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

Abstract

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a highfidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms. Nomenclature C = Backward smoothing gain F = Linearization of f with respect to x f = Low-fidelity atmospheric model equations of motion G = Linearization of f with respect to u g = Gravitational acceleration, m/s 2 H = Linearization of h with respect to x h = Pressure distribution model, Pa I = Identity matrix J = Linearization of h with respect to u k = Integer time index N = Integer time index of final pressure measurement P = Covariance of x after the measurement model update = Static pressure, Pa p = Pressure measurement vector, Pa Q = Process noise spectral densitỹ Q = Process noise covariance R = Pressure measurement covariance matrix R = Pressure measurement covariance matrix augmented with navigation uncertainty R = Planetary radius, m = Specific gas constant, J/kg-K S = Prior covariance of x from low fidelity model T = Prior covariance of x from high fidelity model T = Atmospheric temperature, K u = Vehicle inertial state v n , v e , v d = Vehicle planet-relative north, east, and down velocity components, m/s W o = Discrete-time observability Gramian w n , w e , w d = North, east, and down wind velocity components, m/s X 11 , X 12 , X 22 = Van Loan integral sub-matrices x = Atmospheric sta...

Mars 2020 Entry, Descent, and Landing Instrumentation (MEDLI2)

“…The algorithm is an enhanced version of that used for MEDLI reconstruction [12], and the mathematical details can be found in [5]. At a high level, the algorithm can be described as a weighted least-squares method in which best-fit estimates of the atmospheric conditions (pressure, density, and winds) are computed, given the inertial state of the vehicle (position, velocity, and attitude) and a model of the surface pressure distribution.…”

“…2. The locations of the pressure transducers on the forebody are defined using an optimization algorithm [5] that minimizes errors in reconstruction of vehicle angle of attack and side-slip.…”

An implementation of the cubature Kalman filter for estimating trajectory parameters and air data of a hypersonic vehicle

“…Compared with Karlgaard et al., 31 the air data are not included in the system state vector. This makes system state estimation processes not be affected by the model uncertainties of the air data dynamic.…”

“…By contrast, the Kalman filtering approach can effectively estimate the trajectory parameters and the air data based on the fusion of the data of INS and FADS. Numerous researches 26–31 have presented and developed the Kalman filtering approach. Karlgaard et al.…”

“…Unfortunately, there exists some drawbacks in the above approaches: It is difficult to calculate the Jacobian matrixes. As presented in Karlgaard et al., 31 the pressure model which was built with CFD solutions and the high-fidelity atmosphere models are all numerical models, without any mathematic expressions. This enlarges the difficulty in the linearization of the models with respect to system states; The measured errors of INS have not been taken into consideration.…”