Calibration and Unwrapping of the Normalized Scattering Cross ...

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

Calibration and Unwrapping of the NormalizedScattering Cross Section for the Cyclone

Global Navigation Satellite SystemScott Gleason, Senior Member, IEEE, Christopher S. Ruf, Fellow, IEEE,

Maria Paola Clarizia, Member, IEEE, and Andrew J. O’Brien

Abstract—This paper develops and characterizes the algorithmsused to generate the Level 1 (L1) science data products of theCyclone Global Navigation Satellite System (CYGNSS) mission.The L1 calibration consists of two parts: the Level 1a (L1a)calibration converts the raw Level 0 delay–Doppler maps (DDMs)of processed counts into received power in units of watts. The L1aDDMs are then converted to Level 1b DDMs of bistatic radar crosssection values by unwrapping the forward scattering model andgenerating two additional DDMs: one of unnormalized bistaticradar cross section values (in units of square meters) and a secondof bin-by-bin effective scattering areas. The L1 data products aregenerated in such a way as to allow for flexible processing ofvariable areas of the DDM (which correspond to different regionson the surface). The application of the L1 data products to thegeneration of input observables for the CYGNSS Level 2 (L2) windretrievals is also presented. This includes a demonstration of usingonly near-specular DDM bins to calculate a normalized bistaticradar cross section (unitless, i.e., m2/m2) over a subset of DDMpixels, or DDM area. Additionally, an extensive term-by-termerror analysis has been performed using this example extent ofthe DDM to help quantify the sensitivity of the L1 calibration asa function of key internal instrument and external parameters inthe near-specular region.

Index Terms—Bistatic radar, calibration, cyclone global nav-igation satellite system (CYGNSS), global navigation satellitesystem (GNSS), global positioning system (GPS), reflectometry,scatterometry.

I. INTRODUCTION AND BACKGROUND

A. CYGNSS Mission

THE Cyclone Global Navigation Satellite System (CYGNSS)mission will consist of a constellation of eight satellites (or

observatories) equipped with Global Navigation Satellite Sys-tem (GNSS) bistatic radar receivers, which will map the oceansurface scattered signal power in the vicinity of the specular

Manuscript received December 19, 2014; revised July 2, 2015 andSeptember 23, 2015; accepted November 10, 2015.

S. Gleason is with Southwest Research Institute, Boulder, CO 80302 USA(e-mail: [email protected]).

C. S. Ruf and M. P. Clarizia are with the Department of Atmospheric,Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109USA.

A. J. O’Brien is with the Electrical and Computer Engineering, The OhioState University, Columbus, OH 43212 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2015.2502245

reflection point using time domain and Doppler frequencyfilters. The satellites will orbit in the same plane at an altitudeof approximately 500 km and at an orbit inclination of 35◦.CYGNSS will act as a GNSS bistatic scatterometer capable ofsensing sea-level winds both in global ocean and in tropicalcyclones, including in high-precipitation conditions [1]. Everysecond, the instrument on each observatory will output fourraw delay–Doppler maps (DDMs) from individual satellitereflections tracked on the Earth’s surface.

B. CYGNSS End-to-End Simulator and Level 2 WindRetrieval Algorithm

A GNSS-R end-to-end simulator (E2ES) was developed aspart of the CYGNSS mission. This simulator is described inmore detail in the companion paper [2], and this was intendedto act as a science and engineering development tool for thedetailed testing of the CYGNSS Level 1 [(L1) calibration]and Level 2 [(L2) wind retrieval] algorithms. The baselineCYGNSS L2 wind retrieval algorithm is described in the com-panion paper [3]. The simulator contains an implementation ofthe Zavorotny–Voronovich GNSS-R scattering model [4], real-istic orbit dynamics, and noise models. For the purposes of theL1 calibration, the E2ES was used to generate the lookup tablesfor the effective scattering area DDM needed for the Level 1b(L1b) calibration, which is described in detail as follows.

C. History of GNSS-R Remote Sensing

Using GNSS signals in a bistatic scatterometer-like config-uration was first proposed by Hall and Cordy in 1988 [5].Subsequently, the PARIS altimetry concept was put forwardby Martin-Neira in 1993 [6]. Several years later, the firstdemonstration of wind sensing using Global Positioning Sys-tem (GPS) reflections was carried out by Garrison, Katzberg,and Hill in 1998 from an aircraft [7]. Additionally, severalother researchers have performed experiments from near-Earthplatforms performing wind or wave sensing [8]–[13]. Together,this group of researchers established that GPS signals couldbe used to sense the near-surface ocean wind conditions. Inparallel, several researchers were performing GNSS altimetrystudies, which are not listed here. Additionally, Lowe et al.[14] detected a reflected signal from the SIR-C experimentcarried on the Space Shuttle. This was followed by the GNSS

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2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING

Fig. 1. DDMI processing stages after the antenna. Black boxes indicated gains due to the LNA and front end of the instrument, while gray boxes represent gainsdue to sampling and signal processing.

experiment carried on the UK-DMC satellite, which repeatedlydetected signals from ocean, land, and ice surfaces [15], andby the TechDemoSat mission in 2014, which has generatedmillions of GNSS-R spacecraft measurements [16]. These re-sults demonstrated that GNSS signals are easily detectablefrom a space platform, with the signals clearly responding tosurface conditions. A summary of the GNSS-R technique andits applications can be found in [17]–[19].

After this introduction, an overview of the instrument car-ried on the CYGNSS observatories is presented in Section II.Section III presents the Level 1a (L1a) calibration algorithm.Section IV describes the forward model and calibration param-eters used in the L1b algorithm. Section V describes the L1bcalibration algorithm. Section VI provides a brief description ofthe zenith navigation antenna calibration. Section VII presentsa detailed error analysis of the L1 calibration as applied to theCYGNSS DDM area (DDMA) used in L2 wind retrievals, andSection VIII includes a discussion of the results and conclusions.

II. CYGNSS INSTRUMENT SUMMARY

Each CYGNSS spacecraft carries a delay–Doppler mappinginstrument (DDMI) capable of locating and tracking GPS signalreflections on the Earth surface and mapping the signal powerover a range of time delay and Doppler frequency bins. Eachinstrument uses two Earth-pointing nadir antennas and a singleupward (space)-pointing zenith antenna for navigation and GPStransmitter calibration [1]. The instrument is passive, usingthe signals being transmitted from the GPS constellation. Theinstrument autonomously tracks and processes the incomingsignal to produce reflected signal power over a range of delayand Doppler bins. It outputs four DDMs every second to thespacecraft onboard computer and has been validated on theTechDemoSat satellite launched in 2014 [16]. The spacecraftthen compresses the DDMs and downlinks them for groundprocessing.

At the receive antenna, the broadband thermal noise up-welling from the Earth (denoted antenna noise in this analysis)is added to the surface scattered signal. Additional thermalnoise generated by the instrument electronics is added as thecombined signal passes through the amplification, downconver-sion, and filtering stages of the receiver. The resulting signal is acombination of these three terms, i.e., one signal and two noise,which is then sampled and processed by the receiver firmware.

For calibration purposes, the DDMI can be modeled by asingle gain term applied to the total measured power, where thatgain is a combination of hardware and firmware contributions.The complete set of components contributing to the overall gainof the instrument is shown in Fig. 1.

The components in Fig. 1 are briefly summarized as follows:

1) The low-noise amplifier (LNA) provides the initial signalamplification and is located as close as possible to theantenna. In this analysis, this term includes input andoutput cabling losses. The input to this stage comesdirectly from the science antenna or the blackbody loadresistor (located in the LNA itself).

