How MRU Correction of DP Sensors Works

Introduction: I have an article explaining why dynamic positioning (DP) class 2 & 3 vessels generally require three independent motion reference units (MRUs) and declaring the importance of the correction, but I assumed everyone knew how it worked and didn’t bother explaining it. That was a blind spot on my part and it’s time to fill that gap. We will look at why MRUs are needed and how they are used. Because this article comes out of a message reply, where I couldn’t use pictures, I’m going to use analogies of physical movement that I encourage the reader to use, or at least consider, to help develop an intuitive understanding.

Exercise 1: Make a fist. Imagine that is the DGPS antenna, which receives satellite and correction signals from known locations and times to establish position. Put your arm straight up so the ‘antenna’ is directly above your shoulder. The ‘antenna’ marks your shoulder’s position, because the shoulder is located directly beneath it. If you were to wave your arm left and right then that would reflect roll. Moving the arm fore and aft would reflect pitch and standing straighter or slumping would reflect heave. This sets our analogy/reference.

Exercise 2: Move your arm gently back and forth left and right about 10-20 degrees. Don’t wave like you are looking for attention, but reflect the stately slow steady roll of a ship. Obviously, the fist is rarely directly above the shoulder, but if you are moving evenly, the left and right movements even out and the fist is on the average above the shoulder. This is how older DP systems used to work, they averaged the multiple readings from the same position sensor to eliminate the effect of the moving ship. Technically, they used a low pass filter to achieve the same effect. This is fine if certain assumptions are true, but they sometimes aren’t and we will look at that. For now recognize that a pendulum or metronome’s tip position can be averaged out if the samples are fast enough, taken over long enough, and the movements are even. It’s a decent starting assumption for a big piece of floating steel.

Exercise 3: Repeat exercise 2, but every time the fist reaches the far right, think or say “sample”. If that is the only time position is measured, then the smooth motion that averages out doesn’t matter, because the measurements are all that counts. A system that assumes the shoulder is under the fist can be wrong. Put your fist to the far right of the previous arc. The system assumes that the shoulder is beneath the average of the samples, but all the samples are to the right and there is a gap between a plumb line dropped from your fist and your shoulder. All the samples are to the right, so the shoulder is assumed to be to the right, because that is where the fist was measured to be. That is the error. This usually isn’t a problem for fast sensors like the DGPS or CyScan/Fanbeam, because they can take many samples per second, and ship movement is usually much slower than that. It is a problem for slower sensors - like those that are limited to the speed of sound in water and have long return journeys. Thus, old DP vessels had MRUs for hydro-acoustic position reference sensors (HPRs), but didn’t really need them for light speed sensors. The HPRs needed to know the vessel movement, because the rare signals couldn’t be averaged out and needed mathematically corrected. The movement needs measured and corrected for. If you know the angle of the arm and length of the arm, then the difference could be figured out. Exercise 2 had so many samples during the movement that this wasn’t a problem and could be averaged out.

Exercise 4: Repeat exercise 2, but lean your torso to the side or swing your arm slightly further in one direction than in the other (you might already do this to avoid hitting your head). Averaging the movement of the fist tells its average position, but no longer tells where the shoulder is. The torso lean means the fist no longer averages over the shoulder, and restricting movement in one direction has the same effect. Sampling rate won’t solve this problem, and now the arm length and angle from the vertical becomes important. The average angle could be used, but movement may not be even or predictable, so it’s best to use the angle at the time the position was measured to correct that measurement. So, if you were to repeat the exercise and stop at each measurement, then your measured position, measured angle, and correction calculation will produce correct position measurements. It wouldn’t matter how you bent your torso, because it is possible to correct for it. Being in the right position is the job of the DP system, good measurement is vital to achieving it.

