The new constellation of radio beacons called Coherent Electromagnetic Radio Tomography (CERTO) will be available for measurements of ionospheric total electron content and radio scintillations. These beacons transmit unmodulated, phase-coherent waves, VHF, UHF, and L band frequencies. A fixed radio of 3/8 is used between successive frequencies. Total electron content (TEC) can be measured using the differential phase technique. The range between beacon and receiver is removed from the phase measurements, leaving a differential phase that is proportional to TEC. The three CERTO frequencies cover a wide range for determination of the radio scintillation effects caused by diffraction after propagation though ionospheric irregularities. All of the CERTO beacons are in low Earth orbit with inclinations ranging from equatorial to polar. Each satellite that carries CERTO has other plasma instruments that complement the beacon data. In addition, a Scintillation and Tomography Receiver in Space (CITRIS) instrument will be placed in orbit to detect signals from the CERTO beacons and from the array of 56 Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) VHF/S band radio beacons placed around the word by the French Centre National D'Etudes Spatiales. CITRIS will record ionospheric occultations and radio scintillations with a unique occultation and ground-to-space geometry. New algorithms have been developed for the multifrequency CERTO and CITRIS data to provide improved acquisition and analysis of TEC and scintillation data in ionospheric studies. The data from the CERTO constellation of beacons and receivers may be used to update space weather models.
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 Radio beacons in low Earth orbit (LEO) and ground-based beacon receivers have been used for many years to study the ionosphere. Integrated electron density or total electron content (TEC) has been monitored from LEO satellites after the launch of the first Sputnik in 1957 [Bohill, 1958; Garriott, 1960] and using the transmissions from the U.S. Navy Navigation Satellites (NNSS or TRANSIT) and Russian equivalent (CICADA) satellites [Leitinger et al., 1984]. Following in the concept first proposed by Austen et al. , LEO beacon satellites combined with chains of ground receivers have been used for ionospheric imaging based on computerized ionospheric tomography (CIT). CIT algorithms have been discussed by a number of sources, including the special edition edited by Na , the book by Kunitsyn and Tereshchenko , and the review by Pryse . Bernhardt et al.  described combining radio beacons with other satellite instruments to improve the electron density images recovered from CIT. Instruments which augment space-to-ground TEC measurements for CIT include (1) in situ plasma probes, (2) extreme ultraviolet (EUV) detectors, and (3) GPS occultation receivers.
 Multifrequency radio beacons in low Earth orbit also can be used to detect regions of ionospheric irregularities responsible for radio scintillations. This technique was first used by Yeh and Swenson  to observe fluctuations of radio signals from Sputnik and was implemented for multifrequency use with the Defense Nuclear Agency (DNA) Wideband satellite [Fremouw et al., 1978]. Recently the Naval Research Laboratory (NRL) Coherent Electromagnetic Radio Tomography (CERTO) beacon was added to the Air Force Research Laboratory (AFRL) Communications/Navigation Outage Forecast System (C/NOFS) satellite [de La Beaujardière et al., 2004] to register low-latitude scintillations recorded by the AFRL Scintillation Decision Aid (SCINDA) network of ground receivers [Groves et al., 1997; Caton et al., 2004].
 Because of the utility of multifrequency radio beacons in low Earth orbit, the Naval Research Laboratory has added the three-frequency CERTO beacon to a number of satellites. In addition, a receiver called the Scintillation and Tomography Receiver in Space (CITRIS) was designed by NRL to record ionospheric TEC and scintillation data from both space-based and ground-based beacons. With the CERTO and CITRIS instruments along with ground-based beacons and receivers, the full range of ionospheric measurement geometries illustrated in Figure 1 can be covered. The CERTO beacons transmit to ground receivers for vertical and oblique path measurements that may be used to reconstruct the ionosphere with tomographic techniques [Bernhardt et al., 1998]. The CERTO beacon transmits to the CITRIS receiver to provide the horizontal propagation paths. The addition of these horizontal paths for computerized ionospheric tomography (CIT) provides more faithful reconstructions of ionospheric densities. Also, the ground transmitter broadcasts to the CITRIS receiver in LEO yield samples of the phase fronts and signal amplitudes along the satellite orbit. This data can be processed to provide equivalent phase screens for describing radio scintillations. The primary source of ground radio transmissions will be the French Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) beacons located around the world [Willis, 1996].