2) Within the receiver front end, the signal passes througha commandable gain control, which will be initially cali-brated on the ground using a cold load input source.

3) The signal then passes through several downconversionand filtering stages in the instrument front end to convertthe signal from L-band to an intermediate frequencysuitable for digital processing.

4) The downconverted signal is then sampled and quantizedby the instrument in preparation for the digital signalprocessor. The aforementioned commandable gain con-trol will be set to achieve optimal digital sampling at theanalog-to-digital converter.

5) The digital signal processor consists of an FPGA-and-coprocessor-based system, which cross-correlates thedigital samples, generating the raw Level 0 DDM mea-surements. This block includes the instrument digitalprocessing unit described in more detail as follows.

A. Antennas

For science operations, each CYGNSS satellite carries twosix-element array left-hand circularly polarized nadir antennaswith a peak gain of approximately 14.5 dB (from measure-ments of the 18 flight antennas). The two science antennas aremechanically rolled approximately 20◦ to project their mainbeams out in a wide cross-track pattern, each to opposite sidesof the satellite ground track. Each antenna has, approximately,a 37◦ half-power beamwidth in the cross-track direction and a24◦ half-power beamwidth in the along-track direction. Addi-tionally, the spacecraft has a low-gain (approximately 4 dBiC)right-hand circularly polarized (RHCP) zenith antenna for usein platform navigation and in estimating the GPS signal trans-mit power level. More details on the ground coverage of theobservatory science antennas is included in [2].

B. Blackbody Calibration Loads

A calibration switch is included in the LNA for each ofthe nadir and zenith antennas and its dedicated instrumentchannel. The switch connects the input port of the receivereither to the antenna or to a blackbody calibration target. Thispermits frequent monitoring and correction for the variations


GLEASON et al.: CALIBRATION AND UNWRAPPING OF NORMALIZED SCATTERING CROSS SECTION FOR CYGNSS 3

TABLE ISUMMARY OF CYGNSS L1 DATA PRODUCTS

in the receiver gain by the L1a calibration algorithm. Thetemperature of the blackbody load resistor is monitored with athermistor placed within each LNA. Initial thermal analysis hasshown that the range of temperatures that the LNAs (and hencethe blackbody load resistor) are expected to see is betweenapproximately 14 ◦C and 20 ◦C, with slight variations betweenthe three LNAs due to their locations in the spacecraft.

C. Digital Processing Unit

After the antenna and LNA, the signal enters the receiver,where it is downconverted, digitized, and processed by a delay–Doppler mapping coprocessor. The incoming data are processedusing a frequency-dimension-based fast Fourier transform(FFT) technique known as a “Zoom” Transform Correlator(ZTC) [20]. The output of the ZTC is a mapping of the signal infrequency, i.e., 20 bins at 500-Hz steps, and delay over 128 binsin 0.25-chip steps. The Level 0 DDM downlinked from thespacecraft includes both signal pixels from the physical surfacearea in the vicinity of the specular reflection point and averagednoise pixels preceding the specular point in delay. The scatteredsignal power is processed using a 1-ms coherent integrationinterval in each DDM bin, which is followed by 1 s of non-coherent averaging.

D. CYGNSS L1 Data Products and DDMCompression Algorithm

A summary of the CYGNSS L1 data products is included inTable I. The L1 data products are calculated from the Level 0DDMs and metadata generated by the instrument. The Level 0DDMs are compressed on board the spacecraft, as described inthe following.

The raw DDM generated by the instrument is compressed tomeet the downlink requirements. The DDM data compressionand decimation algorithm preserves the information needed tosupport L1 calibration and L2 wind speed retrieval algorithmsin ground processing. It assumes that all individual pixels in theDDM are retained, if they lie within approximately 50 km ofthe specular point. It also averages and calculates statistics onthe noise pixels preceding the signal in delays without scatteredsignal power to allow for an accurate estimate of the noise floor.Account is taken of the following:

1) The uncertainty in the actual location of the specular pointin the DDM computed by the instrument. The instrumentuses a coarse targeting algorithm accurate to only 1 km,which can result in over 3 chips of error in the targetedDDM center.

2) The region of the DDM in delay and Doppler space thatlies within a 50-km radius of the specular point.

3) The number of bits of information contained in each pixelof the DDM is determined based on the detected mostsignificant set bit in each pixel value. The compression

algorithm stores a sufficient number of bits to capture allof the information in every pixel, without information loss.

4) The DDM samples with delay values before the specularpoint (which contain no reflected signal power), whichare used to estimate the DDM noise floor.

The compressed DDM includes a total of 17 delay bins (at0.25-chip spacing) and 11 Doppler bins (at 500-Hz spacing).The specular point is targeted for delay bin 9 (allowing eightdelay bins after specular and eight behind), and the specularDoppler is targeted for the center bin 5. The total range of delaysamples is given by the sum of the range of delays, over which a50-km footprint can span, plus the uncertainty in determinationof the delay value of the true specular point in the DDM by thecompression algorithm.

The true location is estimated by the compression algorithmto within 1 GPS C/A code chip (approximately 300 m) as thelocation of the maximum value of a low-pass filtered version ofthe full DDM. Subsequently, a more precise geolocation of thespecular reflection point is computed during ground processing,using the method derived in [2]. Noise samples outside thecompressed 17 × 11 DDM are sent to the ground separately.Rows preceding the specular point by at least a chip plus themargin of targeting error are used to ensure that there is noocean surface scattered signal present. At a minimum, the meanvalue of noise pixels and some associated statistics will be sentto the ground for every compressed DDM.

By design, the DDM compression algorithm will preserveall DDM information provided by the instrument with no lossof information, while minimizing the number of bits needed tostore the DDM. Additionally, any specular point location errorsby the instrument will be corrected on the ground and will affectneither L1 calibration nor subsequent wind estimation accuracy.

III. L1A CALIBRATION ALGORITHM: COUNTS TO WATTS

The L1a calibration converts each bin in the Level 0 DDMfrom raw counts to units of watts. Individual bins of the DDMgenerated by the DDMI are measured in raw and uncalibratedunits referred to as “counts.” These counts are linearly relatedto the total signal power processed by the DDMI. In addition tothe ocean surface scattered GPS signal, the total signal includescontributions from the thermal emission by the Earth and thenoise generated by the DDMI itself. The power in the totalsignal is the product of all the input signals, which is multipliedby the total gain of the DDMI receiver. A block representationof the L1a calibration procedure is shown in Fig. 2. The top boxdescribes the open ocean calibration used to update the instru-ment noise lookup tables after launch. The middle box showsthe periodic generation of blackbody calibration DDMs (whichare used during both the open ocean and routine calibrations).The third box shows the routine calibration performed on everyDDM, i.e., four times per second. The value of a DDM bin incounts is related to the arriving signal power in watts by

C = G(Pa + Pr + Pg) (1)

where C are the DDM values in counts outputted from theinstrument at each delay/Doppler bin. Pa is the thermal noise



Fig. 2. Overview of CYGNSS L1a calibration, where CO is the open oceanmeasurement in counts, and CN is the individual DDM noise floor estimate.The determination if a DDM occurs over the open ocean will be performedduring ground processing in the science operations center (SOC). LUT = lookup table; NF = noise figure; DDM = delay Doppler map; SOC = scienceoperations center.

power generated by the antenna (in watts). Pr is the thermalnoise power generated by the instrument (in watts). Pg is thescattered signal power at the instrument (in watts), and G isthe total instrument gain applied to the incoming signal (incounts per watt). The terms C and Pg are functions of delay andDoppler, while Pa, Pr, and G are assumed to be independentof the delay/Doppler bin in the DDM. Noise information iscalculated separately for each DDM, using pixels where nosignal power is present. Previously, in the literature, this regionof the DDM has been referred to as the “Forbidden Zone” [21].These delay and Doppler bins provide an estimate of the DDMnoise power, which is expressed in counts as

CN = G(Pa + Pr). (2)

Assuming that Pa and Pr are independent of delay andDoppler, all of the DDM samples without signal can be usedto estimate the noise level in counts.

