Chapter 9.3.1: INERTIAL SYSTEMS TECHNOLOGIES: Zero-Mean Random Errors

9.3.1 Zero-Mean Random Errors

These are the standard types of error models used in Kalman filtering, described in the previous chapter.

9.3.1.1 White Sensor Noise This is usually lumped together under "electronic noise," which may come from power supplies, intrinsic noise in semiconductor devices, or from quantization errors in digitization.

9.3.1.2 Exponentially Correlated Noise Temperature sensitivity of sensor bias will often look like a time-varying additive noise source, driven by external ambient temperature variations or by internal heat distribution variations.

9.3.1.3 Random-Walk Sensor Errors Random-walk errors are characterized by variances that grow linearly with time and power spectral densities that fall off as 1/frequency² (i.e., 20 dB per decade; see Section 8.5.1.2).

There are specifications for random walk noise in inertial sensors, but mostly for the integrals of their outputs, and not in the outputs themselves. For example, the "angle random walk" from a rate gyroscope is equivalent to white noise in the angular rate outputs. In similar fashion, the integral of white noise in accelerometer outputs would be equivalent to "velocity random walk."

The random-walk error model has the form

The value of Q_ω will be in units of squared-error per discrete time step Δt. Random-walk error sources are usually specified in terms of standard deviations, that is, error units per square-root of time unit. Gyroscope angle random walk errors, for example, might be specified in deg/√h. Most navigation-grade gyroscopes (including RLG, HRG, IFOG) have angle random-walk errors in the order of 10^-3 deg/√h or less.

9.3.1.4 Harmonic Noise Temperature control schemes (including building HVAC systems) often introduce cyclical errors due to thermal transport lags, and these can cause harmonic errors in sensor outputs, with harmonic periods that scale with device dimensions. Also, suspension and structural resonances of host vehicles introduce harmonic accelerations, which can excite acceleration-sensitive error sources in sensors.

9.3.1.5 "1/f" Noise This noise is characterized by power spectral densities that fall off as 1/f, where f is frequency. It is present in most electronic devices, its causes are not well understood, and it is usually modeled as some combination of white noise and random walk.

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Chapter 9.3.1: INERTIAL SYSTEMS TECHNOLOGIES: Zero-Mean Random Errors

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