Inside GNSS Media & Research

MAR-APR 2018

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Page 62 of 67 M A R C H / A P R I L 2 0 1 8 Inside GNSS 63 filter assumes to be faulty actually are faulty. is update is based on the ability of the filter to predict measurements. e better the elemental filter pseudorange and delta range predic- tions match the actually available measurements, the higher the model probability. Aer the measurement processing, a mixing step is exe- cuted. In this mixing step, each elemental filter is reinitialized with a new state estimate and covariance matrix, which are calculated from the model probabilities, state estimates, and covariance matrices of all elemental filters. It is important to note that for the most widely used filter bank, i.e., the Inter- acting Multiple Model (IMM) filter bank, all elemental filters are initialized differently. erefore, state and covariance of each elemental filter must be propagated separately, even if all elemental filters assume the same system model. e main drawback of such a filter bank is the huge com- putational load. In most integrated navigation systems, most of the computational cost is spent in the propagation step. e reason for this is that the state and covariance matrices of the navigation filter must be propagated with a reasonable update rate in order to cope with the vehicle's dynamics. For example, in a GNSS/INS system, several propagation steps are performed (for example, every 5 milliseconds when the inertial sensors provide measurements) before one measurement step takes place, i.e., every second when a typical GNSS receiver provides measurements. With the values given in this example, 200 propagation steps are performed before one measurement step is performed. Within the INLU project, a GNSS/INS integrity algorithm based on a Generalized Pseudo-Bayesian 1 (GPB1) filter bank was developed. e only difference between an IMM and a GPB1 filter bank is the mixing step. For the GPB1 filter bank, the mixing step initializes all elemental filters identically. As all the elemental filters have the same system model — namely the error propagation equations of inertial navigation plus addi- tional states to estimate the inertial sensor biases — the use of a GPB1 filter bank allows INLU to perform propagation steps with one elemental filter only, instead of with each elemental fil- ter of the filter bank. en, when GNSS measurements become available, all elemental filters are initialized with the propagated state and covariance of this first elemental filter before each elemental filter processes the measurements. is approach avoids, to a large extent, the increase in processing complexity typically connected to filter bank integrity algorithms. e best estimate of the filter bank is given by where μ i,k denotes the model probability of the i-th elemental filter at epoch k, is the state estimate of the i-th elemental filter, and N is the number of elemental filters. e calculation of the protection levels for such a filter bank is based on the covariance matrix of the best estimate provided by the filter bank, which is given by where is the covariance matrix of the i-th elemental filter. It has to be noted that in this covariance of the best estimate, not only the covariance matrices of the elemental filters enter, weighted with the model probabilities, but also the spread of the elemental filter solutions with respect to the best estimate. is ensures that this covariance matrix is a conservative estimate of the true covariance matrix. In fact, the way the covariance matrix of the best estimate is calculated is closely related to the protection level calculation in multi-hypothesis solution sepa- ration RAIM, where the protection levels are composed of the spread of each subset solution with respect to the full set solu- tion, and the covariance of the full set solution. In short, hav- ing a best estimate with a guaranteed conservative covariance matrix allows for calculating the protection level by calculating the standard deviations corresponding to a pre-defined integ- rity risk and multiplying the standard deviation taken from the best estimate covariance matrix with this number. More details on this GPB1-based GNSS/INS integrity algorithm can be found in Additional Resources. Application Example: Spoofing Scenario e previously introduced technique is demonstrated with a scenario employing a spoofer using a hardware constellation simulator. e scenario simulates a short drive of a land vehicle. e multipath environment was generated according to the ITU-R P.681 channel model; nominal Galileo and GPS constel- lations were assumed. Additionally, an ideal spoofing of one Galileo and one GPS Open Service signal was simulated. From a certain point in time onwards, a ramp on the pseudoranges of the respective satellites was generated, starting from zero. Using this RFCS scenario, baseband samples were recorded and then post-processed with the PIPE Receiver. Addition- ally, artificial inertial sensor data simulating a medium-grade MEMS was generated. e results of the post processing of the recorded baseband samples are shown in Figure 5 . e trajectory starts in the le upper corner and follows the road that is visible in the Google Earth picture. Two different PVT solvers were used: a snapshot least squares solver that produced the position fixes indicated by the red markers, and the GNSS/INS filter bank approach described in the previous section, indicated by the blue mark- ers. Obviously, the snapshot least squares position fixes, for which no attempt to counter spoofing was made, walks off the road. In comparison, the GPB1-based GNSS/INS integrity algorithm proves to be robust with respect to the simulated spoofing threat. Conclusion To further grow the application of GNSS receivers for land- based applications, the integrity of the computed PVT solu- tions must be ensured for this user community in a comparable fashion as is done for the aviation industry. In doing so, the integrity risks of the respective applications like vehicles in cities and railways have to be accounted for. e list of nomi- nal and non-nominal threats is comprehensive, ranging from false locks during tracking over unintentional interference and

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