Local Area Integrity Monitoring Utilizing Bayesian Statistical Estimation

One of the more difficult problems in a local area DGPS approach and landing system is integrity monitoring of the broadcast corrections. Based on RTCA/DO-217 requirements for Special Category I (SCAT-I) approach and landing systems, a 1x10 -7 error bound must be placed on the differential corrections with an integrity of this bound equal to 1 X 10 -8 [1]. The system must also maintain sufficient continuity of function of 1x 10 -4 Per 150 second approach. Although many factors determine the size of the error bound, such as multi-path mitigation and receiver noise performance, two major impacts on the estimation process are the ability to obtain independent samples and the number of samples available in the time-to-alarm limit. In general, smoothing is utilized in the differential correction generation process. This has the benefit of improving accuracy but causes a problem in that the samples used to determine the error bound become correlated. Thus, standard statistical techniques cannot be applied without accounting for the correlation of the samples. Additionally, using a 2 Hz receiver with a time-to- alarm limit of 3 seconds , the SCAT-I time-to-alarm ground allocation [1] only provides a maximum of 6 samples of data. A traditional statistical or even an interval bounding approach can result in overly conservative error bounds for small sample sizes. An innovative solution to these problems is to use error knowledge available in the form of recently observed error behavior in addition to the current error samples. Prior knowledge of the error statistics is available via measurement noise variances based on S/No and multi-path biases based on receiver performance with respect to elevation angle. Utilizing Bayesian interval estimation bounds allows one to exploit the a priori information about the errors. This method is a natural extension of traditional interval bound estimation approaches which assume an error distribution but ignore available knowledge of the prior error statistics. Bayesian estimation methods are the only valid way to make use of available prior information. This method results in a less conservative error bound on the differential corrections while maintaining both continuity and integrity requirements utilizing a small number of possibly correlated data samples. The objective of this paper is to provide the foundation for the incorporation of Bayesian statistics in Wilcox Electric’s DGLS 2000 SCAT-I approach and landing system. Simulation test results of Wilcox Electric’s integrity monitoring method utilizing Bayesian statistics are also presented. These examples show that the Bayesian method allows for the determination of a 1x10-7 error bound with a confidence of 1x10-8. A continuity example is also developed showing that system continuity of function can be achieved with margin using the Bayesian method.