 The host satellites for the CERTO and CITRIS instruments cover a wide range of altitudes and inclinations for their orbits. Figure 2 lists the planned operation times and orbit characteristics of CERTO beacons in current and future orbits. The altitudes range from 325 to 1500 km. The equatorial region is covered with the AFRL C/NOFS and Brazilian EQUARS satellites at inclinations of 20° or lower. The orbits extend up to midlatitudes with NPSAT1 at 35° inclination and the six Taiwan/U.S.-sponsored COSMIC satellites with 70° inclination. High latitudes are only covered by the U.S. DMSP/F15 satellite at 98° inclination and the Canadian sponsored CASSIOPE/ePOP satellite with 80° inclination. The Air Force STPSAT1 satellite carries the NRL Scintillation and Tomography Receiver in Space (CITRIS) instrument for measurements of TEC and scintillations from the other CERTO beacons as well as from ground-based radio beacons.
 This paper describes the CERTO beacon system. The rationale for the design of the CERTO system is explained in section 2. Section 3 provides the details on the CITRIS receiver that is designed to observe the CERTO beacons from space. Then Sections 4 and 5 describe the algorithms for the ground receivers used to determine TEC and scintillations from the beacon data. Section 6 gives a summary of the CERTO and CITRIS instrument capabilities.
2. Coherent Electromagnetic Radio Tomography (CERTO) Beacon Instrument
 The CERTO instrument was developed to fly on space vehicles to monitor the ionosphere using propagation of continuous wave signals at VHF, UHF, and L band frequencies. The first CERTO beacon was launched in 1999 on the Air Force–sponsored satellite ARGOS. Subsequently, CERTO has been part of the payloads of DMSP/F15, PICOSAT, and the Japanese-sponsored SEEK2 rocket program [Bernhardt et al., 2005], the six Taiwan Sponsored COSMIC satellites [Bernhardt et al., 2001] launched in April 2006. Future CERTO beacons are scheduled to be operated from the U.S. Air Force–sponsored C/NOFS satellite [de La Beaujardière, 2005], the Naval Postgraduate School–sponsored NPSAT1, the Canadian CASSIOPE, and Brazilian-sponsored EQUARS satellites (Figure 3).
 The CERTO beacon system is being flown on the large number of satellites illustrated in Figure 3. The altitude and inclination of each satellite is shown in Figure 2, and representative orbits are illustrated in Figure 4. With this large constellation of CERTO beacons, each ground CERTO receiver will be able to make measurements of ionospheric TEC and scintillations with an average observation time of 8–10 hours per day.
 The Coherent Electromagnetic Radio Tomography (CERTO) system on satellites provides three-frequency beacon transmissions at the frequencies 150.012, 400.032, and 1066.752 MHz. The effective radiated power (EFP) is 1–4 W with right-hand circular (RHC) polarization from a crossed dipole antenna. No modulation is added to the beacon signals to simplify the measurements of radio scintillations. The radio transmissions from CERTO can provide the total electron content (TEC) between the satellite and receiver using the differential phase technique. The TEC data can be used for tomographic imaging of the ionosphere when TEC is measured with a linear array of CERTO receivers. If the array is lined with the orbit of the CERTO beacon satellite in low Earth orbit (LEO), TEC data from vertical and oblique paths through the ionosphere can be processed to yield two-dimensional images of electron density [Bernhardt et al., 1998]. This process is enhanced with additional data from GPS occultations on many of the LEO satellites for reconstructions using computerized ionospheric tomography. Another use of the CERTO systems is scintillation monitoring. Scintillations vary greatly over the VHF, UHF, and L band radio frequency ranges. The CERTO ground receiver can measure phase and amplitude fluctuations for the CERTO radio source. These radio scintillation data can be processed to yield regional maps of radio signal disruptions.