A. Noise Power Expressions

All of the expressions in the following describe noise-onlypower representations and are not calculated from the DDMs.The calibration switch selects between the nadir antenna and

a blackbody target as the source of the input signal to theDDMI. When switched to one of the nadir antennas, the signalwill consist of both thermal emission from the Earth and thescattered GPS signal. The external antenna noise-only portionof this input can be expressed as

Pa = kTaBW (3)

where Ta is the top of the atmosphere brightness temperatureintegrated over the receive antenna pattern, k is Boltzmann’sconstant, and BW = 1/Ti = 1000 Hz is the processed signalbandwidth. The bandwidth of the processed GPS signal at theantenna is determined by the coherent integration processinginterval, which is Ti = 1 ms. When the calibration switchis directed to the blackbody target, the thermal noise powerentering the DDMI becomes

PB = kTBBW (4)

where PB and TB are the blackbody load noise power and theeffective temperature of the instrument blackbody load source,respectively. Because there is no external antenna input whenthe blackbody load is switched in, there is no signal powerpresent. When the CYGNSS observatory is over an area of openocean, with no land present in the main beam of the instrumentsurface antenna footprint, the noise power present in the noise-only pixels of the DDM can be expressed as

PO = kTOBW (5)

where PO and TO are the noise power and antenna beam-integrated brightness temperature of the ocean, respectively.The value of TO can be estimated using a microwave radiativetransfer model forced by known environmental conditions,which are derived either from climatology or by numericalforecast models such as GDAS or ECMWF. The model tem-peratures will be generated using daily inputs of sea surfacesalinity and temperature obtained from the NOAA Global Real-Time Ocean Forecast System.

The effect of wind-induced roughening of the ocean surfaceon its microwave brightness temperature is accounted for in theCYGNSS ocean brightness model, using the excess emissiv-ity model developed for the NASA Aquarius mission, whichincludes a radiometer operating at 1413 MHz [22]. The under-lying specular emissivity model used for CYGNSS is adjustedslightly, relative to the one used by Aquarius, to account for thedifference in operating frequency (1575 MHz for CYGNSS)and for the different range of incidence angles over whichCYGNSS views the ocean. However, the wind rougheningeffect, which is quite small, is assumed to be the same asfor Aquarius. Since radiometric calibration of the CYGNSSinstruments is performed using average measurements of theocean over weeks, observations in higher wind conditions willbe filtered out to reduce the sensitivity of the calibration toerrors in the excess emissivity model and in the reanalysismodel estimates of the wind speed.

The thermal noise power of the DDMI instrument can beexpressed as a function of its noise figure, or

Pr = kTrBW = k [(NF − 1)290]BW (6)



where Pr and Tr are the instrument noise power and temper-ature. The receiver noise figure NF is directly related to theinstrument noise temperature.

B. Generating the L1a Data Product

1) Open Ocean Calibration: The open ocean calibration isused to update the instrument noise (Pr) and receiver gain (G)lookup tables in orbit. As part of the open ocean calibration,two DDMI measurements are used together to estimate theinstrument noise and gain. These are the following:

1) DDM noise floor measurements made over areas of openocean (as determined by the science operations center).This calculation is made using the noise-only pixels ofthe DDM.

2) Measurements of the blackbody target noise levels calcu-lated using a blackbody noise-only DDM.

The ocean noise temperature and the blackbody noise temper-ature provide low- and high-power anchor points with whicha linear calibration curve can be derived. Expressions for theLevel 0 DDM measurements in the open ocean and blackbodystates are given by

CO =G(PO + Pr) (7)

CB =G(PB + Pr). (8)

The receiver gain is found by differencing the average black-body and open ocean counts, resulting in the cancelation of thereceiver noise power Pr, i.e.,

CO−CB=G(PO+Pr)−G(PB+Pr)=GPO−GPB. (9)

Solving for the instrument gain, we obtain

G =CO − CB

PO − PB. (10)

Substituting (10) into (7) gives the instrument noise power as

Pr =POCB − PBCO

CO − CB. (11)

2) Routine DDM Calibration: The routine DDM (in counts)is expressed in (1), which includes the received signal power inwatts Pg . In the case of the routine calibration, the individualDDM noise floor and the blackbody noise temperature providelow- and high-power anchor points used to derive a linear cali-bration equation. The first step in the routine DDM calibrationis to correct every DDM by the estimated noise floor using (2),such that we are left with a signal-only DDM, which is scaledby the instrument gain, as follows:

Cg = C − CN = GPg. (12)

The instrument gain can be expressed by rearranging (12)and setting this equal to the instrument gain estimated directlyfrom the blackbody load DDM calculated from

G =C − CN

Pg=

CB

PB + Pr(13)

where CB is the mean count value of the blackbody load DDM,and PB is the estimated blackbody load noise power estimatedusing the thermistor temperature reading near the blackbodyload in the LNA input into (4). Pr is the best estimate of theinstrument noise power, which was estimated from a noise–figure–versus–temperature lookup table and validated duringthe open ocean calibration sequence. By substituting (13) into(12) and solving for the signal power term Pg , we arrive at thefinal expression for the L1a calibrated DDM as follows:

Pg =(C − CN )(PB + Pr)

CB. (14)

C. Consideration of Time and Temperature Dependencies

All of the terms in (14) are collected at slightly differenttimes than the actual science measurements themselves, andduring these time intervals, it is possible that the noise tempera-tures can vary slightly from the measurement time. The routine1-Hz calibration assumes that gain G, antenna noise temper-ature Ta, and instrument noise power Pr remain reasonablyconstant over the combined collection interval for (1) (DDMto be calibrated), (2) (noise floor estimate for the DDM beingcalibrated), and (8) (the blackbody load noise DDM). Timedependence of each of the terms in the L1a calibration equation(14) are addressed as follows:

1) The science measurement C is made once per second andprovides the reference time for all of the other parameters.

2) The noise measurements CN for each science DDM aremade at delays without signal power, which are only ofthe order of a handful of microseconds from the timeof the science measurement.

3) The blackbody target power PB is determined from aphysical temperature sensor measured at 1 Hz and is nearenough in time to the 1-Hz science measurements thatthe physical temperature will not have changed signif-icantly between the thermistor reading and the sciencemeasurement.

4) The receiver noise power Pr is estimated using a lookuptable derived from extensive prelaunch measurementsand updated on orbit during the open ocean calibrationsequence using (11). It is expected that the LNA perfor-mance will change slightly as the devices age, and theperiodic open ocean calibrations will track these changesover the mission lifetime.

5) The blackbody target measurement CB is made within30 s of the science measurement, and close enough intime that the receiver gain and noise figure have notchanged significantly. Additionally, the blackbody mea-surements will be interpolated to the time of the measure-ment during ground processing.

The open ocean calibration will occur multiple times everyorbit, and the blackbody calibration will be performed every 60 son orbit for each nadir science antenna. The routine calibrationwill be performed at 1 Hz on all DDMs outputted by the DDMI(four per second). Fig. 3 illustrates the actions performed andintervals, for all of the CYGNSS L1a calibration steps.



Fig. 3. CYGNSS L1a calibration timing. The open ocean calibration will occurwhere the science operations center determines that there is no land in theantenna footprint. The blackbody calibration interval is configurable, with adefault of 60 s. The routine calibration is applied to all four 1-Hz DDMsoutputted by the DDMI.

