The trajectory of an interplanetary spacecraft can be used to test gravitation in the Solar System. Its determination relies on radio tracking and is limited by the uncertainty on the spacecraft non-gravitational acceleration. The addition of an accelerometer on board provides another observable which measures the departure of the probe from geodesic motion. Such a concept has been proposed for the OSS mission which embarks the Gravity Advanced Package. This instrument, which is the focus of this article, is designed to make unbiased acceleration measurements.
The Gravity Advanced Package is made of two subsystems: MicroSTAR, an electrostatic accelerometer which inherits mature technology developed at Onera, and the Bias Rejection System used to rotate MicroSTAR with respect to the spacecraft around one axis. MicroSTAR measures the non-gravitational acceleration of the satellite and the measurement noise is characterized by the following power spectrum density 6 (for a measurement range of 1.8 × 10 -4 m.s -2 ):
Thanks to the Bias Rejection System, which rotates the accelerometer of a monitored angle called θ, the quantities measured along the orthogonal axis y and z of the accelerometer are (assuming that there is no quadratic terms and the gain of the instrument is perfectly known)
with a ν (ν ∈ {Y ; Z}) the components of the acceleration in the reference frame of the spacecraft, b y and b z the bias of MicroSTAR on each axis, and n y and n z the measurement noise.
Assuming that N measurements are made with a time step δt, there are 4N unknowns in equations ( 2) and only 2N measurements. Calling x the column vectors whose components are the values of x at each sampling time and using the linearity of the equations, it is however possible to retrieve from the measurements the values of the projection of a Y and a Z on a vector subspace defined by the columns of the matrix V a ∈ M N,pa (p a < N ). If
V a ′ Λ ν b κ = 0, with ν ∈ {c; s} and κ ∈ {y; z}.
(
where
Assuming that the bias on each axis also belongs to a subspace defined by the matrix V b , is is possible to design pattern for the rejection angle θ which fulfills conditions (3). This signal has a period called τ .
In addition to retrieving the unbiased non-gravitational acceleration of the spacecraft, this method allows characterizing the uncertainty on the demodulated quantities V ′ a a Y and V ′ a a Z , given MicroSTAR noise power spectrum density (cf. eq. ( 1)). Assuming that V a ∈ M N,1 (R) and |V a | = 1, the precision on the quantities V ′ a a Y and V ′ a a Z is given by 7
where F δt is the Discrete Time Fourier Transform. One has to notice that the noise is selected, as expected, at the modulation frequency 1/τ .
This demodulation scheme will be validated experimentally at Onera using a pendulum. A control loop allows controlling its inclination to the 10 -9 rad level. It is possible to incline it at a known angle in order to simulate an external acceleration. On this pendulum, an accelerometer is mounted on a rotating stage. There are two goals for this experiment : -Validate the demodulation scheme by showing that it properly separates the bias from the signal of interest allowing to make unbiased acceleration measurements.
-Verify the value of the uncertainty on V ′ a a Y and V ′ a a Z predicted by equation ( 5).
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