Correction: The picture above shows that practical application of this for vessel roll. The vessel rolls around the ship’s center of gravity, so that is the shoulder and the thing we want to know the position of. The DGPS antenna is up in the mast and the distance between it and the center of gravity is called the lever arm. Note how similar this is to the fist and shoulder being connected by the arm. We know how far away the sensor is from the center of gravity from our surveyed and tested offset settings, and we know the angle of the ship inclination measured by the MRU, so when we measure the position of the antenna (fist), we can do some trigonometry to determine the position of the ship (center of gravity/shoulder). If the vessel is inclined 5 degrees to the Port and the antenna is 40m directly above the center of gravity when the ship is vertical, then the center of gravity is 3.5m to the right of the measured antenna position (40m*sin(5deg)=3.5m). This needs done for pitch and roll, but heave isn’t controlled or used by DP. If the measurements were perfect and the vessel stayed on position, then this method would come up with the same answer despite pitch or roll angle.

Complication: This is the typical situation, where the lever arm isn’t in vertical line with the sensor and the surveyed lever arm includes the green length and angle. The MRU measures the angle from the vertical and both angles are used in the correction calculation. The sensors are almost never directly in line with the center of gravity. The sensors are also usually not on the centerline. For example, this side view doesn't show it, but there is probably a DGPS on either side of the mast. This means that someone solving for just pitch effect doesn't use the measured distance and angle from the center of gravity, but just the fore-aft portion of that lever arm in their calculation (the green line & angle shown in the picture). Similarly, solving for just the roll offset would use only the port-stbd portion of the distance and angle. This sounds complex and the DP designer avoids the complication by using 3 dimensional matrix math. This means he can go back to using the 3D lever arm distance and angle to the sensor and the 3D motion measured by the MRU to correct for pitch and roll without breaking it into parts. The 3D math treats the movement as a whole, just as you naturally think of the movement of your raised arm as a whole, and not in terms of X & Y coordinates.

Dangers: If the distance or angle is wrong, or the sensor isn’t rigidly attached to the ship, then the correction will fail.

• If the actual distance was 50m then the 5 degree lean would put the real center of gravity 4.3m away rather than 3.5m. The position would oscillate with the vessel roll due to the distance error. Assuming a 5 degree roll, that would be an apparent periodic movement of 1.6m over one roll period. This could interact with DP control and destabilize position control, so getting and keeping the distances right is important. Systems that allow comparison of position, pitch, and roll trends help detect this.

• Wrong angle gives wrong answer, so we use three MRUs and work at keeping them independent, so a bad sensor will be rejected. This includes risks of common placement (shock, vibration, magnetic). E.g. one ship put them under the workdeck and had them all rejected when a load was dropped. The DP controller compares the inputs and detects and rejects bad sensors and data. A common MRU fault has the potential to affect all position sensors, so common faults need eliminated, including unwanted common protections (“a ship would never move that fast or lean that far” - until a wave hits). Of course, the DP controller is always the common point and controller faults (math, memory, glitch) can mess up the process.

• An HPR transceiver or DGPS antenna mounted on a vibrating pole, or flopping about, will give bad readings and break the assumption of a consistent relationship between sensor and center of gravity. The antenna can be regularly looked at to ensure this isn’t happening. The HPR might need an MRU on the transceiver pole to detect and correct for its movement.

Conclusion: We use MRUs to correct the position reference sensors for the movement of the vessel, so we have consistent corrected measurements. The methodology is similar to how you know where your fist is compared to your shoulder. We normally think the other way (from the shoulder to the hand) but in the dark we figure out where we are by touch and position our movements based on that. Our minds and bodies do this in more complicated ways than machines, but mechanized systems use familiar basic principles. I hope comparison has provided useful insight that will help in operation and troubleshooting.

P.S. Next week’s article will be incidents, so if you want something covered, let me know.

P.P.S. After the death of old Summary earlier this year, I was a little concerned about young DPE. I became more concerned when we didn’t have our second IMCA DP event bulletin of the year by the end of June. That’s uncommon, so I asked. DPE is in new hands and in the works.