D. LNA Gain and Noise Figure Temperature Characterization

The LNA noise figure (related to the instrument noise powerPr) will be thoroughly characterized as a function of temper-ature and stored in a lookup table. The LNA gain and noisefigure profiles over the expected operating temperatures thatthe device will experience on the spacecraft will be generatedprelaunch and periodically updated on orbit using the openocean calibration estimates of the instrument gain and noisefigure, as expressed in (10) and (11), respectively.

The lookup table is indexed using the physical temperature sensor reading located in the LNA. The dependence of G and Pr

on temperature will initially be characterized in prelaunchenvironmental testing, and the first flight lookup tables willbe derived from those test data. Once on orbit, open oceanmeasurements will be used to track changes in G and Pr asthe LNA ages.

E. Illustration of Noise Averaging Effects on L1a Algorithm

The L1a calibration algorithm has been validated using sim-ulated DDMs from the CYGNSS E2ES and by independentanalysis. An example of a simulated Level 0 DDM (in counts)and a calibrated L1a DDM (in watts) are shown in Figs. 4 and 5,respectively.

Fig. 4. Example Level 0 DDM (in counts) after application of the onboardcompression algorithm. The compressed size of the DDM is 17 delay bins(0.25-chip spacing) and 11 Doppler bins (500-Hz spacing).

Fig. 5. L1a DDM (in watts) calculated from the example Level 0 DDM shownin Fig. 4.

The maximum value in counts of the Level 0 DDM (seeFig. 4) will depend on the simulated or actual signal power,and it is generally on the order of several thousands of countsbased on preliminary testing. This includes all the analog anddigital processing gain in the instrument processing chain. TheL1a DDM (see Fig. 5) is calculated using (14) and is essentiallya linear scaling of the Level 0 DDM based on the following:a) the blackbody load power (PB), b) the estimated instrumentnoise power (Pr), and c) the blackbody load DDM mean counts(CB). These values will be constant over all pixels for anyindividual L1a DDM calibration.

A full error analysis of the L1a calibration is performed inSection VII. However, we have included here an example ofthe effect of the number of noise bins used during the L1acalibration, as an illustration of its significance. An exampleof the L1a calibration accuracy as a function of the number



Fig. 6. Summary of L1a errors as a function of number of averaged noise rowsfor each DDM. The vertical line represents 52 rows of noise-only samples.

of noise samples (i.e., pixels used in the estimation of CN ) isshown in Fig. 6. As part of the CYGNSS observatory onboardcompression algorithm, mean noise levels are sent to the groundfor every DDM. Currently, we plan to average a total of 52 delayrows (1040 total noise pixels) when estimating the individualDDM noise floor during the routine calibration. This is basedon two criteria: a) the “knee” in the curve shown in Fig. 6 andb) the usable range of DDM bins which can be guaranteed not tohave signal power present (including the maximum instrumenttargeting error). Row 52 was selected since it is 12 rows behindthe nominal center of the DDM (row 64), and accounts forspecular point targeting errors by the instrument. For the caseof the blackbody DDMs, all 128 delay rows will be averagedbecause no signal is present anywhere in the DDM.

IV. FORWARD MODEL OF SCATTERED SIGNAL POWER

A full expression for the GPS scattered signal power waspreviously derived and published in 2000 [4], as shown in (15).The original representation has been slightly modified in formand variables as follows:

P g

τ ,f=

PTλ2

(4π)3

∫∫A

GTx,yσ

0x,yG

Rx,y(

RRx,y

)2 (RT

x,y

)2La1La2

Λ2τ ;x,yS

2f;x,y

dxdy

(15)

where P g

τ ,fis the coherently processed scattered signal power

in watts. PT is the GPS satellite transmit power, and GTx,y is the

GPS satellite antenna gain. GRx,y is the CYGNSS instrument

receiver antenna gain. RTx,y and RR

x,y are the transmitter-to-surface and surface-to-receiver ranges, respectively. La1 andLa2 are atmospheric losses to and from the surface, respec-tively. σ0

x,y is the normalized bistatic scattering cross section(NBRCS). λ is the GPS signal carrier wavelength (19 cm).Λτ ;x,y is the GPS signal spreading function in delay, and Sf ;x,yis the frequency response of the GPS signal. Exact definitionsof these functions can be found in [23]. The surface integrationarea A includes the entire region of diffuse scattering over the

whole DDM. Within this area, the scattered signal power isprocessed over a range of relative delays τ and Doppler fre-quencies f . Equation (15) assumes a 1-ms coherent integrationtime during signal processing. The coherent integration time of1 ms is based on preliminary analysis performed in [14] and[24]. The former showed the signal coherence to be slightly lessthan 1 ms for a lower orbiting (i.e., faster moving) platform,and the later showed some evidence that the coherence waslonger than 1 ms for a higher orbiting satellite. The fact is thatthe true coherence of the scattered signal for CYGNSS is notprecisely known and is an active area of research. The 1-mscoherent integration time has been partially chosen as a matterof convenience due to the GPS C/A code repeat interval.

Equation (15) can be simplified by calculating effectivevalues for each term under the integral which varies over theextent of the DDM. These values are calculated using theGPS spreading terms over individual delay and Doppler bins.Ideally, all of the terms in the area included in each DDMpixel should be calculated using a full surface integration at agiven reflection geometry. However, in some cases, average orspecular point values can be used as approximations. Therefore,(15) can be simplified using the effective values of severalvariables in each bin, resulting in an expression for individualbins of the DDM, i.e.,

Pg,τ ,f =PTλ2GT

τ ,fσ0τ ,f

GRτ,f

Aτ ,f

(4π)3(RR

τ,f

)2 (RT

τ ,f

)2

La1La2

(16)

where GRτ,f

is the effective receiver antenna gain at each

delay/Doppler bin. RTτ,f

and RRτ,f

are the effective range losses

at each delay/Doppler bin, and Aτ ,f is the effective surfacescattering area at each delay/Doppler bin. The effective scat-tering areas are calculated based on the measurement specificreflection geometry and include the GPS specific delay andDoppler spreading functions.

Note that a bar above a variable in (16) indicates that thatvalue is an “effective” value, which implies the inclusion of theGPS spreading functions in delay and Doppler for each DDMpixel. The difference between effective and average values forthe example of the receiver antenna gain is described in moredetail in Section V.

A. Specular Point Calculation

The L1 data product are calibrated and geolocated usinga precise surface specular reflection point calculation on theground using the CYGNSS E2ES. The E2ES implements a fastiterative method for solving the specular point on the WGS-84Earth model, given the receiver and transmitter locations. Eachiteration actually finds the specular point using a sphericalEarth approximation; however, the radius of the spherical Earthis determined from the full WGS-84 ellipsoid model at theprevious iteration’s specular point location. This results in a fastsolution that quickly converges to the true specular location,and this method has been validated by comparing results fromthe more rigorous method described in [17]. More details on thespecular point calculation can be found in [2].



Fig. 7. Overview of CYGNSS L1b calibration.

