Motion Reference Units (MRU)

An inertial sensor that measures how a vessel rolls, pitches and heaves: how it finds heave, how accurate it is, where to mount it, and how active heave compensation uses it.

By Norwegian Dynamics Engineering · April 2026 · Updated September 2026 · 10 min read

Sealed motion reference sensor bolted to a rigid mounting plate, with cables and labelled X, Y and Z axes.

In brief

A motion reference unit (MRU) is an inertial sensor that measures how a vessel moves: roll, pitch and heave, and on most units the horizontal motions and rates of turn too.
It does not measure heave directly. It integrates vertical acceleration twice and filters out the drift. Real-time heave is typically accurate to 5 cm or 5 % of the heave amplitude, whichever is larger; delayed heave, which arrives a few minutes late, to 2 cm or 2 % on mid-grade units.
Roll and pitch are typically accurate to 0.01 to 0.03° RMS, with outputs at up to 200 Hz.
The MRU measures motion where it sits. A crane’s active heave compensation needs the motion at the crane tip, so the controller carries it over through the surveyed lever arm. A passive compensator needs no MRU.

A motion reference unit is a compact inertial sensor fixed to the hull, often near the vessel’s centre of rotation. It reports how the vessel moves, many times a second. Dynamic positioning, survey sonars, helidecks and motion-compensated cranes and gangways all use its output. In offshore lifting it is the input to active heave compensation.

What an MRU measures

Inside are three accelerometers and three rate gyros, one of each on each axis. The gyros measure how fast the vessel rotates. The accelerometers measure linear acceleration and the direction of gravity, which keeps the angles from drifting. A processor combines the two and outputs:

Angles: roll and pitch, measured against gravity.
Heave: vertical displacement about the point’s mean position, and vertical velocity and acceleration.
Rates and accelerations on all three axes, which a controller uses directly. A DP system uses the roll and pitch to correct its position references.

An MRU does not know where the vessel is. Heave is measured from a mean level, not an absolute height. On many units, yaw comes out as a rate of turn only; true heading comes from a gyrocompass or a GNSS compass. Units that add GNSS positioning are sold as inertial navigation systems.

The six motions

A vessel moves in six ways. It translates along three axes and rotates about the same three:

Figure 1. The six motions of a vessel. Each rotation is drawn in the view where its axis points at the reader: pitch in the side view, roll from astern, yaw from above.

Motion	Axis	What drives it in a seaway
Surge	Along X, fore and aft	Waves from ahead or astern; slow drift
Sway	Along Y, sideways	Beam waves; slow drift
Heave	Along Z, up and down	Every wave; the motion a heave compensator reduces
Roll	About X	Beam seas; lightly damped, so it can build up near the roll period
Pitch	About Y	Head and following seas
Yaw	About Z	Oblique seas; held by the DP system or the autopilot

How a given vessel responds to each wave period is its response amplitude operator (RAO); see vessel motions and RAOs.

How an MRU finds heave

An MRU has no sensor for height. It measures acceleration along its own axes, uses its roll and pitch to resolve the vertical component $a_z$ , removes gravity and integrates twice:

z(t) = \int_0^t \!\! \int_0^{\tau} a_z(s)\,\mathrm{d}s\,\mathrm{d}\tau

A bias grows fast through that double integration: only 0.001 m/s² becomes 1.8 m of false heave in one minute ( $\tfrac{1}{2} b t^2$ ). So the heave processor high-pass filters the result. It keeps the wave-frequency motion and removes the slow drift. The filter has a price: close to its cut-off, in long-period swell, the real-time heave loses some amplitude and runs ahead of the true motion. For a controller, both show up as residual motion.

Figure 2. Heave in a 20 s swell (illustrative). Top: real-time heave, available at once, is a little smaller than the true motion and runs ahead of it. Bottom: delayed heave matches the true motion but is available only a few minutes later.

That is why most MRUs give two heave outputs:

Output	How it is made	Used for
Real-time heave	Filtered only on past data, so it is available at once	Control: active heave compensation and motion-compensated gangways; helideck motion monitoring
Delayed heave	Filtered on data before and after each moment, so it is more accurate but arrives a few minutes late	Survey data processed after the fact, and checking the real-time output

A controller can only use real-time heave. It also needs velocity as much as position: an active compensator drives its winch or cylinder against the heave velocity, and prediction ahead of the measurement covers the delay through the actuator.

Typical accuracy

Datasheets from several makers quote similar figures for current mid- and high-grade units:

Output	Typical specification	What to check
Roll and pitch	0.01 to 0.03° RMS	Static or dynamic figure; they can differ several-fold
Real-time heave	5 cm or 5 % of the amplitude, whichever is larger	The wave periods it applies to, and how it behaves in long swell
Delayed heave	2 cm or 2 %, whichever is larger	The delay, which rules it out for control
Output rate	Up to 200 Hz	Latency is often not on the datasheet: ask for the delay from measurement to output

From public datasheets, 2020 to 2025. Top-grade units reach about 0.008° and 1 cm or 1 % delayed heave. Typical figures; the selected unit’s own datasheet and test conditions decide.

For a lift, the sensor’s own error (5 %, so about 10 cm in a 2 m heave) is rarely the largest. The larger errors usually come from outside the sensor: a wrong lever arm, a misaligned mount, or a signal read at the wrong point.

