Cramér–Rao Lower-Bound Optimization of Flush Atmospheric Data System Sensor Placement

Abstract

Flush atmospheric data systems take measurements of the pressure distribution on the forebodies of vehicles and improve the estimate of freestream parameters during reconstruction. These systems have been present on many past entry vehicles, but design of the pressure transducer suites and the placement of the sensors on the vehicle forebody have largely relied on engineering judgment and heuristic techniques. This paper develops a flush atmospheric data system design methodology using Cramér-Rao lower-bound optimization to define the smallest theoretical variance possible from the estimation process. Application of this methodology yields Pareto frontiers of possible optimal configurations and identifies the number of ports that serve as the point of diminishing returns. The methodology is tested with a simulated Mars entry, descent, and landing trajectory. Nomenclature f = objective function H = measurement sensitivity matrix k = number of sampled points for the objective function n = number of ports P = state covariance matrix p = parameter vector for the objective function R = measurement noise covariance matrix q ∞ = freestream dynamic pressure, Pa α = angle of attack, rad β = sideslip angle, rad σ = standard deviation Subscripts i, j = indices y = y component z = z component Superscriptŝ = nonnormalized value − = mean value

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

“…Another approach, suggested in [45], involves sensor placement optimization that minimizes the trace of a weighted state covariance matrix. This approach has been used in the past for FADS pressure port location optimization in [46][47][48] (minimum root-meansquare errors were used in [46]). This approach has the drawback that the optimal sensor locations become dependent on modeling assumptions such as the process and measurement noise covariance and the choice of the weighting matrix.…”

Analytical Solutions of Generalized Triples Algorithm for Flush Air-Data Sensing Systems

“…However, this may not be the case for optimal sensor placement based on computationally-based rationale [15], which makes the triples algorithm difficult to implement.…”