**INTRODUCTION**

When a MEMS Inertial Measurement Unit (IMU) is operating as a feedback sensor in a motion control system, gyroscope noise is an important behavior to understand because it can cause undesirable physical motion on the platform it is monitoring. Depending on the conditions, there are a number of potential error sources to consider when developing early, application-targeted noise estimates for a particular MEMS IMU. Three common gyroscope attributes to consider in this process are its inherent noise, response to linear vibration and misalignment errors. Figure 1 provides a simple model, which displays several attributes that are influential in evaluating each error source: source, sensor response and filtering. This model provides the baseline for spectral analysis of each of these attributes.

**Figure 1**

Gyroscope Noise Sources and Signal Chain

**INHERENT SENSOR NOISE**

The inherent sensor noise represents the random variation in the gyroscope’s output, when it is operating in static inertial and environmental conditions. MEMS IMU datasheets typically offer the *Rate Noise Density* (RND) parameter to describe their gyroscope’s inherent noise, with respect to frequency. This parameter typically uses units of ^{o}/sec/
√
Hz and is a key part of predicting the inherent noise for a particular filter configuration. Equation 1 provides a simple way to estimate the noise associated with a particular frequency response (noise bandwidth) and RND.

When the RND’s frequency response follows a single-pole or double-pole, low-pass filter profile, the Noise Bandwidth (f_{NBW}) relates to the filter cut-off frequency (f_{C}) according to Equations 2 and 3.

In addition to the RND parameter, datasheets sometimes specify the gyroscope inherent noise for a specific filter configuration, using parameters, such as *Output Noise*, which comes in standard units for angular rate (^{o}/sec) and uses statistical terms, such as root-mean-square (RMS), to describe the noise magnitude.

**LINEAR VIBRATION**

Since gyroscopes measure angular rate of rotation, their response to linear motion introduces error to their measurements. MEMS IMU datasheets typically describe this response to linear motion through parameters such as *Linear Acceleration Effect on Bias or Linear-g*, which typically uses units of ^{o}/sec/g. Linear vibration is a repetitive inertial motion, whose magnitude can be in terms of displacement (m), linear velocity (m/s) or linear acceleration (m/s^{2} or *g*). At a specific frequency of vibration (f_{LV}), the displacement (|d_{LV}|), velocity (|v_{LV}|) and acceleration (|a_{LV}|) magnitude relate to each other according to equation 4.

When the vibration magnitude is in terms of acceleration (g_{RMS}), multiply it by the Linear-g parameter to estimate the resulting noise in the gyroscope measurements. For example, when the ADIS16488A experiences 5g (rms) of vibration, the noise estimate in its gyroscopes will be 0.045 ^{o}/sec (rms), since the Linear-g is equal to 0.009 ^{o}/sec/g.

As shown in Figure 1, gyroscope signal chains often include filters, which can help reduce the noise contribution from linear vibration. Defining the vibration in spectral terms (magnitude, frequency) provides an opportunity to consider the effect of the filters while estimating the noise contribution. The Acceleration Spectral Density (ASD) function is a common way for expressing vibration in spectral terms and typically comes in units of g^{2}/Hz. The following steps provide an example procedure for estimating the noise magnitude when the ASD and the gyroscope’s frequency response (H_{G}) are known: