1.1. Solar Radio Burst Interference to GPS
 There are several different kinds of interference sources to global positioning system (GPS) signals, such as in-band emission, nearby-band emission, harmonics, and jamming, which may potentially disrupt a GPS receiver's signal tracking [Johannessen, 1990; Owen, 1993; Moelker, 1994; Stevens, 1995]. In most cases, such interference comes from radio communications, mobile phones, power lines, radar systems and equipment operated by police and emergency vehicles etc. [Johannessen, 1990; Owen, 1993; Moelker, 1994; Ward, 1994]. Radio frequency interference (RFI) can decrease the GPS signal-to-noise ratio (SNR) by the introduction of additional noise that subsequently leads to degradation in GPS positioning accuracy or a loss of GPS signal in the worst case.
 Solar radio bursts (SRB), a source of radio frequency interference, have been studied for more than 50 years [Reber, 1944; Southworth, 1945]. SRB occur in the solar atmosphere with three different types of radio emission mechanisms, whose frequency band ranges over the entire radio spectrum [Reber, 1944; Kundu, 1965; Castelli et al., 1973; Guidice and Castelli, 1975]. The interference of SRB at radio frequencies was first reported by Hey , who noticed that interference occurred during solar flares. Recent studies also showed that SRB in the spectrum of microwave radio frequencies can disrupt wireless communications, where the threshold was set to about 1000 solar flux units (sfu) (1 sfu = 10−22 W m−2 Hz−1) [Bala et al., 2002]. SRB with flux density above this threshold typically occur once every 3.5 days during maximum solar activities [Bala et al., 2002].
 GPS antennas are designed to be right-hand circularly polarized (RHCP) according to GPS signal RHCP characteristics. Interference signals that do not match the GPS antenna polarization pattern will be reduced in strength dependent upon the degree of mismatch. Klobuchar et al.  has investigated the threshold of radio frequency interference on L1 frequency (1575.42 MHz) due to SRB for GPS signals, with the receiver background noise level (or thermal noise density) set as −201.5 dBW/Hz and the antenna gain as 1 dB. The obtained threshold of SRB interference to phase tracking loop operating at L1 frequency was 40,000 sfu for a randomly polarized solar radio emission and 20,000 sfu for a RHCP emission [Klobuchar et al., 1999]. In the past 40 years, only a few solar radio bursts were observed with peak flux density over 40,000 sfu [Klobuchar et al., 1999; Bala et al., 2002; Nita et al., 2002]. Therefore solar radio bursts were thought to rarely become a potential interference source to GPS signals. In this investigation, we have found that SRB with a flux density of only 12,000 sfu can cause a severe interference to GPS signal tracking.
 In recent years, dual-frequency GPS receivers have been widely employed to estimate ionospheric total electron content (TEC). In order to extract the encrypted GPS L2 signal, codeless or semicodeless technologies are widely used in GPS receivers, which however make GPS L2 signal much more prone to interference [Skone, 2001]. To assess the threshold of GPS L2 signal tracking induced by the correlation-tracking mode employed by dual-frequency receivers, the following equation (1) is derived in our research (according to Spilker , Ward , and Klobuchar et al. ):
where Pthr is the threshold of GPS L2 signal tracking in dB (corresponding to y-axis value in Figure 1); Sr is the power of GPS L2 signal (this value is doubled here since GPS signal power was compared with both interference signal and receiver thermal noise); Nthermal is the receiver background thermal noise density; Lbw is the bandwidth loss on SNR due to bandwidth of GPS signal power spectrum and RF circuit design; A is the antenna effective area in dBmr2; SNRcorr is the correlation gain which is decided by hardware design in order to lock GPS signals; dBLoss is the SNR loss in L2 signal tracking determined by the receiver-tracking mode (codeless or semicodeless, this value corresponds to x-axis value in Figure 1 with a unit of dB); SNRPLL is the SNR detection threshold for phase lock loop used in the GPS receiver; −220 dBW/Hz is the unit transform constant since 1 sfu = −220 dBW/Hz. Shown in Figure 1 are the calculated thresholds (in unit of sfu) of SRB effects on GPS L2 signal using equation (1). To generate the plot, the following values have been applied: Nthermal = −203 dBW/Hz which is a typical value widely used for the analysis of RFI effects [Ward, 1999]; A = 10 log(gλ2/4π) with g = − 3 dB for randomly polarized radiations; Sr = −163 dBW; Lbw = 10 × log10 (500 × 103 Hz) since most L2 signal power is concentrated on the narrow bandwidth region of 500 kHz; SNRcorr = 10 × log10 (1.023 × 106) = 60 dB for 1 ms integration and SNRcorr = 10 × log10 (4 × 1.023 × 106) = 66 dB for 4 ms integration, both computed with respect to a P code chip length of 1.023 × 106 bits; SNRPLL is typically set as 14 dB; As denoted with vertical lines in Figure 1, dBLoss is between 14∼17 dB for semicodeless receiver and between 27∼30 dB for codeless receivers.
