2. Zeroing concepts

In a preimpact sensing system, the accelerometer or pressure sensor does not report "zero" when the vehicle is at rest. It reports whatever voltage or digital count corresponds to its current electrical and mechanical state. Zeroing is the process of establishing a trustworthy reference for that rest state so that every subsequent measurement — and every decision derived from it — is anchored to a known baseline. When that baseline is wrong, the error propagates directly into the firing decision. This section separates the three error mechanisms that corrupt the baseline — offset error, bias, and drift — and shows how each one shifts the effective decision threshold.

Establishing the reference convention

Before discussing error, fix the sign convention, because every number below depends on it. Define the sensor output as S(t) in raw counts, and define the zeroed measurement as:

a(t) = k · (S(t) − Z)

where Z is the stored zero reference (in counts) and k is the scale factor (in g per count). A positive a(t) means acceleration along the defined positive sensing axis. All thresholds in this chapter are expressed in the same positive-axis convention. If a deployment inverts the axis, the sign of every threshold must be inverted with it; mixing conventions is one of the most common causes of a "sensor that fires early."

Offset error versus bias: a distinction that matters

These two terms are often used interchangeably, but they describe different things and demand different corrections.

Offset error is a fixed, deterministic deviation of the output from the ideal value at the reference condition. It is what remains after a single zeroing operation if that operation was performed imperfectly — for example, zeroing while the vehicle sits on a 2° slope, or zeroing before the sensor's internal filter has settled. Offset error is constant for a given zeroing event and can be removed by re-zeroing under correct conditions.

Bias is the sensor's inherent, unit-specific departure from ideal, present even under perfect reference conditions. It arises from manufacturing tolerances, MEMS proof-mass asymmetry, and package stress. Bias is a property of the individual device; two sensors of the same part number will have different bias values within the datasheet's specified window. Bias cannot be eliminated by re-zeroing alone unless the zeroing procedure explicitly measures and stores it — which is exactly what a proper zeroing routine does.

The practical consequence: a zeroing routine that stores Z = S_rest absorbs both the current offset error and the device bias into a single number. That is acceptable only if the reference condition during zeroing matches the reference condition during operation. If the vehicle is loaded differently, parked on a grade, or the sensor is re-mounted, the absorbed offset error becomes a live error term.

Drift: the baseline that moves after zeroing

Drift is the time- and temperature-dependent change of the zero point after calibration. It is the most dangerous of the three because it is invisible at the moment of zeroing and grows silently. Two drift components dominate in preimpact sensing:

• Thermal drift — the zero point shifts with temperature, typically specified as a slope in counts/°C or g/°C. A sensor zeroed in a 20 °C workshop and operated at −10 °C or +60 °C will carry a residual offset proportional to the temperature excursion.
• Long-term (aging) drift — a slow, monotonic wander over months of service, driven by package stress relaxation and dielectric charging. It is small per unit time but accumulates across a service interval.

Drift is not corrected by a single zeroing event; it requires either periodic re-zeroing, temperature compensation using an on-board temperature sensor, or a decision threshold with enough margin to absorb the worst-case drift over the service interval.

How each error shifts the decision threshold

Consider a representative preimpact channel with a nominal firing threshold of T = 8.0 g. The zero reference is stored in counts, and the scale factor is k = 0.004 g/count. Suppose the true rest output should be 2048 counts, but the stored reference is 2060 counts — a 12-count offset error. The measurement then reads:

a(t) = 0.004 · (S(t) − 2060)

At true rest (S = 2048):  a = 0.004 · (−12) = −0.048 g   (should be 0.000 g)
Apparent threshold crossing: the system reaches 8.0 g when
  S = 2060 + 8.0/0.004 = 2060 + 2000 = 4060 counts
True acceleration at that moment: 0.004 · (4060 − 2048) = 8.048 g

The 12-count offset has raised the effective firing threshold from 8.000 g to 8.048 g — a 48 mg late trigger. Small, but it is a systematic bias in one direction, and it stacks with thermal drift. If the thermal drift coefficient is 0.02 g/°C and the operating temperature is 40 °C below the zeroing temperature, the drift alone contributes −0.8 g, which now moves the effective threshold to roughly 7.25 g — an early trigger of 750 mg. The two errors can partially cancel or compound depending on sign, which is why worst-case analysis must consider them independently, not as a single lumped figure.

Budgeting the threshold against the error stack

The engineering response is not to chase a perfect zero but to size the decision threshold so that the worst-case error stack cannot cause a false trigger or a missed trigger. A practical error budget for the example channel looks like this:

With a nominal threshold of 8.0 g and a ±0.90 g stack, the effective threshold can land anywhere between 7.10 g and 8.90 g. If the application requires the trigger to occur no earlier than 7.5 g and no later than 8.5 g, this budget fails and the thermal drift term must be compensated rather than absorbed by margin. That is the real output of a zeroing analysis: not a single corrected number, but a defensible statement of how much threshold uncertainty the design can tolerate.

Verification in practice

To confirm the zero reference is behaving, perform a three-point check rather than a single rest measurement. First, record the rest output at the zeroing temperature and confirm it matches the stored Z within the offset budget. Second, soak the unit at the cold and hot extremes of the operating range and record the rest output at each; the change should track the datasheet drift slope within tolerance. Third, apply a known reference acceleration (a tilt fixture at a measured angle, or a calibrated shaker at low g) and confirm the zeroed reading matches the applied value within the combined offset-plus-bias budget. A unit that passes the first check but fails the second has a drift problem; one that fails the third at constant temperature has a bias or scale-factor problem. Separating these symptoms early prevents the classic misdiagnosis of "replacing a good sensor because the threshold was set against a bad zero."