FLICKER NOISE UPDATE
FLICKER NOISE SIMULATOR

FLICKER NOISE UPDATE

The effect of attitude sensor accuracy and update rate on estimability will be investigated. This is in accordance with an estimability criterion defined by Baram & Kailath (IEEE TAC-33-12 1988) and Baram & Shaked (IEEE TAC-30-5 1985). Preliminary filter covariance results show that the higher-frequency states in the flicker model are not estimable. The augmented filter is compared with an attitude determination filter that is based on the random walk drift model.ДЄn attitude determination Kalman filter that incorporates a model of flicker noise is expected to yield greater performance than a conventional attitude determination filter, particularly when a low-cost gyro with poor drift stability is used, as occurs when using a MEMS gyro.

FLICKER NOISE SIMULATOR

This more realistic gyro simulator is used to evaluate performance of the attitude determination filter augmented with the flicker noise model. One of the flicker noise models has been investigated for use in estimation of time in ensemble atomic clocks, where the clock drift is modeled as flicker noise.ДЄ detailed gyro error simulator also incorporates a flicker noise model Allan variance plots show the validity of the gyro noise model. We will examine, in particular, the estimability of the flicker noise states.ДЄn overview of flicker noise characteristics, modeling, and simulation is given, and two linear time-invariant models that approximate flicker noise are provided. We investigate the feasibility and benefit of using a flicker noise model in an attitude determination Kalman filter. However, gyro drift is typically dominated by flicker noise. Bias stability in the range of 0.01 to 0.001 deg/hr is needed to achieve medium to high performance attitude determination and navigation.ДЄ conventional attitude determination filter models gyro drift as a random walk, and performance analysis via simulation also uses a random walk model. Most small spacecraft require bias stability less than 0.1 deg/hr. The bias instability of MEMS gyros is large (ranging from 0.5 to 35 deg/hr), but it may be several years before MEMS gyros with bias instability less than 0.1 deg/hr become available. MEMS gyros are currently being used on nanosats and cubesats simply because there is no other gyro that has the necessary low mass and power. MEMS gyros are almost ubiquitous in a variety of low-performance applications including nanosats, cubesats, missiles, piloted aircraft, UAVs, munitions, automobiles, robotics, personal navigation, hobby aircraft, and toys. MEMS gyros are attractive for their very low cost, mass, volume, and power. Medium-performance space-qualified gyros include the LN200S (about 0.015 deg/hr bias stability), the 2.5' Honeywell IFOG (0.005 deg/hr bias stability), and the European SAGEM DS HRG (0.01 deg/hr navigation grade, 0.1 to 1.0 deg/hr tactical grade).

The Northrop-Grumman SIRU is a high-performance space-qualified IMU containing four Hemispherically Resonating Gyros with a bias instability of 0.001 deg/hr. Several space-qualified gyros are available with a range of gyro drift stability performance. This is particularly true during long intervals when an attitude update is not available, which occurs on geosynchronous spacecraft. Attitude determination and navigation system performance determined via simulation can be optimistic if flicker noise is omitted from the filter and sensor models. In addition, gyro noise is typically simulated with only quantization, angle random walk, rate random walk or a first-order correlated (Gauss-Markov) noise, and a fixed bias. To date, attitude determination filters and navigation filters have used a rate random walk or a first-order correlated (Gauss-Markov) noise model for the bias instability and therefore are suboptimal. (We have to be careful that we don't confuse bias with bias instability, which are both called drift.) Angle flicker noise (gamma = -1), if present, can be regarded as integrated rate flicker noise. In reference to gyros, rate flicker noise is also known as rate bias instability.

The Allan Variance of 1/f noise is constant with integration time.ДЇlicker noise generally sets the noise floor of gyros and accelerometers, and therefore is a limiting factor in the performance of attitude determination and navigation systems. In this case, the power spectral density, in units of power per Hz, is inversely proportional to frequency and there is equal energy or power in each decade of frequency. For convenience we will consider gamma = 1 (pink noise). Attitude Determination Kalman Filter with a 1/f Flicker Noise Gyro ModelДЇlicker noise processes have a power spectral density (PSD) that decreases as 1/f^gamma, where f is frequency and 0 = 1.

Flicker noise