# Development of multisensor fusion techniques with gating networks applied to reentry vehicles

## Abstract

The problem of model inaccuracy for Extended Kalman Filters (EKF) is addressed in the case of vehicle atmospheric entry tracking and navigation with a filter bank architecture, also called mixture-of-experts, regulated by gating network, which is then tested in two different applications. First, a wind-frame based flight model is developed, which allows for maneuvers, and inclusion of atmospheric and gravity models. This level of complexity allows in theory for better estimation accuracy when used in an EKF, but the filter performance is in part dependent on the accuracy of the vehicle and environment models. The problem is how to deal with imperfect models. The approach treated here, which as already been applied in other domains, is to create a population of filters, each representing a particular modeling of the vehicle and/or environment. The discriminating device between the expert filters is a gating network, which is a simplified single-layer neural network learning in real-time with the help of the statistical information from the filters. The gating network is used to compute a weighted sum of the state estimate from each filter, which is therefore an optimal estimate. The gating network can also be used as an hypothesis tester, which is the case in the first example. The system was applied to the tracking and identification at high altitude of reentering spiraling objects accompanied by decoys. The object is being tracked at high altitude by three ground radars providing a variety of measurements which are treated in parallel by two filters, one being an expert tuned for the real target and the other tuned for the decoy. Experiments show that the regulated bank can rapidly correctly identify the object as being the real target. The second application is precision Mars entry navigation, where the on-board navigation system of a maneuvering Mars lander used a bank of expert EKF, each processing inertial acceleration as measurement, and each designed around a specific realization of the imperfectly known atmospheric density profile. The objective here is less to identify the best performing model than optimizing the overall state estimate by combining the estimate from every filter. The system also periodically restarts the filters with the current optimal estimate so as to keep all the filters competitive during all of the descent. The result is that this mixture-of-experts does not perform better than a dead-reckoning scheme unless one of the density model happens to be relatively close from the real density profile, but that it is more robust than dead-reckoning to loss of data, and can readily adapt additional sources of measurements.