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Columns and Editorials

Wavelets and Notch Filtering

FIGURE 1: Touching wavelet spectra

For the complete story, including figures, graphs, and images, please download the PDF of the article, above.

The use of GNSS for safety critical applications is gaining interest, particularly amongst aviation users, who probably have the most demanding requirements. The GNSS frequency band containing the Galileo E5 and GPS L5 signals is designated as an aeronautical radio navigation service (ARNS) band, which enjoys legal protection from other services not allocated to this frequency on a primary basis.

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By Inside GNSS
December 2, 2010

GNSS Hotspots

One of 12 magnetograms recorded at Greenwich Observatory during the Great Geomagnetic Storm of 1859
1996 soccer game in the Midwest, (Rick Dikeman image)
Nouméa ground station after the flood
A pencil and a coffee cup show the size of NASA’s teeny tiny PhoneSat
Bonus Hotspot: Naro Tartaruga AUV
Pacific lamprey spawning (photo by Jeremy Monroe, Fresh Waters Illustrated)
“Return of the Bucentaurn to the Molo on Ascension Day”, by (Giovanni Antonio Canal) Canaletto
The U.S. Naval Observatory Alternate Master Clock at 2nd Space Operations Squadron, Schriever AFB in Colorado. This photo was taken in January, 2006 during the addition of a leap second. The USNO master clocks control GPS timing. They are accurate to within one second every 20 million years (Satellites are so picky! Humans, on the other hand, just want to know if we’re too late for lunch) USAF photo by A1C Jason Ridder.
Detail of Compass/ BeiDou2 system diagram
Hotspot 6: Beluga A300 600ST

1. STORMY WEATHER
Belgium and Brazil

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By Inside GNSS

Measuring GNSS Signal Strength

Q: What is the difference between SNR and C/N0?

A: GPS receivers built for various applications, such as handhelds, automobiles, mobile phones, and avionics, all have a method for indicating the signal strength of the different satellites they are tracking. Some receivers display the signal strength in the form of vertical bars, some in terms of normalized signal strength, and others in terms of carrier-to-noise density (C/N0) or signal-to-noise ratio (SNR).

The latter two terms are regularly used so interchangeably that their fundamental differences are often overlooked. A full understanding of the differences between SNR and C/N0 is useful both for users of GPS receivers and for GPS receiver designers and testers.

SNR and C/N0
SNR is usually expressed in terms of decibels. It refers to the ratio of the signal power and noise power in a given bandwidth.

SNR(dB) = S  – N

S is the signal power, usually the carrier power expressed in units of decibel/milliwatt (dBm) or decibel/watts (dBW);
N is the noise power in a given bandwidth in units of dBm or dBW.

C/N0, on the other hand, is usually expressed in decibel-Hertz (dB-Hz) and refers to the ratio of the carrier power and the noise power per unit bandwidth.

For the GPS L1 C/A signal, one can consider the received signal power as the power of the original unmodulated carrier power (at the point of reception in a receiver) that has been spread by the spreading (ranging) codes when transmitted from a satellite. We can express C/N0 as follows:

C/N0 (dB-Hz) = C – (N – BW) = C – N0 = SNR + BW     

where:

C is the carrier power in dBm or dBW;
N is the noise power in dBm or dBW;
N0 is the noise power density in dBm-Hz or dBW-Hz;
BW is the bandwidth of observation, which is usually the noise equivalent bandwidth of the last filter stage in a receiver’s RF front-end.

Typical values in an L1 C/A code receiver are as follows:

C/N0: ~ 37 to 45dB-Hz

Receiver front-end bandwidth: ~ 4MHz => BW = 10*log (4,000,000) = 66dB
SNR = C/N0 – BW => SNR ~ (37 – 66) to (45 – 66) => SNR ~ -29dB to -21dB

In order to determine C/N0, then, one clearly needs to determine the carrier power and noise density at the input to the receiver.

Noise and Signal Power
The sources of white noise in a GNSS receiver are usually described by the antenna noise temperature and the receiver noise temperature. The antenna temperature models the noise entering the antenna from the sky whereas the receiver noise temperature models the thermal noise due to the motion of charges within a device such as the GPS receiver front-end. These noise sources specify the noise density.

. . .

Signal and Noise Paths from Antenna to Receiver
. . .
When considering signal and noise paths through the front-end, one needs to consider the noise figure of the various components in the front-end. The noise figure is given as

NF = SNRin / SNRout

and provides an estimate of the amount of noise added by an active component, such as a low-noise amplifier (LNA), or even a passive component, such as a filter or the cable.

. . .

Taking into consideration the noise environment and the receiver front-end components, the C/N0 of a particular tracked satellite will scale relative to the signal power. The signal power of the various satellites being tracked by the receiver will vary in relation to the satellite elevation angle due to differences in path loss and the satellite and receiver antennas’ gain patterns. So, for example, if the signal power varies ±4dB of the nominal signal power of -158.5dBW, the corresponding C/N0 will vary from 38.5dB-Hz to 46.5dB-Hz. 

