Multi-Sector Active Yaw/Pitch/Roll Compensation

• What is Multi-Sector Active Motion Compensation ?.
• How can it be applied simultaneously to pitch, roll and yaw?.
• Simulation examples (100-900m).

The newest generation of multibeam sounders are now being offered with "Yaw Stabilisation". What is this, and how does it work?. The example we will use here is the Simrad EM300 model that is just coming onto the market.

For a conventional multibeam system with a single fore-aft transmit line array, a single transmit beam pattern is usually generated to cover the full angular sector from side to side. This transmit beam pattern may be steered fore or aft of the plane orthogonal to the ships head. This will provide a means of pitch stabilising the centre beam in the event of pitching. The same beam steering however, will overcompensate for those beams off nadir. As a result most multibeam manufacturers who implement conventional active pitch steering choose an incidence angle away from nadir at which the pitch compensation will be exact (for example 53 degrees off nadir for an EM3000). Inboard the beams will be undercompensated and outboard of this point they will be overcompensated (see Figure 2d).

If in contrast to pitch stabilisation we wish to attempt yaw stabilisation, we note that from a single line array we can only compensate one side at a time. The only way around this is to have two or more transmit beams (at discrete frequency bands) that transmit with independent (and inverse) beam steering. This was implemented by the GLORIA systems (Somers et al., 1984) many years ago. This is ideal for a sidescan geometry like GLORIA because the yaw stabilisation worked for the far range but failed drastically for the near nadir (which is irrelevant for a sidescan) where a pitch compensation was really required.

What the Simrad EM300 is now reported to do is to transmit a sequence of pulses separated in frequency (by about 500Hz). Each transmission closely follows the prior one (a few milliseconds apart only) so that all the pulses are in the water at the same time (one does not have to do sequential pinging after receiving each sectors echos). Each sector (9 sectors are used) has a discrete steering angle which is designed to optimise the combined effect of pitch and yaw stabilisation for that particular sector alone. As with conventional single sector systems the roll stabilisation occurs on the receive and can be performed independently for every beam. However, in this case the location of each sector must be adjusted for the roll at the time of transmit.

This can be seen graphically in Figure 1. Whereas on the right hand side we see a cone representing the axis of a single transmit beam pattern (with only one discrete steering angle), on the left hand side we see that the transmit pulse is broken up into a series of cone sectors, each with discrete steering angles.

Figure 1a: showing the single sectors of a conventional transmit and the resulting distribution of solutions	Figure 1b: showing the multiple sectors of the sequential transmits and the resulting distribution of solutions

How can it be applied simultaneously to pitch, roll and yaw?

If the above method is used it can improve both the pitch stabilisation and simultaneously allow yaw stabilisation. Fig. 2a shows the ideal situation. Fig 2b shows the problem in instantaneous yawing away from the mean course. Fig 2c. show how the 9 independent sectors may be individually steered to compensate for yaw to achieve a solution closer to the case of Fig. 2a.

Alternately if Pitch is the problem, Fig 2d shows the conventional method of single sector pitch compensation (with the problems discussed above). In contrast, Fig. 2e shows how using 9 independent sectors, a much better approximation of the case of Fig. 2a can be achieved.

We have considered the yaw and pitch cases in isolation. In reality we wish to compensate for both simultaneously. For the conventional case (Fig. 2d) a non-ideal result occurs. But for the nine sector case we can continue to approximate a straight line (Fig. 2e).

Figure 2a: ideal - level case

Figure 2b: no compensation - yawed only case

Figure 2c: Active Yaw compensation (9 Sectors)- yawed only case

Figure 2d: Single Sector Pitch compensation - pitched only case

Figure 2e: Active Pitch compensation (9 Sectors)- pitched only case

Figure 2d: Single Sector Pitch compensation - pitched and yawed case

Figure 2d: Active Pitch and Yaw compensation (9 sectors) - pitched and yawed case

In summary, if the 9 sector method can be implemented it:

• improves the ability to do pitch compensation,
• allows for the first time, yaw compensation and
• can perform both operations at the same time.