 The CERTO beacon provides continuous wave transmissions from satellites at VHF (150.012 MHz), UHF (400.032 MHz), and L band (1066.752 MHz) frequencies. These frequencies were chosen for a number of reasons. The VHF and UHF CERTO frequencies are in the “navigation” band allocated near 150 and 400 MHz. This band has been previously used by a number of U.S. satellites, including TRANSIT, OSCAR, RADCAL, and GFO. The Russian low Earth orbit (LEO) navigation satellites COSMOS also radiated signals in this band. The ratio between two pairs of frequencies in this band is 8/3. The specific frequencies of 150.012 and 400.032 MHz are used by RADCAL and GFO as well CERTO and are called the “geodetic” frequencies. One reason for using these two frequencies with CERTO is that existing ground receivers for TRANSIT and other systems can receive the geodetic transmissions to provide the total electron content (TEC) of the ionosphere. The two frequencies have also been used to detect VHF phase scintillations where the UHF channel provided a phase reference [Coker et al., 2004]. With CERTO, the L band can be used as a phase reference, and phase scintillations at both VHF and UHF can be obtained simultaneously.
 In strongly scintillated environments, an L band frequency is required as a reference for both TEC and scintillation measurements. The third CERTO L band frequency at 1066.752 MHz was chosen to be exactly 8/3 times the UHF frequency of 400.032 MHz. This ratio has several advantages. First, a coherent downconverter can be used to translate the higher-frequency pair (400.032 and 1066.752 MHz) to the low frequency pair (150.012 and 400.032 MHz) so that existing two-frequency receivers can be modified for the upper frequency pair. Second, if all three frequencies are received simultaneously, the TEC can be measured with improved accuracy for the absolute TEC value and, if the receiver loses lock on the TEC, the TEC data gap can be more accurately filled than if only two frequencies were used. Finally, the L band frequency is high enough to be relatively insensitive to ionospheric scintillations.
 The block diagram for the generation of signals with the CERTO beacon is illustrated in Figure 5. The CERTO beacon is designed with a minimum of phase-locked loops and no digital synthesizers or microprocessors to prevent single-event upset (SEU) effects from radiation belt particles. A reference crystal oscillator with frequency f0 is selected as a common submultiple of the generated frequencies. For the three-frequency CERTO beacon, this frequency is f0 = 16.668 MHz. Integer frequency multiplication is used to step the frequency up to the transmission frequencies. For the three frequencies (f1, f2, f3) = (150.012, 400.032, 1066.742) MHz, the three integer multipliers are (n1, n2, n3) = (9, 24, 64), respectively. By coherently generating the frequencies from a common oscillator, phase locking is guaranteed. Without this phase locking, ionospheric TEC could not be measured with the CERTO ground receivers. The three frequencies are amplified and split into quadrature (I and Q) channels. After further amplification they are combined with a triplexer so that the beacon provides two ports with three-frequency in-phase (I) and quadrature phase (Q) signals. Further details on the beacon design can be found in the patent by Reinhart et al. .
 The CERTO antenna operates simultaneously at 150, 400, and 1067 MHz using a crossed dipole with reflectors (Figure 6). Resonant traps along the dipole adjust the electrical length of the elements so that the antenna looks like a half wavelength at each of the three frequency bands. Tuned half-wavelength reflectors are located approximately one-quarter wavelength down the antenna boom from the radiating dipole elements. These reflectors improve the antenna pattern with enhanced gain in the forward direction. The antenna boom is aligned with the vertical axis in the nadir direction from the satellite. If the antenna is mounted on the satellite approximately one-quarter VHF wavelength from the spacecraft, the 150 MHz reflectors can be eliminated, and the ground plane of the satellite replaces the reflectors. An optional S band antenna can be mounted at the end of the boom for measurements near 2 GHz. As discussed later, this S band antenna is required for observing the 2036.25 MHz signals from the ground DORIS beacons.