Interpretation and Significance of C/N0
From our discussions thus far, the C/N0 output by a receiver clearly provides an indication of the signal power of the tracked satellite and the noise density as seen by the receiver’s front-end.

Two different GPS receivers connected to the same antenna and tracking the same GPS satellite at the same time may output different C/N0 values. If one assumes that the C/N0 values are computed accurately by both the receivers, the differences in the C/N0 values can be attributed to differences in the noise figure of the two front-ends and/or the receivers’ respective band-limiting and quantization schemes.

. . .

Receiver Acquisition, Processing Blocks, and SNR
The signal-to-noise ratio is most useful when considered within the baseband processing blocks of a GNSS receiver. In dealing with SNR, the bandwidth of interest needs to be specified. Typically the noise equivalent bandwidth is used, which is defined as the bandwidth of an ideal (i.e., brick-wall) filter whose bandwidth when multiplied by the white noise density of N0/2 will result in the total noise power at the output of the original filter. 

. . .

The improvement in SNR as the result of a longer integration occurs because of the reduction in the noise equivalent bandwidth. Note that the performance of the PLL and FLL in the presence of thermal noise is further affected by the bandwidths of the respective loops themselves. The integration time in this case establishes the input SNR and the loop update time for the respective loops.

Interpretation and Significance of SNR
As we have seen, the SNR in a GPS receiver depends on the receiver’s front-end bandwidth, acquisition, and tracking parameters. Referencing just the SNR value in a GPS receiver does not usually make sense unless one also specifies the bandwidth and processing stage within the receiver.

The SNR is very useful when evaluating the performance of the acquisition and tracking stages in a receiver. For example, when performing Monte Carlo simulations, the SNR needs to be determined at the various stages of the signal processing chain to properly simulate the receiver. In simulations the required C/N0 needs to be first converted to an SNR from which the appropriate noise variance can be readily determined.

Furthermore, the SNR is an indication of the level of noise present in the measurement, whereas C/N0 alone does not provide this information.

In conclusion, we can see that both the C/N0 and SNR are useful quantities that can be used when designing, evaluating or verifying the performance of a GPS receiver. However the use of one quantity over the other very much depends upon the context and the purpose for which the signal quality measurement is being made or is to be used for and this should be carefully considered when choosing between the two.

(For Angelo Joseph’s complete answer to this question, including formulas and tables, please download the full article using the pdf link above.)

Additional Resources
For information on how C/N0 is computed within a GNSS receiver, refer to the GNSS Solutions columns by B. Badke (InsideGNSS, September/October 2009) and E. Falletti et alia (January/February 2010).

 

By Inside GNSS

Frank Czopek

Frank & Jeanine at the Wild Animal Park

SIDEBAR: Frank Czopek’s Compass Points

Frank Czopek and his brothers used to go to the 1970s Detroit version of Craigslist — Trading Times — to buy two or three non-functioning Chevrolet Corvairs (air-cooled rear engine-mounted) cars, at $25 apiece.

They hoped to turn the junkers into a single functioning automobile over a weekend. Unfortunately, the results did not last long; so, the process was repeated often. But they sure had fun!

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By Inside GNSS
October 1, 2010

GNSS Hotspots

One of 12 magnetograms recorded at Greenwich Observatory during the Great Geomagnetic Storm of 1859
1996 soccer game in the Midwest, (Rick Dikeman image)
Nouméa ground station after the flood
A pencil and a coffee cup show the size of NASA’s teeny tiny PhoneSat
Bonus Hotspot: Naro Tartaruga AUV
Pacific lamprey spawning (photo by Jeremy Monroe, Fresh Waters Illustrated)
“Return of the Bucentaurn to the Molo on Ascension Day”, by (Giovanni Antonio Canal) Canaletto
The U.S. Naval Observatory Alternate Master Clock at 2nd Space Operations Squadron, Schriever AFB in Colorado. This photo was taken in January, 2006 during the addition of a leap second. The USNO master clocks control GPS timing. They are accurate to within one second every 20 million years (Satellites are so picky! Humans, on the other hand, just want to know if we’re too late for lunch) USAF photo by A1C Jason Ridder.
Detail of Compass/ BeiDou2 system diagram
Hotspot 6: Beluga A300 600ST

1. GARMIN RECALL
Olathe, Kansas USA

√ In late August, Kansas-based GPS consumer manufacturer Garmin International Inc. recalled 1.25 million Nuvi GPS units whose batteries can overheat and catch fire. In September, Nissan and Suzuki recalled Nuvi units in their vehicles. Check the special recall website to see if you are affected.

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By Inside GNSS

Launch Fever

It is not all about the satellites, of course.

And, despite the thrill of launches — the Fourth of July and every other national holiday celebration all grown up — it’s not about the rockets.

When evaluating the progress of GNSS programs, however, satellites and launches are a way to keep count — in fact, it is the way most of us do keep count.

By that measure, then, the numbers are adding up quickly.