V. L1B CALIBRATION ALGORITHM: WATTS TO SIGMA0

The L1a calibrated DDM represents the received surfacesignal power in watts over a range of time delays and Dopplerfrequencies. Before any geophysical parameters can be esti-mated, these power values must be corrected for non-surface-related terms by inverting the forward model shown in (16),based on the familiar radar equation. In effect, this equationis unwrapped or solved for the parameter of interest, i.e.,the bistatic radar cross section. The CYGNSS L1b calibrationgenerates two data products associated with each L1a DDM:1) a bin-by-bin calculation of the surface bistatic scatteringcross section σ (not normalized by scattering area) and 2) bin-by-bin values of the effective scattering areas (calculated asdescribed in the following). These two products will allow usersto normalize values of σ to values of σ0 (scattering cross sectionper meter squared), over configurable surface extents using theeffective scattering area of each DDM bin. The L1a values arecorrected for the effects of the transmit and receive antennas,range losses, and other non-surface-related parameters. Anoverview of the CYGNSS L1b calibration is shown in Fig. 7.The aforementioned left box shows a summary of the metadatacollected by the spacecraft and sent to the ground. The flowdown from the top right is the estimation of the GPS transmittertransmit power and antenna gains. The bottom right box showsthe CYGNSS E2ES inputs and outputs. All of these elementscome together in the middle during the L1b calibration.

A. Calculating an NBRCS

The bin-by-bin sum of scattering cross sections (σtotal), andthe bin-by-bin sum of effective scattering area (Atotal) can becalculated using individual DDM pixels to arrive at an effectivenormalized radar cross section value, i.e., σ0, over selectedregions of the DDM. The resulting expression for σ0 is given by

σ0 =σtotal

Atotal=

∑Ni=1

∑Mj=1 στi,fj∑N

i=1

∑Mj=1 Aτi,fj

(17)

where N and M represent the range of DDM bins for delay andDoppler, respectively, used in calculating both the scatteringcross section and effective scattering area DDMs. Dependingon the application and the L2 remote sensing algorithm andsurface resolution requirements, different regions of the DDMcan be used to calculate a single or multiple values of σ0.

B. Region of DDM Used in CYGNSS L2 Wind Retrievals

The L2 CYGNSS wind retrieval data products use a subsetof pixels of the downlinked compressed DDM consisting of3 delay bins and 5 Doppler bins centered at the specular point.This subset of DDM bins is used to calculate σ0 for the baselineCYGNSS L2 wind retrieval algorithm. This region correspondsroughly to a 25 km × 25 km surface region, often less, en-abling averaging of consecutive DDMs during retrievals. Thewind estimation retrieval model used to generate the baselineCYGNSS L2 wind retrievals is described in [3]. This value ofσ0, which is specific to the CYGNSS L2 baseline wind retrievalalgorithm, is calculated using (17) with N = 3 and M = 5,respectively. This is referred to in the following as the DDMAused specifically for the CYGNSS L2 wind retrievals.

C. Expression for Bistatic Radar Cross Section

The final expression for the L1b σ DDM can be derivedfrom the expression of the signal forward model, as shown in(16), by solving for the NBRCS term σ0. Since the L1b sigmaproduct will not be normalized, we have removed A from (16)and replaced the normalized radar cross section σ0 with theunnormalized σ. The result expression for σ is given by

στ ,f =Pg,τ ,f (4π)

3La1La2Iτ ,fPTλ2GT

SPGRSPR

TotalSP

(18)

where the individual terms in (18) are as follows:

1) Pg,τ ,f is the L1a calibrated signal power at a specific

delay (τ ) and Doppler (f) bin.2) RTotal

SP is the total range loss from the transmitter to thesurface plus the surface to the receiver at the specularpoint. When using a relatively small area of the DDMnear the specular reflection point, this value can be ap-proximated as the total range from the transmitter to thespecular point to the receiver. This term is included in thedenominator because it is calculated as a loss RTotal =(1/(RR)

2)(1/(RT )

2).

3) La1 and La2 are the estimated atmospheric loss correc-tions from the transmitter to the surface and surface toreceiver, respectively.



4) Iτ ,f is an additional term used to correct for losses in-troduced by the DDMI. These include the 2-bit samplingcorrection and possibly a roll-off correction in the outerDoppler bins due to processing losses inherent in the ZTCof the instrument [20].

5) PT and GTSP are the GPS satellite transmit power and

antenna gain at the specular point, respectively. Thesevalues are estimated as part of mapping the GPS satelliteeffective isotropic radiated power (EIRP) pattern of theGPS transmitters.

6) GRSP is the receiver antenna gain at the specular point.

When using a relatively small area of the DDM nearthe specular reflection point, and making the measure-ment with a relatively wide-beam antenna, the differencebetween the specular, average, and effective values isacceptably small. The difference between the specularpoint and effective receiver antenna gain is analyzedfurther in the next section.

D. Effective and Average Calibration Parameters

The influence of the spreading functions and the impact ofsimplifications during the L1b calibration needs to be carefullyconsidered. The primary simplifications in this regard are usingthe specular point values of receiver and transmitter antennagains and path loss values in place of effective values. TheCYGNSS measurements have been modeled in detail usingthe E2ES [2]. Using a long-duration E2ES run, we assessedthe impact of using specular point approximations for severalparameters on the L2 wind retrievals. This analysis showed thatapproximating the receiver antenna gain, transmitter antennagain, and path losses at the specular point still allowed us tomeet our wind speed retrieval requirements [3]. With regardto the receive antenna pattern, given its relatively wide mainbeam and surface footprint, the difference between the effectiveand specular point values of the receiver antenna gain (over anapproximately 25 km × 25 km area) is reasonably close.

1) Difference Between Effective and Physical Receiver An-tenna Gain: The effective receiver gain can be expressed as

GREff(τ , f) =

∫∫A

GR(x, y)Λ2τ ;x,yS

2f ;x,y

dxdy. (19)

Meanwhile, the average value of the receiver gain in eachDDM pixel can be expressed as

GRAvg(τ , f) =

1

Aτ ,f

∫∫A

GR(x, y)dxdy. (20)

Fig. 8 shows the difference between a) the receiver antennagain at the specular point, b) the average receiver gain overphysical surface area bins within the 3 × 5 DDMA, and c) theeffective antenna gain over the same physical surface area binswithin the 3 × 5 DDMA. The average antenna gain is calculatedusing (20), while the effective values are calculated using (19).Subsequently, the offset between the curves is removed toshow the relative difference between the values as a functionof incidence angle. It is evident that, over the physical area

Fig. 8. Average and effective antenna gains with offset between them removedas a function of incidence angle at 90◦ azimuth angle.

on the surface roughly corresponding to the 25 km × 25 kmobservation resolution, all three values (after offset removal) areclose. By removing the offset between the curves, the relativedifference in the variables can be observed. The averaged valuesand the effective value within the near-specular point pixelsare all within a couple tenths of a decibel of each other overthe complete range of reflection geometries, and within theorder of magnitude of errors examined in the error analysis asfollows. However, as more pixels in the DDM are included,the effective values can start to diverge from the average andnear-specular effective values. This could very well result inthe use of effective values resulting in improved L2 wind speedretrievals for techniques that use larger areas of the DDM.

2) Calculating Effective and Physical Scattering Areas: Asingle delay/Doppler bin will contain the captured scatteredpower from a distinct physical region on the ocean surface.For each delay/Doppler bin in the DDM, this region will varyboth in actual physical size (on the ground surface area) andeffective area (including GPS spreading functions). The GPSspreading functions (in both delay and Doppler) increase theeffective area of each delay/Doppler bin, causing power to be“spread” into adjacent delay and Doppler bins from outside thegeometry-determined physical scattering area. These functionschange the overall power observed. These values are calculatedwithin the CYGNSS E2ES using a surface integration and bin-by-bin application of the GPS spreading functions using anFFT technique [2]. The physical area of each DDM bin can becalculated as follows:

Aτ ,f =

∫∫A

dxdy. (21)

An example of the physical scattering area for a typical DDMis shown in Fig. 9. Note that points up to and before the specularpoint bin (i.e., at delays shorter than the specular reflectionpoint delay) have no physical surface scattering area. The powerreceived in the bins before the specular point is due to power



Fig. 9. Physical scattering area (in square meters) for an example DDMreflection geometry. Note that delays before the specular reflection point anddelays at and ahead of specular at increasing Doppler also do not correspond toany physical surface region.