 The crossed-dipole antenna was designed to provide right-circular polarization (RCP) electromagnetic radiation to receivers on the Earth. Circular polarization is achieved by feeding the two dipoles in quadrature from the CERTO beacon. The antenna patterns provide about 4 dB gains along the antenna boom. The grain drops to 2 dB at an angle of 40° from the boom. Two satellites (DMSP/F15 and NPSAT1) transmit CERTO signals with linear polarization. For these, the CERTO antenna is a single trapped monopole using one of the elements from the dipoles shown in Figure 6. Linear polarization from an omnidirectional monopole was used instead of RCP from a dipole so that both ground receivers and space-based receivers can record the CERTO signals. NPSAT1 with a CERTO beacon is being launched with STPSAT1 with a multifrequency receiver that can lock on to CERTO transmissions. This receiver called CITRIS is described in section 3.
 The CERTO/CITRIS antenna was designed to provide good illumination of the Earth from a nadir-pointing space-based antenna. Samples of the measured antenna patterns for the antenna are shown in Figure 7.
 One requirement for selection of a satellite that hosts CERTO is that other scientific instruments must be available for measuring the ionosphere. The CERTO beacon is complementary to these instruments for obtaining data on electron densities and locating ionospheric irregularities. Table 1 lists the categories of instruments on each satellite.
Table 1. CERTO Beacons With Plasma Instrumentation
SSEIS Ne, V
B field, E field, neutral N, V
COSMIC (six orbits)
FAI-auroral imager (visible, IR)
IRM, SEI, plasma, Ne, V, T
Plasma wave, B field, neutral N, V
 GPS occultation receivers provide TEC and scintillation observations through the ionosphere on horizontal paths from the LEO satellite to the GPS beacons at an altitude of 20,200 km. These observation paths fill in the vertical and oblique paths provided by the ground CERTO receivers. Computerized ionospheric tomography (CIT) of the ionosphere is made more accurate with the addition of the GPS occultations to the CERTO measurements [Bernhardt et al., 1998].
 Two types of optical detectors are flown with the CERTO beacons. The Tiny Ionospheric Photometer (TIP) on the six COSMIC satellites and the EQARS satellite directly measure the F region plasma using radiative recombination emissions at extreme ultraviolet (EUV) wavelengths. When the O+ ion recombines with electrons, the O atom is left in an excited state, which radiates a photon at 135.6 nm. The TIP instrument detects the intensity of this emission to yield the vertical integral of the [e−] [O+] concentrations. The primary utility of the TIP instrument is to monitor the columnar content of the plasma density during the night. TIP and CERTO can work together on the COSMIC or EQUARS satellites to yield improved tomographic images of the nighttime ionosphere [Bernhardt et al., 1998]. The visible imagers on CASSIOPE record 630 nm (red line) emissions from the airglow and aurora. These emissions are produced by energetic electron impact on atomic oxygen in the upper atmosphere or by dissociative recombination of O2+ and electrons. The auroral imager on CASSIOPE will detect regions of ionospheric disturbances related to electron precipitation in aurora. These regions can also be imaged with the CERTO system by employing the radio beacon technique for ionospheric tomography [Pryse et al., 1998].
 In situ probes of the plasma complement the integrated plasma density measurements of CERTO. First, accurate measurements of electron density at the satellite can provide an upper boundary condition for computerized ionospheric tomography. Combining both TEC and in situ data in tomographic reconstructions of the F region plasma has the potential to yield improved accuracy. Second, in situ measurements of electron density fluctuations are a proxy for radio scintillations. Amplitude and phase scintillations recorded on ground receivers from CERTO transmissions require proper alignment of the transmitter and receiver with propagation though plasma irregularities below the satellite orbit. Estimates of transionospheric scintillation effects can be obtained using the measurements of irregularities at the satellite and extending this structure to the intervening region below the satellite to form a phase screen. Diffraction by this phase screen yields an estimate of the scintillation pattern. Comparison with actual measurements with VHF/UHF and L band propagation from CERTO may be employed to validate the estimation procedure.
