We are currently witnessing the implementation of two types of navigation systems in AUVs (and some ROVs). The first incorporates a large number of instruments (redundant in some cases) to permit dead-reckoning navigation. The second is an integrated navigation system from the aviation market, often based on laser gyro technology.

The first type (dead-reckoning navigation) has an advantage in that it is relatively inexpensive, but its drawback is limited performance. The second type (the aeronautical navigation system) has the advantage of high performance, but has three substantial problems: very high cost, export difficulties, and unsuitability for underwater applications, which in turn requires further technical development in most cases.

In order to make AUV technology more competitive in terms of cost and performance, it was therefore imperative to develop a special inertial navigation system (INS) offering performance at least as good as that of the units manufactured for the aviation industry, and at much lower cost. This has been made possible thanks to so-called fiber optic gyroscope (FOG) technology.

Fiber Optic Gyroscopes
France's Ixsea SAS (formerly Photonetics) has been developing and manufacturing fiber optic gyroscopes for 15 years now, concentrating in recent years on marine and submarine applications. For example, the Octans, a unique combination of gyrocompass and motion sensor, was the first system based around FOG technology, and is now fitted in more than 150 surface vessels, ROVs and AUVs around the world.

In 2000, Ixsea developed an INS embodying the state-of-the-art in fiber optic technology and incorporating a Kalman filter specifically dedicated to AUV applications. This unit, known as the U-Phins, can be easily connected to a GPS, a Doppler velocity log, a depth sensor, and an acoustic positioning system (USBL or LBL).

Before describing the U-Phins unit, it is important to go back over the technology underlying all INS: the gyroscope. In the present instance, the technology developed at Ixsea is the fiber optic gyroscope.

FOG technology is based on the Sagnac effect, which is also used in laser gyros. The Sagnac effect occurs in ring interferometers. In the case of the FOG, such an interferometer is formed by a coil of optical fiber, into which light is injected at both ends.

It is possible to provide a straightforward (but incorrect from the physicist's point of view) explanation of this: When the coil begins to turn due to an external rotation, one of the two bursts of injected light (the one traveling in the same direction as the movement) is accelerated by the rotation, whereas the other (traveling in the opposite direction to the movement) is slowed by that same rotation.

In theory, this explanation is not satisfactory because the speed of light is identical in all reference systems, whether they are in movement or not, and it is necessary to use the Relativity theory developed by Einstein in the early 20th century if the Sagnac effect is to be explained satisfactorily.

In practice, the coil of optical fiber is associated with a large number of components embodying the current state-of-the-art in optoelectronic technology.

For example, the light source used by Ixsea derives from the all-optical amplifier technology (the relevant term here is Erbium Doped Fiber Amplifier, or EDFA) used for very high rate transoceanic transmissions, such as the optical cables linking Europe and the US.

Ixsea holds key FOG patents, and was focused from the outset on high performance capabilities to meet French Ministry of Defense, European Space Agency, NASA, and French Space Agency requirements. Since 1996, the company has developed and manufactured inertial systems for attitude control (the Octans range) and navigation (the Phins range). The FOGs used in the INS units in the Phins range offer performance levels typical of aeronautical gyro units. Ixsea also manufactures FOGs offering even higher performance for earth observation from satellites in orbit.

The advantages of this technology are high performance, total absence of moving parts (which in turn ensures good integrity in mechanically stressful environments), low power consumption, and price.

Inertial Navigation Systems
The key component of an inertial unit is the gyro. To understand this concept, we need to begin by explaining what an inertial navigation system actually is. In general terms, an INS comprises three components:

• An inertial measurement unit (IMU) formed by three gyros and three accelerometers. This is the "body" of the unit.
  
• A calculator allowing navigation parameters to be determined on the basis of the output provided by the IMU: attitude (heading, pitch and roll), speed, and position. This is the "brain" of the unit.
  
• A Kalman filter allowing navigation error to be "adjusted" with the help of external sensors. This is what might be called the "eye" of the unit.

As we shall see, inertial navigation is compromised by an error that grows over time, and this is why it is difficult to keep to a heading for very long with a blindfold. When we have our eyes open, navigation errors are corrected in real time, thanks to the images captured by our retinas.

The Importance of Gyros
In practice, an inertial navigation system determines position and attitude by integrating data from gyros and accelerometers. Of these two types of sensors, the gyro is the source of the largest errors.