To illustrate the effect that Active Yaw compensation has I have taken a representative range of water depths and used the following parameters:

• speed - 10 knots
• 150 degree angular sector
• 1 degree beam width
• 1 degree beam spacing
• depths including:
  
  100m -- (0.6 second ping interval)
  300m -- (1.6 second ping interval)
  500m -- (2.6 second ping interval)
  700m -- (3.6 second ping interval)
  900m -- (4.6 second ping interval)
  

Figure 3: 5 minute time series of motion history used

As you will note, the vessel was rolling heavily (~+/- 2-5 degrees) with a charactersitic period of about 6-8 seconds. The pitch was far less pronounced at ~+/-1-2 degrees. The yaw consisted on two characteristic periods:

- a 1-2 minute period zig zig due to the manual line keeping and
- a ~ 6-8 second period ~+/- 1-2 degree yaw associated with the wave motion

• with roll and pitch stabilisation (but no yaw)
  (see Figures 4 a-e)
  
• with roll, pitch and yaw stabilisation (9-sector)
  (see Figures 5 a-e)
  

Note that the several minute period yawing motion just introduces a crabbing effect into the coverage but does not actually generate holes in the data. It is just the rapid rate of change of headings associated with the yaw in the ocean wave spectrum that is the problem.

Note also that the yaw example used here was only a +/-1 to 2 degree signal (characteristic of seastates 4 or less) and thus as the seastate worsens the anomalies would grow. For a vessel working in the open ocean up to seastate 6 the anomalies would probably be much more severe (depending specifically on the characteristic seakeeping of the particular vessel).

Figure 4a: 100m - 10knots - 150 degree swath - no yaw stabilisation

Figure 4b: 300m - 10knots - 150 degree swath - no yaw stabilisation

Figure 4c: 500m - 10knots - 150 degree swath - no yaw stabilisation

Figure 4d: 700m - 10knots - 150 degree swath - no yaw stabilisation

Figure 4e: 900m - 10knots - 150 degree swath - no yaw stabilisation

As you will note, the degradation of coverage due to yaw becomes worse with depth. This is because the inter ping period is becoming larger and approaching the worst case of being 0.5 times the wave period (or alternately 1.5 or 2.5 etc..). For this worst case, if the shot went off at the peak instantanteous yaw divergence from the mean track, the next shot will occur when the instantaneous yaw divergence is a maximum in the opposite direction.

As expected the peak in yaw distortion occurs in the 500-700m range as the ping period approaches half the wave period.

And if we run through the same series of depths using the 9-sector Yaw stabilisation method used by an EM300 we get the following series of results:

Figure 3a: 100m - 10knots - 150 degree swath - with yaw stabilisation

Figure 3a: 300m - 10knots - 150 degree swath - with yaw stabilisation

Figure 3a: 500m - 10knots - 150 degree swath - with yaw stabilisation

Figure 3a: 700m - 10knots - 150 degree swath - with yaw stabilisation

Figure 3a: 900m - 10knots - 150 degree swath - with yaw stabilisation

(the step-like artifact in the outer part of the swath is actually a integer roundoff error in the model, not a result of the real algorithm).

In general, I think this is a far improved result!. Yaw stabilisation becomes significant in water depths greater than about 300m. Note also however, that the multi-sector method allows improved pitch stabilisation also. The coverage loss due to imperfect pitch compensation does not change with water depth (in fact it gets more pronounced in shallower water where the effect of sonar compute time starts to noticeable slow down the ping rate). Thus 9 sector stabilisation is important in shallow water too (perhaps I should run off a series of simultations to show this also?).

But this is all a theoretical model. How well does it really work in practise?

Figure EX1a: data collected in 900m of water with yaw-stabilisation disabled

Figure EX1a: data collected in 900m of water with yaw-stabilisation enabled