 One limitation of using in situ observations as a proxy for scintillations is that the irregularity structures may not rise to the altitude of the satellite. Figure 8 illustrates this effect for the numerical simulation of a postsunset equatorial bubble 1 hour after the start of the instability process. At this time, strong scintillations are recorded in the VHF beacon channel, but the highs of the disturbance have not yet risen to the altitude of the satellite. In this case, however, downward viewing optical instruments such as TIP can record the reduction in EUV fluxes associated with a vertical integration though the bubble structure. Consequently, both the down-looking EUV sensors and in situ plasma probes can be used as proxies for radio scintillations, and the CERTO beacon can provide observational validation of this technique by direct measurement of the radio scintillations.
 Finally, the other sensors on the satellites, such as magnetometers, neutral density and wind detectors, plasma wave and electric field instruments, and energetic particle detectors, do not directly augment the TEC and radio wave scintillation measurements of the CERTO/CITRIS instruments, but they provide independent data on processes that affect the electron density structures. Electric fields and neutral winds are responsible for driving plasma interchange instabilities that produce field-aligned irregularities at all latitudes. Energetic particles directly ionize the neutral atmosphere to yield regions of enhanced absorption and high-latitude sporadic E, both of which may be monitored by the VHF transmissions from the CERTO beacons. During magnetic storms, magnetic field fluctuations and large electric fields are coincident with enhancements of the midlatitude nightside trough in the ionosphere that may be imaged using CIT.
3. Scintillation and Tomography Receiver in Space (CITRIS) Instrument
 With the large number of CERTO beacons planned for deployment in low Earth orbit, a companion receiver was developed to provide satellite-to-satellite links for measurements of TEC and radio scintillations. The CITRIS receiver is designed to provide global ionospheric measurements with simultaneous reception of the CERTO frequencies at 150.012, 400.032, and 1066.752 MHz. When CITRIS is launched on STPSAT1 into the same orbit as the NPSAT1 with a CERTO beacon, the tangent path geometry between the two satellites will be maintained for a period of years. Atmospheric drag will cause the STPSAT1 to drop to a lower altitude and to move at a faster speed than NPSAT1. The two satellites will be released together. They will slowly separate and, after about 150 days, come back together for closest approach interactions. Unique occultation measurements will be made with this pair of satellites. When the tangent height of the occultation path is below the ionosphere, the path will scan an ionospheric irregularity twice at two distances from the CITRIS receiver. Paths A and B in Figure 9 illustrate two of these times. The change in propagation angle through the irregularity will yield two different TEC signatures from the irregularity. Amplitude fluctuations from the irregularity will change on the two paths because the diffraction is affected by the distance from the irregularity to the receiver. Back propagation can be used to determine the location of an irregularity along a line-of-sight propagation path as was demonstrated for L band GPS occultations by Sokolovskiy et al. . The CERTO/CITRIS occultation data will be used to locate ionospheric irregularities using both TEC and scintillation data. Algorithms are being developed to isolate multiple irregularities from the VHF, UHF, and L band occultation data provided by this unique pair of instruments.
 The CITRIS receiver will have dual-frequency (UHF/S band) mode to observe the global array of ground beacons in the DORIS system. The Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) system provides a precise orbit determination and location system using Doppler shift measurement techniques. A global network of 56 Doris beacons has been deployed by Centre National D'Etudes Spatiales (CNES), the French space agency, and is operated by Collecte Localization Satellites (CLS) in France. The DORIS system is currently carried by TOPEX/Poseidon, Spot 2, and Spot 4, and will be flown on the future Jason-1, Envisat, and Spot 5 satellites. The ground DORIS beacons transmits continuous wave signals at 401.25 and 2036.25 MHz with 0.4 s of modulation every 10 min. The DORIS receivers use these transmissions to provide satellite positions with better than 10 cm accuracy. The effects of the ionosphere are removed by considering the frequency dependency of the VHF and S band signals. The DORIS receivers yield total electron content as a byproduct of this correction process. The CITRIS receiver has been designed to provide ionospheric TEC and radio scintillation data as its primary product. Satellite position may also be provided using Doppler ranging techniques. The DORIS frequencies were added to the CITRIS receiver because they are ideal for ionospheric measurements and because the locations of the DORIS beacons cover the Earth (Figure 10).