This can be easily understood where attitude is concerned, and heading in particular. An integrated navigation unit determines the heading by measuring the speed of rotation of the earth. This means, in effect, that determining the heading comes down to finding geographical North, which is by definition the point at which the terrestrial axis of rotation meets the surface of the earth.

In order to measure the speed of rotation of the earth (360 degrees in roughly 24 hours, given a speed of 15 degrees per hour), we therefore need gyros, and the more accurate they are the more precise the heading indicated will be.

For example, with gyros accurate to 0.01 degree per hour (this is the case for the FOGs used in the Phins), the speed of rotation of the earth can be measured at the equator to an accuracy of 0.01/15 = 0.006 radians, or 0.03 degrees. This explanation also shows that a navigation unit does not drift where attitude is concerned (that is, error does not vary with time), but it does present an absolute level of uncertainty.

Where positioning accuracy is concerned, it may seem surprising that the accuracy provided by the gyros has more impact than that of the accelerometers, but it is nevertheless the case. This is due to the fact that navigation in fact occurs on a sphere, the earth. It will therefore be readily understood that traveling along a straight line on the earth comes down in fact to a rotation, and that rotation is detected by the gyros.

In practice, gyros are subject to a zero-error known as gyro bias: When there is no rotation, a gyro should indicate zero, but in fact measures something that is the bias value. When an inertial navigation system is immobile, the gyros measure bias values that are integrated by the calculator and the unit thinks that it is rotating, and therefore advancing across the surface of the terrestrial globe, which generates a position error. It will be understood that position error shows linear growth over time and there is a direct relationship between the accuracy of a gyro and position drift.

For example, by using a gyro accurate to 0.01 degree per hour, navigation error on the terrestrial surface grows at the speed of 0.01 degree per hour, or 0.6 arc minute per hour. Since an arc minute on the terrestrial globe is equivalent to one nautical mile, this therefore corresponds to position drift of 0.6 nautical mile per hour. This is known as "drift in pure inertial mode," and will allow an aircraft, for example, to travel for hours without need of external error adjustment.

The Kalman Filter
That being said, position drift can be easily reduced by observing the external world. An aircraft adjusts its position error when approaching an airport with the help of the air traffic controllers, who can determine its position using radar imagery.

The idea of observing the external world in order to adjust the whole range of errors can be applied in real time, thanks to what is called a Kalman filter. A Kalman filter permits optimum merging of data from a number of sensors that are independent of each other. For example, a position given by an inertial navigation system, plus a position given by a GPS unit, or one speed indicated by the inertial unit and another from a speed log.

In fact, the idea underlying a Kalman filter is to use comprehensive modeling of the way system errors change over time, the system being defined by a number of variables, which may be available externally or even hidden. These variables are called system states, which explains why we often talk in terms of the "number of states" of a Kalman filter.

For example, an inertial navigation system possesses states that are available and visible as output for the user: the three position errors, the three speed errors and the three attitude errors. But these nine errors (states) are in fact interlinked and due principally to errors in the sensors, in the present instance gyros and accelerometers (the six bias values of the six sensors, for example).

It is possible to describe changes over time in these errors by a set of interlinked differential equations, and it is therefore possible to anticipate errors at any given instant and to compare them with those deriving from external sensors. This comparison therefore allows the visible system states to be adjusted, along with the hidden states, making it possible to enhance the whole set of navigation data.

As an example, a Doppler velocity log is connected to an inertial navigation system via a Kalman filter. Comparison of information on vessel speed deriving both from the INS and the speed log will clearly make it possible to obtain an adjustment of speed drift, and therefore position drift. However, it also allows information to be obtained on the bias values of the gyros, and therefore to compensate for their error, thus enhancing the accuracy of the heading provided by the inertial unit.

There is another method of determining position using a "black box" system, which is the name given to dead-reckoning navigation, a system very familiar to sailors. If we constantly determine both heading and speed, it will be possible to determine our position by integrating the speed vector obtained by multiplying these two pieces of information. This is what is usually done in a treasure-hunt game. The paces are counted (speed integration) in a direction defined by a compass.

It is easy to see that the error in dead-reckoning navigation will grow, not with time, but with distance covered, which explains why it is always expressed as a percentage. This is because heading error leads to a lateral error in position, and speed error to a longitudinal error that grows linearly with increasing distance from the point of departure.

