How Much Stabilisation Do You Actually Need?

Two questions decide whether a stabilisation specification is any good, and neither of them is “how many microradians”.

The first is how much the platform moves. The second is how much of the picture the sensor sees. Together they set how much disturbance the system has to reject, and that number can be calculated before anyone has been asked for a quotation.

Rejection ratio

The useful figure of merit is the ratio between the disturbance going in and the line-of-sight motion coming out.

rejection ratio = platform disturbance amplitude ÷ residual line-of-sight motion

A ratio of 8 means that when the platform rolls through 8°, the line of sight moves by 1°. It is a ratio, so it carries no units and it can be compared between systems of different sizes — which is exactly what a bare microradian figure cannot do.

Deriving the requirement from the sensor

Here is the part that gets skipped. The residual motion you can tolerate is not a matter of taste; it follows from the field of view.

A target must stay inside the frame to be tracked, and in practice inside the middle of it — an operator loses a target that is skating around the edge long before it leaves. Take the usable fraction as about half the narrow-field angle of view.

Our thermal channels illustrate the range. A SEG14 at full optical zoom is looking through a very narrow window; a wide-field day channel is not. The narrower the window, the higher the rejection ratio has to be for the same platform.

Worked the other way round: a sensor with a 2° narrow field of view can tolerate roughly 1° of residual motion. On a vehicle stationary with its engine running, where the disturbance is on the order of ±0.5°, no stabilisation is needed at all. On the same vehicle moving across country, where ±5° is realistic, the requirement is a rejection ratio of about 5. On a small boat it might be ±15°, and the requirement climbs to 15.

Same sensor, same positioner, three completely different specifications — determined by the platform, not by the optics.

Frequency matters as much as amplitude

A rejection ratio quoted as a single number is incomplete in the same way a stabilisation figure is. Every closed-loop system rejects low-frequency disturbance well and high-frequency disturbance poorly, because the loop needs time to measure an error and drive it out.

Mounting	Typical frequency	Typical amplitude	What sets it
Fixed mast, wind	0.2–2 Hz	small, sustained	structural sway
Vehicle, stationary, engine on	20–60 Hz	very small	engine and auxiliaries
Vehicle, moving off-road	1–8 Hz	large	suspension and terrain
Small craft in a seaway	0.1–1 Hz	very large	wave period

Two observations follow. Wind sway on a mast and wave motion on a boat are slow, and a control loop of modest bandwidth handles both. Engine vibration is fast and small, and no reasonable loop will follow it — but it usually does not need to, because the amplitude is below the tolerable residual anyway. The difficult case is the middle row: a vehicle moving over rough ground produces disturbance that is both large and fast enough to sit near the top of the loop’s useful range.

So the question to put to a supplier is not “what is your rejection ratio” but “what is it at 2 Hz, and at 5 Hz”. A system quoted at a single frequency has been characterised at the frequency that flattered it.

What the loop is actually doing

The architecture is unremarkable and worth stating plainly, because the places it can be got wrong are not.

An inertial sensor measures the rate at which the head is being disturbed. That measurement is combined with the axis position from the encoder to form an error signal, and a control loop drives the motors to cancel it. The sensor sees motion in space; the encoder sees motion relative to the base; neither alone is sufficient.

Three details decide whether it works:

Latency. Every millisecond between the disturbance being sensed and the motor responding is phase lag, and phase lag turns correction into amplification at the frequencies that matter. This is why the loop lives close to the drive electronics.

Drift. A rate sensor integrated over time walks away from truth. The encoder anchors it — the slow, absolute reference correcting the fast, relative one. A design that trusts the inertial sensor alone will hold a target for a minute and lose it over an hour.

Bandwidth. Raising it improves rejection at the frequencies that matter and admits more sensor noise. There is an optimum and it depends on the payload; this is why the loop is tunable rather than fixed.

Our PED12 carries gyro stabilisation with dual-loop control and a published stabilisation accuracy of 0.04°; the gimbals in the thermal imager range integrate the sensor and the stabilised mount as one assembly, which removes the alignment term between them entirely.

Specifying it

Four lines are enough:

1. Platform and condition — “wheeled vehicle, moving, unimproved road”, not “vehicle”.
2. Disturbance amplitude and frequency band — measure it if you can; a day with an inertial logger on the actual platform is worth more than any assumption.
3. Sensor narrow field of view — from the datasheet.
4. Required rejection ratio at the stated frequencies — derived from the three above, not copied.

A requirement written this way can be tested. A requirement written as a single angle cannot, because there is no way to know what disturbance it was meant to survive.

Related reading: the error budget inside the stabilisation figure itself is taken apart in what a line-of-sight stabilisation figure actually costs, and the pointing terms that remain once the platform is still are covered in the target location error budget.