 The CITRIS receiver may operate in either CERTO or DORIS mode (Figure 11). The electromagnetic waves are received at VHF, UHF, and L band using the CERTO antenna illustrated in Figure 6. An additional compact dipole was added to the end of the antenna boom for the S band DORIS signals. The antenna cables feed the radio signals to the CITRIS receiver, where they are coherently downconverted to an intermediate frequency (IF) to 12 MHz. The IF bandwidths are chosen to accommodate Doppler shifts associated with the relative motion of the beacons and receiver. Analog-to-digital conversion yields data that are processed by a digital signal processor (DSP) consisting of a graychip and a flight-qualified signal-processing microcomputer. The program in the DSP unit tracks the received signals to yield complex amplitudes (I and Q components) for each channel. The phase and amplitude measurements are translated into TEC and radio scintillations using algorithms discussed in the next sections.
4. Determination of Ionospheric Parameters From CERTO Beacon Signals
 The received complex amplitude in the receiver can be processed to yield total electron content and to provide estimates of the plasma medium that has produced the diffraction pattern responsible for amplitude and phase scintillations. The phase (in wavelengths) received from a satellite signal passing through the ionosphere is given by
where S is range to satellite, = 40.3 in mks units, F is frequency, c = 3 × 108 m/s is light speed, ds is the path increment, and ηa is the system phase bias. To convert the phase in wavelengths to the phase in radians, multiply by 2π. The integral ∫Nds is called the total electron content (TEC). The differential phase for transmissions between frequency fa and frequency fb is
where ηab = ηa − ηb is the differential phase bias, which is a constant error term. This phase difference Pab is constructed inside the receiver with an ambiguity of one cycle. Note that the function is not transitive, so Pab ≠ Pba and that because of the negative phase delay of the ionosphere, Pab < 0.
 Consider three beacon frequencies based on the ratios na:nb:nc, where na, nb, and nc are integers. The frequencies generated by these ratios are given by fa = naf0, fb = nbf0 and fc = ncf0, where f0 is the base frequency. Using (2), the differential phase for each frequency pair is
where the subscripts a and b denote an arbitrary frequency pair. The numeric indices 1, 2, or 3 will denote ordered frequencies such that f1 < f2 < f3 and n1 < n2 < n3. The TEC is obtained from the differential phase using
where Ψab ≡ C0f0 is the TEC ambiguity and Γab ≡ C0f0 ηab is the TEC bias error.
 The measured phase from each pairs of frequencies for CERTO can be used to provide a measurement of TEC using (4). CERTO was designed to provide three frequency transmissions with na = n1 = 9, nb = n2 = 24 and nc = n3 = 64. The specific transmitter frequencies are
where f0 = 16.668 MHz. The numerical formulae for the differential phase of each frequency pair are found from (3) as
The TEC ambiguities for each frequency pair is found from (6) to be
For instance, a change in differential phase of one wavelength as defined by (2) using the f1 = 150.012 MHz and f2 = 400.032 MHz frequencies yields a change of measured TEC by 0.13 TECU where 1 TECU = 1016 m−2.