In the case of an INS, position error does not depend on distance but on time, and does not therefore depend on the speed of the vehicle carrying it. Another difference, by far the most important, is that an inertial navigation system can correct its hidden states using a Kalman filter. In the case of dead-reckoning navigation, a Kalman filter can also be used to correct the position, but this filter will not enable correction of the biases intrinsic to the sensors, since they are not modeled within the filter. In practice, assuming equal sensor performance, an INS will give much better results than dead-reckoning.

AUV Navigation
In the case of AUVs, navigation is usually based on dead-reckoning as described previously. It is therefore self-evident that the claimed performance, generally in the region of few tenths of a percent of the distance traveled, is poor when considered in relation to the demands of the types of mission entailed by AUV applications.

Some AUVs use navigation units derived from those employed in the aviation industry, but these units must be adapted for underwater applications, are very costly and difficult to export due to the fact that they were originally developed for military applications.

For these reasons, Ixsea developed the U-Phins navigation unit specifically for AUV applications, part of their Phins range of inertial navigation systems. The U-Phins unit incorporates three 0.01 degree per hour FOGs, three accelerometers, and a real-time calculator. It was designed to be as compact as possible and to consume little power (typically 12 Watts) to enable its integration into AUVs.

One of the key components of the U-Phins is its Kalman filter, developed by Ixsea. This filter enables the U-Phins to be connected to the sensors usually employed on an AUV and to adjust the unit's errors, thereby enhancing its performance in terms of position, speed and attitude. A Doppler Velocity Log enables measurement of vessel speed with high accuracy when the seabed is detected. A depth sensor allows adjustment of depth error. A GPS enables initialization of the navigation unit at the surface. And a USBL acoustic positioning system allows adjustment of the unit when the AUV dives.

One of the advantages of the U-Phins is that its Kalman filter is preprogrammed using a complete library of standard equipment. It is not therefore necessary to configure the unit, but simply "tell" it which brands and models of equipment are connected.

Naturally, the performance offered by the navigation unit will depend on the type of equipment connected and the mission history. A typical AUV mission is generally a survey mission at seabed level. This survey mission usually consists of a square site survey based on a number of parallel lines equally spaced in each direction.
Typical AUV Mission

Phins performance can be predicted during a "typical" survey mission, with the following error models used for the external sensors:

• DVL white noise 0.00325m per second standard deviation.
  
• DVL misalignment 0.2 degree maximum modeled as a random constant.
  
• DVL scale factor 0.2 percent maximum modeled as a first order Markov process.
  
• USBL ± 0.5 percent of depth white noise error.
  
• DGPS ± 10m CEP 95 white noise error.

When it reaches the seabed, the AUV receives DVL information with 0.00325m per second standard deviation. Using these data it performs a 10-minute calibration circuit. Finally, the AUV begins the square survey site trajectory using the Doppler log alone.

Concerning the square 1km x 1km site survey area, each line is separated from the next by 100 meters and the total course of the AUV during this survey is approximately 29km, including the dive to 6,560 feet (2,000m), the calibration turn and the square survey itself. The total survey time is over five hours.

The survey can be divided into five stages: five minutes of convergence, five minutes of DGPS assistance, 25 minutes of diving with USBL, eight minutes of calibration turn with Doppler Log, and four hours and 40 minutes of actual survey time using a Doppler Log.

The growth of the position error during the survey is linear in first approximation. The slope of the position error curve is 2.5m per hour. The linear error is due mainly to the difficulty of evaluating speed log misalignment and scale factor.

The maximum position error during the mission is 10m, which corresponds to 0.03 percent of the total survey distance. This figure has to be compared to usual errors in the range of 0.1 to one percent.

Moreover, according to the previous result, it seems that the principal sources of error are speed log misalignment and log varying scale factor. Assuming log misalignment to be null, a simulation can show that the error standard deviation at the end of the survey would have been 4m.

Ixsea has been working on an automatic alignment procedure intended to ensure perfect alignment of the two instruments. Regardless, U-Phins is the state of the art where this technology is concerned and is significantly less expensive than units used in aircraft, which were developed for radically different applications. U-Phins is already used in a number of AUVs, and its presence in the underwater industry continues to grow. UW