Hypersonic State Estimation Using Frobenius-Perron Operator Parikshit Dutta * Raktim Bhattacharya † Aerospace Engineering Department, Texas A&M University, College Station, TX 77843-3141. This paper presents a nonlinear state estimation algorithm that combines Frobenius- Perron operator theory with Bayesian estimation theory. The Frobenius-Perron operator is used to predict evolution of uncertainty in the nonlinear system and obtain the prior probability density function in the estimation process. Bayesian update rule is used to determine the posterior density function from the available measurements. The framework for this filter is similar to particle filters where the density function is sampled using a cloud of points and the system dynamics is integrated with these points as the initial con- dition. The key issue in particle filters is that the weight for the sample points are typically determined using histograms, to obtain the prior density function, and thus requires many samples for acceptable accuracy. Moreover, the weights of majority of the particles con- verge to zero after a few iterations, rendering them useless for state estimation purposes. This issue can be resolved with the application of the Frobenius-Perron operator which determines the time evolution of the weights along sample paths. This greatly simplifies the determination of the prior density function and can be achieved with fewer sample points. Consequently, the associated computational time is also greatly reduced. The pre- sented algorithm is demonstrated on a hypersonic reentry problem with uncertain initial states, with given initial probability density functions. The performance is compared with particle filters and it is observed that the proposed algorithm is computationally superior as expected. I. Introduction Entry, descent, landing of a hypersonic vehicle on the surface of Mars is a topic of research receiving much attention in recent years. The expected mass of the next Mars Science Mission Laboratory is approximately 2800 Kg at entry, which is required to land within few kilometers of robotic test sites. The requirement of high accuracy when landing in proximity of the target region is a key challenge of high mass entry. It is therefore necessary to estimate states and parameters of the reentry vehicle when uncertainties are present in initial conditions. High nonlinearity of reentry dynamics, coupled with lack of frequent sensor updates make the estimation problem difficult to solve. Sequential estimation algorithms, based on Monte-Carlo (MC) simulations are most commonly used in such cases. However for systems having three or more di- mensions, MC based techniques may be computationally expensive as ensemble size required to guarantee convergence, increases exponentially with number of states. The objective of this paper is to demonstrate ap- plication of a new nonlinear estimation algorithm to hypersonic flight problems and highlight its superiority, in terms of error convergence and computational efficiency, over the popular particle filtering based methods. * Graduate Student, p0d5585@aero.tamu.edu † Assistant Professor raktim@aero.tamu.edu 1