Fig. 10. Effective scattering area (in square meters) corresponding to thephysical scattering area shown in Fig. 9. This DDM of effective scattering areais a key output product of the L1b calibration, which allows users to calculatenormalized values of σ0 .

being spread into these bins by the GPS spreading functionsfrom physical areas near the specular point. The effectivesurface scattering area for each delay/Doppler bin is expressedas the ambiguity function weighted surface integration, i.e.,

Aτ ,f =

∫∫A

Λ2τ ;x,yS

2f ;x,y

dxdy (22)

where the delay spreading function Λτ ;x,y and the Dopplerspreading function Sf;x,y are integrated over the physicalsurface corresponding to each individual delay/Doppler bin.Fig. 10 shows the effective scattering area DDM correspondingto the physical scattering areas illustrated in Fig. 9.

Fig. 11. L1a DDMA values versus the Nature Run wind speed truth reference.Without the L1b corrections of the DDMA model function, the correlationbetween the observable and the simulated wind speed is suboptimal.

E. Characterizing the GNSS Transmitters

The GPS transmitted power PT and transmitter antenna gainGT can be estimated using a parameterized model of the GPSantenna pattern and a locus of measurements over the entire bot-tom sphere of the GPS antenna pattern using direct signal powermeasurements from the DDMI zenith navigation antenna. Thebaseline GPS antenna patterns will be based on the patternsreleased in [25] and [26]. Currently, the yaw attitude of theGPS constellation satellites is not being considered but could beif necessary using the model published by Bar-Sever [27]. Theknown patterns are consistent enough in yaw as to be within theallocated margin of error. With the off-boresight angle (θ) andazimuth angles (φ) calculated relative to the GPS satellite frameof reference, the GPS transmitter EIRP, which includes the GPStransmit powerPT and antenna gainGT , can be estimated usingthe radar equation and indexed as follows:

EIRPa =(P lTG

lT

)(θ, φ) =

P ldR

2D(4π)2

GDλ2(23)

where P ld is the received direct signal power from satellite l,

RD is the direct signal range (the distance between the GPStransmitter and the receiver), GD is the zenith antenna gain,and λ is the GPS L1 wavelength.

F. Validation of the L1b Algorithm

The L1b algorithm was validated using CYGNSS E2ESsimulations. The L1b σ DDM calculated from the L1a DDMin Fig. 5 is shown in Fig. 13. The DDM of σ together withthe DDM of effective scattering areas (shown in Fig. 10) wereused to calculate σ0 observables for a 13-day Nature Runsimulation, which included a realistic hurricane [2]. The NatureRun hurricane simulation is described in detail in [28]. The13 days’ worth of DDMs where then calibrated and inputtedinto the CYGNSS L2 wind speed retrieval algorithm.

The results of the L1a and L1b DDMAs with respect toNature Run wind speeds are shown in Figs. 11 and 12. Whendesigning the L2 wind retrieval model functions, the calibrationto the L1b DDMA is essential to maintain the required windspeed sensitivity in the wind speed retrieval. The improvementin the spread of the model function relationship between the



Fig. 12. L1b DDMA values versus the Nature Run wind speed truth reference.With respect to the spread of points in Fig. 11, the correlation between theobservable and the simulated wind speed is significantly improved.

observable and Nature Run reference wind speed is clearlyevident in Fig. 12 after the application of the L1b calibration.Complete details of the L2 wind retrieval algorithm and valida-tion are included in the companion paper [3].

VI. ZENITH ANTENNA CALIBRATION

The zenith antenna gain is used in the mapping of the GPStransmit power and antenna gains described in Section V-E. Thecalibration (signal power in watts) of the direct signals receivedby the zenith antenna is performed along the same general linesas the nadir antennas, with a number of important differences.The power estimates of the received direct signals are used tomap the power and antenna gains of the GPS transmit antennas.Important considerations in the calibration of the zenith signalpower (with respect to the nadir antenna channels) include thefollowing:

1) The zenith antenna calibration load cannot be switchedas often as the nadir antennas because switching to theblackbody calibration load on the zenith channel willcause a navigation outage (and a corresponding sciencedata outage) for up to 30 s.

2) The reference noise floor is not computed as noise samplesin a DDM, but as the output of a separate noise channel.

3) The reference noise floor is more susceptible to biasesdue to cross-correlated power of other GNSS satellites inview. The effect of cross-correlated power on the noisefloor estimate will be tested prelaunch and a correctionapplied if necessary.

4) The cold source reference antenna noise temperature isthe deep space noise temperature (as opposed to the openocean noise temperature).

The longer blackbody calibration interval means that thecalibration algorithm has to rely more strongly on a well-characterized LNA noise figure as a function of temperatureto estimate changes to the zenith channel receiver noise. Ac-curately determining the zenith LNA temperature performanceand limiting the gradient of the temperature fluctuations seen bythe LNA will be of critical importance to accurately determin-ing the noise and signal power coming from the zenith antennachannel.

VII. ERROR ANALYSIS

During this error analysis, the uncertainties present in theCYGNSS L1 calibration algorithm are generally considered asindependent uncorrelated error sources. The method for thiserror analysis is based on that presented in [29].

A. Error Analysis Methodology

The total error in the L1a or L1b calibrated DDM is the rootof sum of squares (RSS) of the individual error sources in theindependent terms of their respective expressions, which can beexpressed generically as

ΔLa,b1 =

[x∑

i=1

[E(qi)]2

] 12

(24)

where La,b1 is the L1a or L1b calibrated DDM values, x is the

number of independent error terms, and qi are the respectiveerror parameters. The individual error terms can be estimatedby taking the partial derivatives of the calibration equation, suchthat each error term in the process can be quantized as

E(qi) =

∣∣∣∣∣∂La,b1

∂qi

∣∣∣∣∣Δqi. (25)

B. Quantifying L1a Errors

In the case of the L1a calibration, the final expression for theL1a DDM in (14) can be substituted into (25), such that

E(pi) =

∣∣∣∣∂Pg

∂pi

∣∣∣∣Δpi (26)

where the individual error quantities are defined as follows:p1 = C, p2 = CN , p3 = PB , p4 = Pr, and p5 = CB . The1-sigma uncertainties in these quantities are expressed as Δpi.Evaluating the partial derivative error terms, we obtain

E(C) =PB + Pr

CBΔC (27)

E(CN ) =PB + Pr

CBΔCN (28)

E(PB) =C − CN

CBΔPB (29)

E(Pr) =C − CN

CBΔPr (30)

E(CB) =(C − CN )(PB + Pr)

C2B

ΔCB (31)

where the error terms are defined as follows:

1) ΔC: The error inherent in the Level 0 DDMs fromthe instrument is due to the quantization error in theraw DDM bins. From the CYGNSS DDM compressionalgorithm, each DDM bin will be quantized over a rangeof 9 bits, resulting in an error of 1/29.

2) ΔCN : The error in the estimate of the normal DDMnoise floor is a function of the number of noise samplesavailable. See Fig. 6.

3) ΔPB is the error in the estimate of the blackbody loadDDM noise power, which is related to the error in theblackbody temperature according to (4) and assumed tobe 2 ◦C in this analysis.



