Existing networks of precisely surveyed GNSS receivers that are used for dGNSS or RTK positioning techniques can be used to measure GNSS time across a territory or region such as a country. The measured GNSS time base signals from each receiver are then fed back to a collating service, similar to the existing dGNSS/RTK systems, which also receives an accurate time base signal from a trusted third-party time base supplier which maintains a trusted time base. The collating service then compares the GNSS time signals from the network of GNSS receivers with the trusted time base and determines whether the GNSS time signals are accurate when compared to the trusted time base, and if they are not accurate, calculates the error. The collating service may provide the calculated error to users and the necessary correction that needs to be applied to measured GNSS time to obtain accurate UTC time.

Systems and methods of heading determination with global navigation satellite system (GNSS) signal measurements are provided herein. A pair of antennas may be separated by a known baseline length and mounted on a vehicle. A GNSS receiver may obtain pseudorange and carrier phase measurements for GNSS satellites within view. An LRU may estimate carrier phase ambiguities and a two-dimensional vector, using the known baseline length and a linearized measurement model. The LRU may determine integer ambiguities using the estimated carrier phase ambiguities. The LRU may determine assumed wrong fixes of the integer ambiguities and a probability of almost fixed value. The LRU may store the set of integer ambiguities. The LRU may determine, from accumulated data over measurement epochs, updated integer ambiguities. The LRU may correct the carrier phase measurements using the updated integer ambiguities. The LRU may compute the heading using the corrected carrier phase measurements.

A method of determining a posterior error probability distribution for a parameter measured by a Global Navigation Satellite System (GNSS) receiver. The method comprises receiving a value for each of one or more GNSS measurement quality indicators associated with the GNSS measurement of the parameter. The or each received measurement quality indicator value is provided as an input into a multivariate probability distribution model to determine the posterior error probability distribution for the GNSS measurement, wherein the variates of the multivariate probability distribution model comprise error for said parameter, and the or each measurement quality indicator.

A method of determining a posterior error probability distribution for a parameter measured by a Global Navigation Satellite System (GNSS) receiver. The method comprises receiving a value for each of one or more GNSS measurement quality indicators associated with the GNSS measurement of the parameter. The or each received measurement quality indicator value is provided as an input into a multivariate probability distribution model to determine the posterior error probability distribution for the GNSS measurement, wherein the variates of the multivariate probability distribution model comprise error for said parameter, and the or each measurement quality indicator.

Systems and methods for use in navigating aircraft are provided. The systems can use Geometry Redundant Almost Fixed Solutions (GRAFS) or Geometry Extra Redundant Almost Fixed Solutions (GERAFS) to compute high confidence error bounds for a heading angle estimate or pitch angle derived using signals received on at least two antennas.

An aircraft receives pseudorange input from a plurality of satellites of an augmentation system. Each pseudorange input includes a precise position solution and error data. The aircraft receives a high frequency measurement from an inertial navigation system. The aircraft applies the precise position solution, error data, and high frequency measurement to a set of parallel Schmidt extended Kalman filters to produce a corrected position solution and integrity data. The aircraft applies the integrity data to a receiver autonomous integrity monitoring system to produce a protection level for the corrected position solution. The aircraft performs an aircraft operation using the corrected position solution and protection level.

Techniques for detecting GNSS spoofing using inertial mixing data are disclosed. One or more navigation parameters are determined by at least one GNSS receiver and a plurality of IRS from at least two periods of time. The navigation parameters from the GNSS receiver(s) and the IRS are compared at each time period, and the difference(s) between the compared navigation parameters are further compared to generate at least one differential value. A system can detect GNSS spoofing by comparing the at least one differential value to a suitable threshold. In one aspect each IRS navigation parameter is compared with a corresponding GNSS navigation parameter, wherein the plurality of differential values is mixed before threshold comparison. In another aspect, each IRS navigation parameter is mixed before comparison with a GNSS navigation parameter, and the resulting differential value is then compared against a threshold.

Techniques for detecting GNSS spoofing using inertial mixing data are disclosed. One or more navigation parameters are determined by at least one GNSS receiver and a plurality of IRS from at least two periods of time. The navigation parameters from the GNSS receiver(s) and the IRS are compared at each time period, and the difference(s) between the compared navigation parameters are further compared to generate at least one differential value. A system can detect GNSS spoofing by comparing the at least one differential value to a suitable threshold. In one aspect each IRS navigation parameter is compared with a corresponding GNSS navigation parameter, wherein the plurality of differential values is mixed before threshold comparison. In another aspect, each IRS navigation parameter is mixed before comparison with a GNSS navigation parameter, and the resulting differential value is then compared against a threshold.

An autonomous vehicle, system and method of operating an autonomous vehicle. The system includes a communication module and a processor. The communication module sends a first set of Global Positioning Satellite (GPS) data over a first communication channel and a second set of GPS data over a second communication channel. The second set of GPS data is an authenticated data set. The processor operates the autonomous vehicle using the first set of GPS data, and compares the first set of GPS data to the second set of GPS data to verify the integrity of the first set of GPS data. A first value for a vehicle parameter based on the first set of GPS data is compared to a second value for the vehicle parameter based on data from a vehicle-based sensor. The first set of GPS data is rational when the difference is less than a selected threshold.

An autonomous vehicle, system and method of operating an autonomous vehicle. The system includes a communication module and a processor. The communication module sends a first set of Global Positioning Satellite (GPS) data over a first communication channel and a second set of GPS data over a second communication channel. The second set of GPS data is an authenticated data set. The processor operates the autonomous vehicle using the first set of GPS data, and compares the first set of GPS data to the second set of GPS data to verify the integrity of the first set of GPS data. A first value for a vehicle parameter based on the first set of GPS data is compared to a second value for the vehicle parameter based on data from a vehicle-based sensor. The first set of GPS data is rational when the difference is less than a selected threshold.