GPS World, September 2010

RECEIVER DESIGN Security ÅFIGURE 2 Spatial sampling of the antenna trajectory into M subinterval segments potential 2L GNSS signals as the antenna is spatially moved through the trajectory The complex baseband signal at the output of the antenna denoted by r t can be expressed as where i is the GNSS signal index the superscripts A and J indicate authentic and jamming signals respectively p t shows the physical position vector of the moving antenna phase center relative to a stationary spatial coordinate system A i p t t and J i p t t give the channel gain for the authentic and the spoofi ng signals of the ith SV at time t and position p c i t is the PN coding modulation of ith GNSS signal A i and i are the code delay of ith PN sequence corresponding to the authentic and the spoofi ng sources respectively f Di J A and f J are the Doppler frequency of the ith Di authentic and the spoofi ng signals and w t represents the complex baseband of additive noise of receiver antenna For convenience it is assumed that the signal index i 1 2 L is the same for the spoofi ng and authentic GNSS signals The spoofer being aware of which signals are potentially visible to the receiver will transmit up to L different spoofi ng signals out of this set Another simplification that is implied by Equation 1 is that the message coding has been ignored which is justifiable as the GNSS signals are being tracked such that the message symbol modulation can be assumed to be removable by the receiver by some ancillary process that is not of interest in the present context The objective of the receiver despreading operation is to isolate the channel gains A p t t J p t t which are raw observables used in the subsequent detection algorithm It is assumed that the GNSS receiver is in a signal tracking state Hence it is assumed that the data coding code phase of the spreading signal and Doppler are known inputs in the despreading operation The two outcomes of the ith despreading channel for authentic and jamming signals are denoted as r A t and r J t respectively i k as shown in Figure 1 This notation is used for convenience and not to imply that the receiver has knowledge of which of the pair of GNSS signals corresponds to the authentic or spoofer cases The receiver processing will test each signal for authenticity to select the set of L signals that are passed to the navigation estimator The despread signals r A t and r J t are i k collected over a snapshot interval of t 0 T As the notation is simplified if discrete samples are considered this interval is divided into M subintervals each of duration T such that the mth subinterval extends over the interval of m 1 T m T for m 12 M The collection of signal over the first and mth subintervals is illustrated in FIGURE 2 T is considered to be sufficiently small such that A i p t t or J k p t t is approximately constant over this interval leading a set of M discrete samples for each despreading output From this the vectors form of channel gain sample and outputs ÅFIGURE 3 Spoofing detection and mitigation methodology GPS World September 2010 www gpsworld com 30