How to read an IMU datasheet: bias instability, ARW, VRW and g-sensitivity

01

What do Typ, Max and σ mean on a datasheet line?

Epson's datasheets state that Typ. values are average values or 1σ values, and that Max./Min. values are design values or factory test values. All values in Table 1.3 apply at 25 °C, 3.3 V supply, 0 °/s and at most ±1 G unless noted otherwise. Woodman notes that bias stability is usually specified as a 1σ value in °/h.

A 1σ spread means some units lie outside it. If the spread is Gaussian, about 32 % of units fall outside ±1σ and 5 % outside ±2σ (own calculation). For a worst-case design, multiply the 1σ value or ask for the distribution.

02

Which "bias" is which?

The Epson PDG datasheets list three gyro bias lines that answer different questions.

1. 01Bias instability (Average): how much the bias wanders within one run in a constant environment, without switching off. ECSS (ESA) calls this in-run bias stability. It is read from the flat region of the Allan deviation.
2. 02Repeatability (1σ, turn-on to turn-on): how far the bias moves from one switch-on to the next. Epson defines it as the estimated variation during 5 consecutive days. ECSS describes it as random in magnitude but constant in time during one run.
3. 03Initial error (1σ, over the temperature range): the bias you can expect anywhere in the stated temperature range, before your own calibration. For MEMS gyros, the bias–temperature relationship is often highly nonlinear (Woodman).

03

Why are the three bias numbers so far apart?

For the M-G366PDG0 the three lines read 1.2 °/h, 36 °/h and 360 °/h. Each step is a factor of 30 or 10 (own calculation). Across the four models below, initial error is 240 to 720 times the bias instability.

The bias instability is reachable only if your system estimates the actual bias at every start-up and tracks it over temperature. A system that cannot hold still at start-up and has no aiding source should plan with the repeatability or the initial error. How a residual gyro bias turns into angle and position error over time is covered in our GNSS-denied error budget.

Start-up estimate: averaging a stationary M-G366PDG0 (ARW 0.08 °/√h) for 30 s leaves a white-noise uncertainty of about 0.9 °/h (4.8 °/h / √30, own calculation). That is already below the 1.2 °/h bias instability, so averaging much longer adds little.

04

How do you read an Allan deviation plot?

On the log-log plot of σ(τ) over averaging time τ, each noise type has a characteristic slope (Nirmala et al., Table 1):

1. 01Slope −1/2: white noise (angle random walk). Read σ at τ = 1 s (Woodman). In °/h, divide by 60 to get ARW in °/√h.
2. 02Slope −1: quantization noise at short τ.
3. 03Slope 0: the flat region, where bias instability is read. For the bias instability coefficient B, the flat level is σ ≈ 0.664 · B (Hiller, 2021).
4. 04Slope +1/2: rate random walk, read at τ = 3 s on the extrapolated line (Nirmala et al., Table 1).
5. 05Slope +1: rate ramp.

Reporting the Allan minimum itself or B = σ_min / 0.664 makes about a 1.5× difference (own calculation). The Epson datasheets give bias instability as "Average" and show typical Allan curves that Epson marks as not guaranteed. If you compare IMUs from different sources, ask which convention each one uses.

05

How do you convert ARW and VRW into noise density?

ARW in °/√h relates to the noise power spectral density by ARW = (1/60) · √PSD, with PSD in (°/h)²/Hz (Woodman). By the same logic, 1 (m/s)/√h corresponds to about 1,700 µg/√Hz (own calculation, g = 9.80665 m/s²).

Epson also lists a noise density measured between 10 and 20 Hz. It does not equal ARW × 60. For the M-G366PDG0, 0.08 °/√h × 60 gives 4.8 (°/h)/√Hz, but the datasheet states 6.9 (°/h)/√Hz. For the four models below, the stated density is 1.2 to 1.5 times the converted value, for both gyro and accelerometer (own calculation). The datasheet does not explain the difference. Use the noise density line for RMS noise in a given bandwidth, use ARW for angle growth over time, and don't mix figures from different conventions.

Worked example (own calculation), M-G366PDG0:

1. 01Rate noise density from the datasheet: 6.9 (°/h)/√Hz = 0.0019 (°/s)/√Hz.
2. 02RMS rate noise with a filter set to an assumed 100 Hz noise bandwidth: 0.0019 × √100 ≈ 0.019 °/s.
3. 03Angle random walk from ARW 0.08 °/√h: 0.033° (1σ) after 10 min, 0.08° after 1 h.
4. 04Accelerometer: VRW 0.02 (m/s)/√h converts to about 34 µg/√Hz; the datasheet's noise density line says 50 µG/√Hz.

06

What is g-sensitivity and why does it matter?

g-sensitivity is the change in gyro bias per g of linear acceleration. Epson lists it as "Linear Acceleration Effect": 18 (°/h)/G (Average) for all four models below. ECSS lists specific force among the bias sensitivities. Xing et al. describe it as one of the more important factors for the dynamic accuracy of MEMS gyros.

Assuming a linear effect, 0.5 G of sustained manoeuvre acceleration shifts the bias by about 9 °/h (own calculation). That is 7.5 times the 1.2 °/h bias instability of the M-G366PDG0. On vehicles, robots and machines that accelerate hard, this line can matter more than the bias instability.

07

Which datasheet lines should you check?

08

What do the Epson figures look like side by side?

All values are Typ. from Table 1.3 of the current full datasheets at 25 °C. Initial error and repeatability are 1σ values; the other lines are averages.

Sources: Epson full datasheets M-G330PDG0, M-G366PDG0, M-G370PDG0 (E Rev1.2) and M-G570PR20 (E Rev1.3), Table 1.3. All models are available on request; full datasheets on request.