TABLE IIROUTINE L1A SIGNAL POWER CALIBRATION ERRORS. ALL UNITS IN DECIBELS. IN BOTH WIND CASES,

THE NOISE FLOOR WAS COMPUTED USING 52 ROWS (20 PIXELS PER ROW) OF NOISE PIXELS

Fig. 13. L1b DDM of (unitless) σ values. This DDM of σ is combined withthe DDM of effective scattering areas to generate σ0 (σ per square meter) foruse in L2 wind speed estimation. The number of pixels used is flexible andwill depend on the application and inversion technique. The CYGNSS L2 windretrieval uses a 3 delay bin × 5 Doppler bin DDMA.

4) ΔPr is the error in the temperature-versus-LNA-noise-figure lookup table.

5) ΔCB is the error in the estimate of the blackbody DDMnoise floor.

Quantitative values for each or the error components listedearlier and the RSS total for two wind retrieval conditions areshown in Table II. The analysis of winds below 20 m/s assumeda σ0 value of 20 dB, while the regions above 20 m/s assumed aσ0 of 12 dB. These values were estimated using the model forσ0 published in the Zavorotny and Voronovich model [4].

C. Quantifying L1b Errors

In order to assess the error in the normalized radar crosssection, i.e., σ0, expressed in (17), (18) has been normalizedby the effective scattering area and considered for DDM binsin the CYGNSS L2 DDMA regions (3 delays × 5 Dopplers;see Fig. 13), i.e.,

σ0DDMA =

Pg,DDMA(4π)3La1La2I

PTλ2GTSPG

RSPR

TotalSP ADDMA

. (32)

The total error in the L1b DDM is the RSS of the individualerrors contributed by the independent terms of (32). Substitut-ing this equation into (25) results in

E(qi) =

∣∣∣∣∂σ0DDMA

∂qi

∣∣∣∣Δqi (33)

where the error terms are defined as follows: q1 = Pg, q2 =La12, q3 = RR, q4 = RT , q5 = PT , q6 = GT , q7 = GR, andq8 = A, respectively. The partial derivatives of the individualerror terms can be expressed as

E(Pg,DDMA)=(4π)3

(RR

SP

)2 (RT

SP

)2La1La2

PTλ2GTSPG

RSPADDMA

ΔPg,DDMA

(34)

E(La12)=Pg,DDMA(4π)

3(RR

SP

)2 (RT

SP

)2PTλ2GT

SPGRSPADDMA

ΔLa12 (35)

E(RR

SP

)=

2Pg,DDMA(4π)3(RR

SP

) (RT

SP

)2La12

PTλ2GTSPG

RSPADDMA

ΔRRSP

(36)

E(RT

SP

)=

2Pg,DDMA(4π)3(RR

SP

)2 (RT

SP

)La12

PTλ2GTSPG

RSPADDMA

ΔRTSP

(37)

E(PT )=Pg,DDMA(4π)

3(RR

SP

)2 (RT

SP

)2La12

(PT )2λ2GTSPG

RSPADDMA

ΔPT

(38)

E(GT )=Pg,DDMA(4π)

3(RR

SP

)2 (RT

SP

)2La12

PTλ2(GT )2GRSPADDMA

ΔGT

(39)

E(GR)=Pg,DDMA(4π)

3(RR

SP

)2 (RT

SP

)2La12

PTλ2GTSP

(GR

SP

)2ADDMA

ΔGR

(40)

E(A)=Pg,DDMA(4π)

3(RR

SP

)2 (RT

SP

)2La12

PTλ2GTSPG

RSP(ADDMA)2

ΔADDMA.

(41)

Again, the error analysis was performed for both cases ofwinds below 20 m/s (with σ0 = 20 dB) and winds greater than20 m/s (with σ0 = 12 dB).

Errors for the remaining terms of the L1b calibration wereestimated using best estimates. Table IV shows the input errorvalues used for the low-wind and high-wind cases, respectively.

1) Monte Carlo Simulation: The inputs to the L1a erroranalysis were generated using a Monte Carlo simulation andbundled into an overall error in the receiver antenna gain, whichwas then rolled into the overall error budget. This overall errorin the antenna gain (GR

SP) is determined by several parameterslisted in Table III as follows and used as input conditions tothe Monte Carlo simulation. The simulation was then run overone million times at random geometries to produce distributionsof the total antenna gain error as a function of measurement



TABLE IIIERROR ALLOCATIONS FOR THE RECEIVER ANTENNA GAIN

TABLE IVL1B CALIBRATION ERROR ANALYSIS INPUT PARAMETERS

TABLE VL1B CALIBRATION ALGORITHM ERRORS (IN DECIBELS)

geometry. Each parameter in the Monte Carlo simulation in-cluded in Table III is described as follows:

1) Spacecraft Pointing Knowledge: This is an estimate of theerrors in the CYGNSS observatory star tracker attitudeestimation knowledge, which is based on the star trackerspecification and attitude determination simulations.

2) Star Tracker Optical/Mechanical Boresight Misalign-ment, Star Tracker to Nadir Antenna Misalignment, andMechanical-Electrical Nadir Antenna Boresight Misalign-ment errors: These values have been initially estimated(conservatively) using mechanical, structural, and ther-mal analysis. However, in addition to a purely analytic/mechanical alignment, an optical alignment cube-basedtransformation calculation will be attempted, which couldsignificantly decrease this error.

3) Repeatability of Antenna Gain: The 18 CYGNSS flightantennas have been delivered and pattern analysis un-dertaken. Using the measured standalone antenna gainpatterns, the 1-sigma value of the measured pattern vari-ability has been calculated.

4) Antenna Pattern Uncertainty: This estimate was arrived atusing a combination of error analysis connected to the an-echoic chamber measurement setups and confidence in ourmodeling tools’ ability to predict the measured patterns.A modeling effort is under way to estimate the changes inthe antenna patterns, which will occur when the antennasare added to the spacecraft. Preliminary pattern simulationresults and additional baseline pattern testing of an antenna

mounted to a spacecraft mock-up have allowed us to gen-erate an estimate we have confidence in for this parameter.

D. Rolled-Up L1 Calibration Errors

The rolled-up L1 calibration error was estimated using theresults of the analysis earlier, over all accumulated steps of theL1 calibration. This includes rolling the estimated 1-σ error inthe L1a calibration into the results of the L1b error analysis (seeTable IV). The final estimate of the total L1 calibration errorsat the end of the L1b stage consists in taking the RSS of allof the individual error terms contributing to the L1b correction,including the L1a calibration errors shown in Table II. Quan-titative values for the total rolled-up L1 calibration error areincluded in Table V.

The justification for each of the errors in the rolled-up L1error budget, which is included in Table V, is discussed brieflyas follows.

1) Rolled-up L1a error E(Pg): Values taken from Table IIbased on the rolled-up RSS analysis for the individualL1a error terms. Analysis was done at two different windspeeds to present a high-wind and low-wind case.

2) Total atmospheric modeling error E(La12): Due to itsL-band frequency, the atmospheric attenuation errors areexpected to be very small [30]. The GPS constellation is,by design, relatively immune to atmospheric conditions,due to its transmit frequency. One of the advantages ofGNSS-R is its ability to “see through” rain and measurethe surface.



3) Total range error E(RR) + E(RT ): This error is deter-mined by the uncertainty in three values: a) the observatory(or receiver) position, b) the GPS satellite (or transmitter)position, and c) the estimate of the specular reflectionpoint on the surface. The receiver position is expected tobe accurate to less than 5 m [31]. The GPS transmitterpositions will be known during postprocessing to lessthan 1 m [32]. The specular point accuracy is expectedto be accurate to within a kilometer [2]. The total effectof all these errors is expected to be nearly negligible.

