Deriving Confidence from Artificial Neural Networks for Navigation
Joseph Curro, Air Force Institute of Technology John Raquet, Air Force Institute of Technology
Location: Big Sur
Artificial Neural Networks (ANNs) are increasing used in modeling and prediction due to advances in deep learning architecture and training. As ANNs become a viable option for making state or measurement predictions in navigation, special care must be taken in order to determine the confidence (covariance) of the predictions. A special kind of ANN output called Mixture Models approximates the prediction distribution with a mixture of known distributions such as Gaussian distributions. This allows the ANN to output more than a single point estimate. The prediction mixtures can then be converted into a form for processing by a filter. In this paper an ANN is trained to model state dynamics or propagation and outputs a Gaussian Mixture Model (GMM). A second ANN is trained to model the measurement equation to convert measurements to state estimates again represented as a GMM. Both GMMs are simplified into a single Gaussian distribution for inclusion into an EKF. An experiment was conducted using VLF signals as measurements to an EKF with an ANN trained propagate model. This method shows an improvement when the ANN covariance estimate is to determine the state dynamics and measurement noise compared to using static estimates for the state dynamics and measurement noise. Thus, the GMM output allows the modeling and prediction power of ANN to be used in standard navigation filters with minimal changes.