 For the CERTO three-frequency system, the definition of differential phase is extended on the basis of the concept of determining the period where two differential phase wavelengths realign in phase. The value for this improved TEC ambiguity is determined by equating TEC defined by (4) for all differential phase measurements. The TEC obtained for the arbitrary frequency pairs (a, b) and (a, c) are set equal to each other to yield the relationships between corresponding differential phases
where ab = Pab − ηab and ac = Pac − ηac are the bias-corrected differential phases. Unless the denominators are relatively prime, there is a greatest common divisor (GCD) that can be factored out of (8). The GCD is defined as
 The algorithm for determining the TEC from the three-frequency differential phase measurements is based on restraining the integral number of ambiguities using finite number theory. The procedure for finding the TEC is to form the integer equation on the basis of (8) with the GCD factor removed:
Elementary number theory [Niven and Zuckerman, 1966] provides the Euclidean algorithm for finding the family of solutions to the integer equation (10). Define the associated integer equation
noting that the factors of xab and xac are relatively prime. The recovered TEC is given by the result
where the mod 1 function is used to restrict the values from acxab − abxac to the range 0 to 1 wavelengths and k is an integer representing the steps in the TEC ambiguity. Using a = 1, b = 2, and c = 3 yields the largest TEC ambiguity.
 If the measured differential phases including biases (Pac and Pab) are substituted into (12), the recovered TEC is given by
is the three-frequency TEC bias error. From (13), it is easy to see that the three-frequency ambiguity is given by
Using three CERTO frequencies, TEC ambiguity is found from (15) as
 The three frequencies 150.012, 400.032, and 1066.752 MHz can provide TEC measurements with an ambiguity of about 8.3 TEC units (1 TEC unit = 1016 el m−2). To determine the formula for translation of differential phases into TEC, the integer values for (n1, n2, n3) = (9, 24, 64) are substituted into (9), (10), and (11) to give
 The integer solution to (17) is x12 = 7 and x13 = 8. Using measured pairs of differential phases (P13, P12), the TEC is found by substituting numerical values in (13) to give
where ηabc = Γabc = (ηacxab − ηabxac)mod 1 is the three-frequency, differential phase bias error.
 Neglecting the bias errors, the minimum values of TEC estimates obtained with each pair of transmitted frequencies and all three frequencies are illustrated in Figure 12. The two-frequency technique yields TEC estimates that are too ambiguous for determination of the actual TEC without additional information. The three-frequency technique provides a wide range of unambiguous TEC that can more easily to be used to estimate absolute values. Figure 12 also shows that all three of the two-frequency ambiguities come together at the value of the three-frequency ambiguity. This provides the basis for the three-frequency algorithm that can be implanted by the TEC receivers. Note that loss of TEC measurements for a few TEC units will prohibit reconstruction of the two TEC data records, but the three-frequency algorithm can be used to piece together the TEC record over the data gap. The three-frequency TEC algorithm yields improved resolution of the ambiguities inherent in the differential phase TEC measurement technique. This improved resolution will improve the results of computerized ionospheric tomography and the assimilation of beacon data into space weather models.
5. Scintillation Parameters and Inverse Diffraction Analysis
 The receiver algorithms for processing scintillation data use the complete amplitude and phase description of the sampled wave. One commonly used parameter to characterize the scintillation environments is the S4 index, defined as the normalized square root of the received power given by
where Wa is the received power at frequency fa, and 〈·〉 is a temporal average. A second scintillation index is the standard deviation of the phase given by
where ϕa is the received phase in radians. The ground-based CERTO receivers and the CITRIS receiver in orbit can provide these parameters as part of their data records.
 Using a spaced-based receiver like CITRIS to capture the complex amplitude of the beacon transmission from the ground-based beacons like DORIS permits reconstruction of an equivalent phase screen. The space-based receiver samples the phase front of a diffracted wave generated from a point source on the ground. Back propagation of the diffracted wave toward the source yields an altitude when most of the amplitude fluctuations in the wave have vanished and only phase perturbations in the wave remain. This altitude is considered as the location of the phase screen, and the phase variations can be scaled to the equivalent changes in refractive index at the screen. In regions near the equator, the field-aligned irregularities form a diffraction region that is uniform along the magnetic field direction. This property can be used for inverse diffraction analysis of the data in a fashion similar to that described by Sokolovskiy et al. .