4) GPS transmitter EIRP error E(PT ) + E(GT ): As dis-cussed in Section V-E, the GPS transmitter EIRP (trans-mit power plus antenna gain) will be estimated froma lookup table computed using direct signals. A set ofbaseline GPS antenna patterns (for approximately 2/3 ofthe constellation) has been released by Lockheed Martin.These patterns have been used to generate the preliminaryerror estimates for the uncertainty in the GPS powerand antenna gain which inputs into the L1b calibration.However, the unknown GPS transmit power levels haveled us to set this error term very conservatively.

5) Receiver antenna gain error E(GR): This is com-puted using a Monte Carlo simulation, as described inSection VII-C1 and summarized in Table III.

6) Effective scattering area error E(A): Since the reflectiongeometry is well known with relatively low errors, theCYGNSS E2ES is able to calculate physical and effectivescattering areas to a relatively high accuracy. The valuesselected were based on the worst case errors that could beexpected from the simulator.

The difference in the rolled-up L1a calibration term betweenthe high-wind and low-wind cases is what drives most of theoverall difference in L1 calibration error between the two windspeed cases. The aforementioned results show that the L1bcalibration for the high-wind case is about 20% better (forthis general example) than the low-wind case. Note that thisis not an indication that the L2 wind retrievals will be betterat high winds than low. In fact, the opposite occurs. The signalsensitivity to surface winds is still much better at low windsthan high winds, as demonstrated in [3].

VIII. CONCLUSION AND DISCUSSION

This paper has described in detail the CYGNSS L1 calibra-tion algorithms. These data products and the associated meta-data will be made publicly available to the scientific communityon the NASA PO-DAAC for the development of alternativealgorithms.

A complete error analysis was performed based on the base-line CYGNSS L2 wind retrieval algorithm, with the resultingerrors expected in the total rolled-up L1 calibration estimated.In Table V, the total error in the L1 calibration is estimated tobe 0.82 dB (1-sigma) and 0.70 dB (1-sigma), for the wind speedcases below and above 20 m/s, respectively.

The errors for the high- and low-wind-speed cases stud-ied earlier are both within the requirement allocated for theCYGNSS L1 calibration algorithm. The CYGNSS L1 errorrequirement is 1 dB (1-sigma).

The error term of greatest concern in the L1a calibration ismaintaining an accurate determination of the instrument noisepower Pr (particularly after launch as the instrument ages). Er-rors in the estimation of the instrument noise can greatly affectthe L1a calibration, more so at low winds. This places addedimportance on the open ocean brightness temperature model,which will be used after launch to perform the open oceancalibrations used to update the instrument noise lookup tables.

With regard to the L1b calibration, the term of greatest inter-est is the GPS transmit power and antenna gains. Since we onlyhave prelaunch patterns of a segment of the constellation, greatcare will be needed to generate GPS satellite unique antennapatterns and transmit power estimates. By using the directsignal power levels, we expect to be able to gather sufficientmeasurements of the direct signal power to make accurate mapsof transmitted power for each GPS satellite. Additionally, all ofthe accumulated errors influencing the receive antenna powerestimates can have a significant effect on the calibration. Thishas necessitated detailed modeling of the science antennas asmounted on the spacecraft and required us to take extra stepsto ensure accurate knowledge of the alignment between themeasured/modeled science antenna patterns and the spacecraftattitude control system.

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Scott Gleason (M’09–SM’14) received the B.S.degree in electrical and computer engineering fromThe State University of New York at Buffalo,Buffalo, NY, USA; the M.S. degree in engineeringfrom Stanford University, Stanford, CA, USA; andthe Ph.D. degree from the University of Surrey,Surrey, U.K.

He is a Principal Scientist with the Southwest Re-search Institute, Boulder, CO, USA. He is a Coinvesti-gator on the Science Team and an Instrument Scientistfor the NASA Cyclone Global Navigation Satellite

System (CYGNSS) mission. He has worked in the areas of astronautics, remotesensing, and Global Navigation Satellite Systems for over 20 years, includingat NASA’s Goddard Space Flight Center; Stanford’s GPS Laboratory; SurreySatellite Technology Ltd.; Concordia University, Montreal, QC, Canada; andthe National Oceanography Centre, Southampton.

Christopher S. Ruf (S’85–M’87–SM’92–F’01) re-ceived the B.A. degree in physics from Reed College,Portland, OR, USA, and the Ph.D. degree in electri-cal and computer engineering from the University ofMassachusetts at Amherst, Amherst, MA, USA.

He was previously with Intel Corporation;Hughes Space and Communication; the NASA JetPropulsion Laboratory; and Pennsylvania State Uni-versity, State College, PA, USA. He is currently aProfessor in atmospheric science and space engineer-ing with the University of Michigan, Ann Arbor, MI,

USA, and a Principal Investigator of the Cyclone Global Navigation SatelliteSystem NASA Earth Venture mission. His research interests include GlobalNavigation Satellite System reflectometry remote sensing, microwave radiom-etry, atmosphere and ocean geophysical retrieval algorithm development, andsensor technology development.

Dr. Ruf is a member of the American Geophysical Union, the AmericanMeteorological Society, and Commission F of the Union Radio ScientifiqueInternationale. He was a former Editor-in-Chief of the IEEE TRANSACTIONSON GEOSCIENCE AND REMOTE SENSING (TGRS), and he has served on theeditorial boards of Radio Science and the Journal of Atmospheric and OceanicTechnology. He has been the recipient of four NASA Certificates of Recognitionand seven NASA Group Achievement Awards, as well as the 1997 TGRS BestPaper Award, the 1999 IEEE Resnik Technical Field Award, the 2006 IGARSSBest Paper Award, and the 2014 IEEE GRSS-S Outstanding Service Award.

Maria Paola Clarizia (M’14) received the M.S.degree in telecommunications engineering (summacum laude) from the University of Sannio, Benevento,Italy, in 2007 and the Ph.D. degree in global nav-igation satellite system (GNSS) reflectometry fromthe School of Ocean and Earth Science, Universityof Southampton, Southampton, U.K.

She was a Research Engineer in the field ofSAR altimetry and GNSS reflectometry with StarlabBarcelona SL, and a Research Scientist in the field ofGNSS reflectometry with the Natural Environment

Research Council (NERC), National Oceanography Centre, Southampton. InApril 2013, she joined the University of Michigan, Ann Arbor, MI, USA, as aPostdoctoral Research Fellow, developing wind speed retrieval algorithms forthe NASA Cyclone Global Navigation Satellite System (CYGNSS) mission.Her research is focused on GNSS reflectometry, altimetry, GNSS radio oc-cultation, sea surface simulations and electromagnetic scattering models, dataanalysis, and statistical processing.

Dr. Clarizia is a member of the European Geophysical Union and theAmerican Meteorological Society.

Andrew J. O’Brien received the B.S., M.S., and Ph.D. degrees from The OhioState University, Columbus, OH, USA, in 2005, 2007, and 2009, respectively,all in electrical engineering.

He is currently a Research Scientist with The Ohio State University Electro-Science Laboratory, where he was a Graduate Research Associate, from 2005to 2009, working in the area of adaptive GPS antenna arrays and precise GlobalNavigation Satellite System (GNSS) receivers. He supports the Cyclone GNSS(CYGNSS) Science Team through development of end-to-end simulations. Hisresearch interests include GNSS antenna arrays, adaptive antenna electronics,airborne geolocation, radar systems, and spaceborne GNSS remote sensing.

http://www.sstl.co.uk/Products/Subsystems/Downloads/DATASHEET-SGR-ReSI

http://www.sstl.co.uk/Products/Subsystems/Downloads/DATASHEET-SGR-ReSI

https://igscb.jpl.nasa.gov/

https://igscb.jpl.nasa.gov/

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