm ºÐÇØ´É. Code phase measurement´Â 1m ºÐÇØ´É.

Carrier phase Â÷ÀÌÀÇ 2¥ðN ambiuity¸¦ ÇØ°áÇϱâ À§ÇØ ´Ù¾çÇÑ ¾Ë°í¸®ÁòÀÌ °³¹ßµÇ¾ú´Ù. À§¼ºÀÌ ±Ëµµ¸¦ »ó´çÈ÷ ºñÇàÇÒ ¶§±îÁö ±â´Ù·Á¼ N °áÁ¤. L1°ú L2¸¦ »ç¿ëÇÏ¿© wide-laneÀ» Çü¼ºÇÏ¿© ¼ö½ÊÃÊ ¾È¿¡ NÀ» °áÁ¤ÇÒ ¼ö ÀÖ´Ù. L1/L2/L5 ½ÅÈ£¸¦ ÀÌ¿ëÇÏ¿© NÀ» ½±°Ô °áÁ¤ÇÒ ¼ö ÀÖ´Ù.

Non-dispersive Áö¿¬(ºñÀÌ¿ÂÃþ Áö¿¬): L1/L2/L5 ½ÅÈ£¸¦ ÀÌ¿ëÇϸé ÃÑ Áö¿¬Áß ÀÌ¿ÂÃþÁö¿¬°ú ºñÀÌ¿ÂÃþÁö¿¬(´ë±âÀ¯ÀüÀ²Áö¿¬)À» ±¸ºÐ.

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