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By Inside GNSS
September 15, 2010

A Search for Spectrum: GNSS Signals in S-Band, Part II

GNSS utilization of the S-band portion of the radio spectrum provides some challenges to designers of both GNSS navigation signals as well as signals used by other services, in terms of interference avoidance and signal power.

An important existing user of S-band spectrum is the Globalstar communications satellite system. The voice and data services provided by Globalstar employ the 2483.5–2500 MHz band for its satellite downlink communications to user terminals. Additionally, these satellites use multi-beam antennas to enable frequency reuse.

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By Inside GNSS
August 27, 2010

The Missing ICD

Successful launch of three Compass (Beidou-2) satellites so far this year and reports of another two planned later in 2010 have elevated awareness of China’s accelerating GNSS program.

Added to the two spacecraft placed in orbit in 2007 and 2009, that would bring the modernized Beidou constellation up to seven — halfway to the 13 or 14 satellites planned for the regional system scheduled to be available by 2012.

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By Inside GNSS
August 26, 2010

GNSS Hotspots

One of 12 magnetograms recorded at Greenwich Observatory during the Great Geomagnetic Storm of 1859
1996 soccer game in the Midwest, (Rick Dikeman image)
Nouméa ground station after the flood
A pencil and a coffee cup show the size of NASA’s teeny tiny PhoneSat
Bonus Hotspot: Naro Tartaruga AUV
Pacific lamprey spawning (photo by Jeremy Monroe, Fresh Waters Illustrated)
“Return of the Bucentaurn to the Molo on Ascension Day”, by (Giovanni Antonio Canal) Canaletto
The U.S. Naval Observatory Alternate Master Clock at 2nd Space Operations Squadron, Schriever AFB in Colorado. This photo was taken in January, 2006 during the addition of a leap second. The USNO master clocks control GPS timing. They are accurate to within one second every 20 million years (Satellites are so picky! Humans, on the other hand, just want to know if we’re too late for lunch) USAF photo by A1C Jason Ridder.
Detail of Compass/ BeiDou2 system diagram
Hotspot 6: Beluga A300 600ST

1. WHO WON?
Portland, Oregon and Munich, Germany
√ Judges all over the world are poring over 357 GNSS app innovations submitted to the 2010 European Satellite Navigation Contest from Europe, Australia, the Middle East, Taiwan and North America.  Inside GNSS’s USA Challenge will announce our five finalists at ION GNSS 2010 in Portland, Oregon. The winners will celebrate on October 18 in Munich.

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By Inside GNSS
August 17, 2010

A Search for Spectrum

FIGURE 1: Example of accuracy close to one centimeter provided by the integer ambiguity resolution on undifferenced phase (IARUP) technique using GPS L1 and L2 signals

In recent years, researchers have explored possible new allocations for Radio Determination Satellite Service (RDSS) and Radio Navigation Satellite Service (RNSS) spectrum from a regulatory point of view. These studies have mainly discussed S-band and C-band in addition to L-band.

The International Telecommunications Union (ITU) Radio Regulations define RNSS as a subset of RDSS. Although the allocations are differentiated — RDSS usually has a paired uplink — both can actually be used for satellite navigation.

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By Inside GNSS

A Fully Digital Model for Kalman Filters

Q: Is it possible to define a fully digital state model for Kalman filtering?

A: The Kalman filter is a mathematical method, purpose of which is to process noisy measurements in order to obtain an estimate of some relevant parameters of a system. It represents a valuable tool in the GNSS area, with some of its main applications related to the computation of the user position/velocity/time (PVT) solution and to the integration of GNSS receivers with an inertial navigation system (INS) or other sensors.

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By Inside GNSS
July 23, 2010

GNSS Hotspots

One of 12 magnetograms recorded at Greenwich Observatory during the Great Geomagnetic Storm of 1859
1996 soccer game in the Midwest, (Rick Dikeman image)
Nouméa ground station after the flood
A pencil and a coffee cup show the size of NASA’s teeny tiny PhoneSat
Bonus Hotspot: Naro Tartaruga AUV
Pacific lamprey spawning (photo by Jeremy Monroe, Fresh Waters Illustrated)
“Return of the Bucentaurn to the Molo on Ascension Day”, by (Giovanni Antonio Canal) Canaletto
The U.S. Naval Observatory Alternate Master Clock at 2nd Space Operations Squadron, Schriever AFB in Colorado. This photo was taken in January, 2006 during the addition of a leap second. The USNO master clocks control GPS timing. They are accurate to within one second every 20 million years (Satellites are so picky! Humans, on the other hand, just want to know if we’re too late for lunch) USAF photo by A1C Jason Ridder.
Detail of Compass/ BeiDou2 system diagram
Hotspot 6: Beluga A300 600ST

1. EARTHQUAKE!
Seattle, Washington USA
√ Want to know where an earthquake will occur and how big it will be? The Pacific Northwest Geodetic Array (PANGA) geodesy lab can tell you. They use 350 continuously operating high-precision GPS receivers and can analyze and share quake data in less than a minute. (Fact: A megaquake is likely 50 miles from Seattle).

PANGA’s website

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By Inside GNSS