 According to the results shown in Figure 1, the threshold is about 1.0 × 106∼4.0 × 106 sfu for full code correlation of GPS L2 signal, about 2.0 × 104∼1.0 × 105 sfu for semicodeless receivers and about 1,000∼8,000 sfu for codeless receivers. The threshold therefore varies for different types of receivers.
1.2. SRB on 28 October 2003
 A strong solar radio burst was observed recently on 28 October 2003 and the maximum X-ray flux X17.2 occurred at 1104 UT as recorded by Geosynchronous Operational Environment Satellites (GOES). The data from the National Geophysical Data Center (NGDC)'s Radio Solar Telescope Network (RSTN) and some other European solar astronomy observatories showed that the SRB on microwave band mainly occurred at two time periods on 28 October 2003, namely 1102∼1112 UT and 1142∼1200 UT [National Geophysical Data Center, 2004; Swiss Federal Institute of Technology, PHOENIX-2 ETH, available at http://www.astro.phys.ethz.ch/rapp/catalog/catalog_nf.html#phoenixII; Astronomical Institute, Academy of Sciences of the Czech Republic, Solar radio event archive info, available at http://sunkl.asu.cas.cz/∼radio/info.htm]. The frequency band of SRB that we are concerned about in this paper is the microwave one where GPS frequencies are located. In the first period, the peak value of the solar flux at 1415 MHz reached 7,000 sfu. It reached 12,000 sfu in the second period. During both periods, losses of tracking to GPS signals have been observed by many International GPS Service (IGS) dayside stations. A correlation analysis on the rate of loss of lock at solar radio flux at 1415 MHz indicated that, taking GPS station NKLG as an example, it had a correlation index r = 0.75 which is much higher than correlation indices in other frequency bands. In section 2, we will provide a global distribution of the tolerance conditions for the IGS network to this event during the first time period (1102∼1112 UT). In section 3, a global map of loss of lock will be generated for periods 1051∼1100 UT and 1112∼1116 UT (before and after the peak solar flux), corresponding to the pre-effects and posteffects of the SRB on GPS receivers, respectively.
 During the super flare, with sudden enhanced X-ray flux from the Sun, the ionospheric TEC experienced a sudden enhancement due to extra ionization by solar X-ray and extreme ultraviolet (EUV) flux. The largest TEC enhancement occurred at equator dayside regions with a value reaching 15 TEC units, (TECU) (1 TECU = 1016 el m−2). Large sudden TEC enhancements will cause loss of lock on GPS L2 signal tracking as well [International GPS Service (IGS), 1998, 1999a, 1999b]. A sudden TEC enhancement was observed during 1102∼1106 UT, and it has four minutes overlap with the time period 1102∼1112 UT during which GPS signal loss of lock was noticed. Therefore TEC sudden enhancement could be another source affecting L2 signal tracking since different types of GPS receivers have used different tracking techniques to acquire GPS L2 signal and their capability in SRB interference resistance will be different. Considering the above, different types of GPS receivers should be analyzed in the evaluation of SRB's effects on GPS L2 signal tracking.