Integrity monitoring of navigation systems using Baye's rule

A navigation system that receives signals from a plurality of transmitters and identifies an error producing transmitter, comprising:

• means for transmitting a signal that causes at least one of the plurality of transmitters to transmit a signal;
• means for receiving the transmitted signals;
• means for determining ranges for the transmitters;
• means for determining a least square residual error using said ranges;
• means using said least square residual error and Bayes Rule for determining a conditional probability that a transmitter is an error producing transmitter, including means for determining an estimate of a sum of the squares of the least square residual error for a reduced system which does not use said transmitter, and means for determining a conditional probability of said least square residual error using said sum of the squares of the least square residual error for said reduced system;
• means for estimating a first loss associated with each of the transmitters using said ranges;
• means for estimating a second loss associated with a hypothesis that said transmitter is the error producing transmitter using said conditional probability and said first loss estimate, including means for estimating a third loss which is associated with an incorrect hypothesis by taking a difference between a first loss associated with said error producing transmitter and a first loss associated with a second transmitter, and means for providing a sum of a plurality of third losses which are associated with a plurality of incorrect hypothesis, and means for multiplying said third loss by a conditional probability that said second transmitter is the error producing transmitter;
• and
• means for selecting a minimal second loss to identify the error producing transmitter.

A GPS navigation system that receives signals from a plurality of satellites and identifies an error producing satellite, comprising:

• means for transmitting a signal that causes at least one of the plurality of satellites to transmit a signal;
• means for receiving the transmitted signals;
• means for determining ranges from the satellites;
• means for determining a least square residual error using said ranges;
• means using said least square residual error and Bayes Rule for determining a conditional probability that a satellite in an error producing satellite, including means for determining an estimate of a sum of the squares of the least square residual error for a reduced system which does not use said satellite, and means for determining a conditional probability of said least square residual error using said sum of the squares of the least square residual error for each reduced system;
• and
• means for selecting a maximum conditional probability to identify the error producing satellite.

A GPS navigation system that receives signals from a plurality of satellites and identifies an error producing satellite, comprising:

• means for transmitting a signal that causes at least one of the plurality of satellites to transmit a signal;
• means for receiving the transmitted signals;
• means for determining ranges from the satellites;
• means for determining a least square residual error using said ranges;
• means for determining a conditional probability that a satellite is an error producing satellite using said least square residual error and Bayes Rule, including means for determining an estimate of a sum of the squares of the least square residual error for a reduced system which does not use said satellite, and means for determining a conditional probability of said least square residual error using said sum of the squares of the least square residual error for said reduced system;
• means for estimating a second loss associated with a hypothesis that said satellite is the error producing satellite using said conditional probability and said first loss estimate, including means for estimating a third loss which is associated with an incorrect hypothesis by taking a difference between a first loss associated with said satellite and a first loss associated with a second satellite, means for forming a sum of a plurality of third losses which are associated with a plurality of incorrect hypotheses, and means for multiplying said third loss which is associated with an incorrect hypothesis by a conditional probability that said second satellite is the error producing satellite;
• and
• means for selecting a minimal second loss to identify the error producing satellite.