Chapter 9.5.1: INERTIAL SYSTEMS TECHNOLOGIES: Error Sources

9.5.1 Error Sources

9.5.1.1 Initialization Errors Inertial navigators can only integrate sensed accelerations to propagate initial estimates of position and velocity. Systems without GNSS aiding require other sources for their initial estimates of position and velocity. Initialization errors are the errors in these initial values.

9.5.1.2 Alignment Errors Most standalone INS implementations include an initial period for alignment of the gimbals (for gimbaled systems) or attitude direction cosines (for strapdown systems) with respect to the navigation axes. Errors remaining at the end of this period are the alignment errors. These include tilts (rotations about horizontal axes) and heading errors (rotations about the vertical axis).

Tilt errors introduce acceleration errors through the miscalculation of gravitational acceleration, and these propagate primarily as Schuler oscillations (see Section 9.5.2.1) plus a non-zero-mean position error approximately equal to the tilt error in radians times the radius from the earth center. Initial azimuth errors primarily rotate the system trajectory about the starting point, and there are secondary effects due to coriolis accelerations and excitation of Schuler oscillations.

9.5.1.3 Sensor Compensation Errors Sensor calibration is a procedure for estimating the parameters of models used in sensor error compensation. It is not uncommon for these modeled parameters to change over time and between turnons, and designing sensors to make the parameters sufficiently constant can also make the sensors relatively expensive. Costs resulting from stringent requirements for parameter stability can be reduced significantly for sensors that will be used in integrated GNSS/INS applications, because Kalman filter-based GNSS/INS integration can use the differences between INS-derived position and GNSS-derived position to make corrections to the calibration parameters.

These nonconstant sensor compensation parameters are not true parameters (i.e., constants), but "slow variables," which change slowly relative to the other dynamic variables. Other slow variables in the integrated system model include the satellite clock offsets for selective availability (SA).

The GNSS/INS integration filter implementation requires models for how variations in the compensation parameters propagate into navigation errors. These models are derived in Section 9.3 for the more common types of sensors and their compensation parameters.

9.5.1.4 Gravity Model Errors The influence of unknown gravity modeling errors on vehicle dynamics is usually modeled as a zero-mean exponentially correlated acceleration process (see Section 8.5)

where Δt is the filter period, the correlation time

ν_horizontal is horizontal velocity, d_correlation is the horizontal correlation distance of gravity anomalies (usually on the order of 10⁴-10⁵ m), w_k is a zero-mean white-noise process with covariance matrix

is the variance of acceleration error, and I is an identity matrix. The correlation distance d_correlation and RMS acceleration disturbance a_RMS will generally depend upon the local terrain. Here, d_correlation tends to be larger and a_RMS smaller as terrain becomes more gentle or (for aircraft) as altitude increases.

The effects of gravity modeling errors in the vertical direction will be mediated by vertical channel stabilization.

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Chapter 9.5.1: INERTIAL SYSTEMS TECHNOLOGIES: Error Sources

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