A system and for determining precision navigation solutions decorrelates GPS carrier-phase ambiguities derived from multiple-source GPS information via Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) algorithms. The set of decorrelated floating-point ambiguities is used to compute protection levels and the probability of almost fix (PAF), or the probability that the partial almost-fix solution corresponding to the decorrelated ambiguities is within the region of correctly-fixed or low-error almost-fixed ambiguities. While the PAF remains below threshold and the protection levels remain below alert levels, the optimal navigation solution (floating-point, partial almost-fix, or fully fixed) is generated by fixing the decorrelated ambiguities are one at a time in the LAMBDA domain and replacing the appropriate carrier-phase ambiguities with the corresponding fixed ambiguities, reverting to the last solution if PAF reaches the threshold or if protection levels reach the alert levels.

A system and for determining precision navigation solutions decorrelates GPS carrier-phase ambiguities derived from multiple-source GPS information via Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) algorithms. The set of decorrelated floating-point ambiguities is used to compute protection levels and the probability of almost fix (PAF), or the probability that the partial almost-fix solution corresponding to the decorrelated ambiguities is within the region of correctly-fixed or low-error almost-fixed ambiguities. While the PAF remains below threshold and the protection levels remain below alert levels, the optimal navigation solution (floating-point, partial almost-fix, or fully fixed) is generated by fixing the decorrelated ambiguities are one at a time in the LAMBDA domain and replacing the appropriate carrier-phase ambiguities with the corresponding fixed ambiguities, reverting to the last solution if PAF reaches the threshold or if protection levels reach the alert levels.

A method for calibrating spatial errors induced by phase biases having a detrimental effect on the measurements of phase differences of radio signals received by three unaligned receiving antennas of a vehicle. An inter-satellite angular deviation of a pair of satellites is estimated in two different ways: on the basis of the respective positions of the vehicle and of the satellites to obtain a theoretical inter-satellite angular deviation; and on the basis of the respective directions of incidence of the satellites relative to the vehicle, which are determined from phase measurements, to obtain an estimated inter-satellite angular deviation. The space errors are estimated on the basis of said theoretical and estimated inter-satellite angular deviations. Also, a method and system for estimating the attitude of a vehicle, in particular a spacecraft.

A method for calibrating spatial errors induced by phase biases having a detrimental effect on the measurements of phase differences of radio signals received by three unaligned receiving antennas of a vehicle. An inter-satellite angular deviation of a pair of satellites is estimated in two different ways: on the basis of the respective positions of the vehicle and of the satellites to obtain a theoretical inter-satellite angular deviation; and on the basis of the respective directions of incidence of the satellites relative to the vehicle, which are determined from phase measurements, to obtain an estimated inter-satellite angular deviation. The space errors are estimated on the basis of said theoretical and estimated inter-satellite angular deviations. Also, a method and system for estimating the attitude of a vehicle, in particular a spacecraft.

An apparatus includes a controller coupled to at least two antennas and one or more sensors. An initial azimuth value for the apparatus is determined based on output of the one or more sensors. Respective phase differences between satellite signals received from respective satellites at the at least two antennas are detected, and respective phase difference values for the respective satellites are calculated based on the initial azimuth value, a distance between the at least two antennas in the apparatus, and positions of the respective satellites. An actual azimuth angle of the apparatus is identified based on the initial azimuth value from the output of the one or more sensors and variations between the respective detected phase differences and the respective calculated phase difference values for the respective satellites.

An apparatus includes a controller coupled to at least two antennas and one or more sensors. An initial azimuth value for the apparatus is determined based on output of the one or more sensors. Respective phase differences between satellite signals received from respective satellites at the at least two antennas are detected, and respective phase difference values for the respective satellites are calculated based on the initial azimuth value, a distance between the at least two antennas in the apparatus, and positions of the respective satellites. An actual azimuth angle of the apparatus is identified based on the initial azimuth value from the output of the one or more sensors and variations between the respective detected phase differences and the respective calculated phase difference values for the respective satellites.

A small-sized state calculating device which may acquire a highly-precise state calculation value is provided. The state calculating device may include antennas, receiving parts, a phase difference calculating part and an operation part. The receiving parts may calculate carrier phase measurements PY.sub.A, PY.sub.B and PY.sub.C of GNSS signals received by the antennas, respectively. The phase difference calculating part may set the antennas to be switched between a master antenna and a slave antenna, and calculate the plurality of inter-antenna phase differences Δζ.sub.AB, Δζ.sub.BC and Δζ.sub.CA, for every combination of the master antenna and the slave antenna, using the carrier phase measurements PY.sub.A, PY.sub.B and PY.sub.C. The operation part may calculate an attitude angle AT using the plurality of inter-antenna phase differences Δζ.sub.AB, Δζ.sub.BC and Δζ.sub.CA.

A small-sized state calculating device which may acquire a highly-precise state calculation value is provided. The state calculating device may include antennas, receiving parts, a phase difference calculating part and an operation part. The receiving parts may calculate carrier phase measurements PY.sub.A, PY.sub.B and PY.sub.C of GNSS signals received by the antennas, respectively. The phase difference calculating part may set the antennas to be switched between a master antenna and a slave antenna, and calculate the plurality of inter-antenna phase differences Δζ.sub.AB, Δζ.sub.BC and Δζ.sub.CA, for every combination of the master antenna and the slave antenna, using the carrier phase measurements PY.sub.A, PY.sub.B and PY.sub.C. The operation part may calculate an attitude angle AT using the plurality of inter-antenna phase differences Δζ.sub.AB, Δζ.sub.BC and Δζ.sub.CA.

A differential global positioning system (DGPS) processor can include an almost fixed integer ambiguity (AFIA) module for generating in real-time a multiple dimensional state vector of integer ambiguities and multiple dimensional corrections. The AFIA module can use double difference (DD) measurements for pseudo-range (PR) and carrier phase (CP) pairs generated from at least three global positioning system (GPS) receivers. A DGPS processor can be included in a high data rate real time attitude determination (RTAD) system to achieve high heading accuracy with high integrity.

A differential global positioning system (DGPS) processor can include an almost fixed integer ambiguity (AFIA) module for generating in real-time a multiple dimensional state vector of integer ambiguities and multiple dimensional corrections. The AFIA module can use double difference (DD) measurements for pseudo-range (PR) and carrier phase (CP) pairs generated from at least three global positioning system (GPS) receivers. A DGPS processor can be included in a high data rate real time attitude determination (RTAD) system to achieve high heading accuracy with high integrity.