Mounting and the lever arm

The MRU reports the motion of the point where it is fixed. A crane tip 30 m away moves far more, because rotation adds to it: one degree of bow-up pitch lifts a point 30 m forward by

\Delta z = L \sin\theta = 30\ \text{m} \times \sin 1^\circ \approx 0.52\ \text{m}

Figure 3. The MRU at O sits near midships, close to the centre of rotation; the crane tip P is 30 m forward. When the bow pitches up by

\theta

, P rises by

L\sin\theta

, about 0.52 m per degree at 30 m, while O barely moves.

The controller therefore carries the motion over from the sensor O to the crane tip P, using the vessel’s rotation rate $\boldsymbol{\omega}$ and the lever arm $\mathbf{r}_{OP}$ between them:

\mathbf{v}_P = \mathbf{v}_O + \boldsymbol{\omega} \times \mathbf{r}_{OP}

This holds for a point fixed to the hull. While the crane slews or luffs, the tip also moves relative to the hull, and the controller adds that velocity from the crane’s own angle sensors. A heave compensator uses the vertical component, $v_{P,z}$ . Many MRUs can also output the motion at configured remote points from the same offsets. Either way, the installation decides the accuracy:

Place it near the centre of rotation, on stiff structure, away from engines and other sources of vibration.
Align it with the vessel’s axes and record any mounting offset: a misaligned sensor reports roll and pitch about the wrong axes and carries the motion to the wrong point.
Survey the offsets from the MRU to every point that needs motion, and check signs and units against the controller’s frame.
Plan for faults: a second MRU and a defined response to a lost or implausible signal, before the lift, not during it.

MRUs in heave compensation

In a crane’s active heave compensation, the MRU is the input. The controller takes the real-time motion, carries it over to the crane tip, predicts ahead to cover the actuator’s delay, and drives the winch or cylinder against it. How still the load hangs depends on the whole chain: the MRU’s accuracy and latency, the prediction, and the actuator’s speed and force. The sensor alone does not hold the hook still.

A passive compensator needs no MRU. Its gas spring responds to the load itself, so it isolates the load from the crane tip’s heave with no motion measurement at all. ANTARES, our adaptive passive unit, adds automatic damping control from its own sensors while the load support stays passive. VEGA, our in-line active compensator in development, combines MRU-driven active cylinder control with automatic damping control. The active and passive comparison goes through when each fits.

IMU, VRU or MRU

The names overlap between makers, but they describe how much processing the unit does:

Label	What it gives	Typical use
IMUinertial measurement unit	Raw acceleration and rotation rate on three axes	The sensor inside the others; its output needs processing
VRUvertical reference unit	Roll and pitch, sometimes heave	Attitude for antennas, sensors and simpler motion monitoring
AHRSattitude and heading reference system	Roll, pitch and heading; no heave	Attitude and heading where heave is not needed
MRUmotion reference unit	Roll, pitch and processed heave, usually surge and sway too, and rates on all three axes	DP, survey, motion-compensated cranes and gangways
INSinertial navigation system	An MRU’s outputs plus position and true heading, with GNSS	Navigation and survey positioning

For active compensation, the label matters less than the outputs: real-time heave and its velocity, at the point the controller needs, with a stated latency.

Frequently asked questions

What is a motion reference unit (MRU)?

An inertial sensor fixed to a vessel that measures its motion: roll, pitch and heave, and on most units the horizontal motions and rates of turn. It combines three accelerometers and three rate gyros with a processor, and outputs at up to 200 Hz. Dynamic positioning, survey and active heave compensation use its signal.

How does an MRU measure heave?

It measures acceleration along its own axes, resolves the vertical component with its roll and pitch, removes gravity, integrates twice and high-pass filters the result to remove drift. Real-time heave is available at once and is used for control; delayed heave uses data from after each moment, so it is more accurate but arrives a few minutes late and suits survey processing.

How accurate is an MRU?

Typical datasheet figures: roll and pitch 0.01 to 0.03° RMS, real-time heave 5 cm or 5 % of the heave amplitude (whichever is larger), delayed heave 2 cm or 2 % on mid-grade units; top-grade units reach about 0.008° and 1 cm or 1 %. Check whether a figure is static or dynamic, the wave periods it applies to, and the latency.

What is the difference between an IMU, a VRU and an MRU?

An IMU gives raw acceleration and rotation rate. A VRU processes them into roll and pitch, sometimes heave. An AHRS adds heading but no heave. An MRU adds processed heave, usually surge and sway too, and rates on all three axes. An INS adds GNSS position and true heading.

Where should an MRU be mounted?

Near the vessel’s centre of rotation, on stiff structure away from vibration, aligned with the vessel’s axes. Survey the offsets to every point that needs motion: the controller carries the motion to the crane tip through that lever arm, and a 1° pitch moves a point 30 m away by about 0.52 m.

Does passive heave compensation need an MRU?

No. A passive compensator’s gas spring responds to the load itself, with no motion measurement. Active heave compensation needs an MRU, because its controller drives the winch or cylinder against the measured motion.

Basis and sources

Public datasheets for motion reference units from several makers, 2020 to 2025: roll, pitch and heave accuracy, delayed heave, output rates and remote monitoring points.
Rigid-body kinematics for the lever-arm transfer, $\mathbf{v}_P = \mathbf{v}_O + \boldsymbol{\omega} \times \mathbf{r}_{OP}$ .
Norwegian Dynamics’ knowledge-hub articles on active heave compensation and vessel motions.