 The mathematic description of this process is given by Fresnel diffraction theory in a vacuum [Goodman, 1968] for an electromagnetic wave passing though a refracting layer. From (1), the ionospheric phase screen can be represented by
where λa = c/fa is the radio wavelength, and the variation in electron density is assumed to be a function of horizontal distance x in a thin layer at altitude z = 0. A spherical wave passing through this screen is given by
 For propagation in free space, the amplitude distributions given by (22) can be described as an angular spectrum of plane waves. Each plane wave component propagates in a straight line and can be reassembled into a diffracted wave at some distance z from the phase screen. The diffracted wave is thus described by
The satellite receiver in low Earth orbit measures U1 at a number of radio wavelengths. The equivalent phase shifted wave surface U0 can be found by taking the Fourier transform of received data, multiplying by the Fresnel kernel given by exp[j π fx2 λaz], and taking the inverse Fourier transform of the result. This procedure reversed the process described by (23). This process will be used to analyze the 401.25 and 2036.25 MHz DORIS signals measured using the CITRIS receiver. The results of this analysis will test the assumptions of (1) equivalent thin phase screens and (2) one dimensionality of the screen in alignment with the satellite orbit.
 As illustrated by Figure 8, the CERTO beacon signals may be received by a stationary receiver on the ground. It is not correct to use the inverse diffraction analysis for amplitudes received from an orbiting beacon under these conditions. The moving beacon in space launches a series of spherical waves that is only sampled at one location by the receiver. The series of complex amplitude data received on the ground is not amenable to inverse diffraction analysis.
 On the basis of the experience of previous beacon satellite systems, a new array of beacons will be placed in low Earth orbit over the next 5 years. These CERTO beacons will provide continuous wave, radio sources of VHF, UHF, and L band transmissions. Ten or more CERTO beacon systems in low Earth orbit will have the ability to determine the TEC and multiband scintillations. The CERTO frequencies were chosen to optimize resistance to noise, resolution of TEC ambiguities, and scintillation coverage. Using the VHF channel, the resolution of the CERTO system is ∼10–3 TEC units. This resolution is needed to track small ionospheric fluctuations such as traveling ionospheric disturbances (TIDs), scintillation instability onsets, wave refraction effects, etc. The ambiguity of the three-frequency CERTO system is 8.3 TEC units. This ambiguity is required to determine absolute TEC and can add improved reliability for tomography processing of the TEC data to yield ionospheric images. The three-frequency TEC algorithm permits restoration of absolute TEC after a signal dropout and gives improved resistance to TEC receiver noise. The CERTO beacons on C/NOFS, COSMIC, NPSAT1, CASSIOPE, EQUARS, etc. will complement each other for operations with inclinations from 15° to 98°, providing a wide range of spatial and temporal sampling of the ionosphere. Once the CERTO beacons are in orbit, ground receivers are needed to provide the global ionospheric measurements.
 As a companion to the CERTO beacons, the CITRIS instrument will be launched into a 35° inclination orbit on STPSAT1. This receiver will be uniquely placed to observe the companion CERTO beacon on NPSAT1 in the same orbit, the other CERTO beacons at other inclinations, and the ground network of DORIS beacons.
 This research was sponsored by the Office of Naval Research. The authors are grateful to Ivan J. Galysh, Graybill P. Landis, Thomas F. Rodilosso, Douglas E. Koch, Thomas L. Macdonald, Matthew G. Long, Wendy L. Lippincott, and James P. Barnes of the NRL Space Systems Development and Spacecraft Engineering departments for design and fabrication of the CITRIS receiver and testing of the CERTO/CITRIS antennas. The CERTO beacon was jointly designed by NRL and Matt Mason of Syntech Engineering. The CERTO beacon program has been partially sponsored by the Air Force Research Laboratory for the C/NOFS satellite, the Taiwan National Space Program Office for the COSMIC program, and Air Force Space Test Program for NPSAT1.