One nautical mile per month fog-based strapdown inertial navigation system: A dream already within reach?

ISSN 2075�1087, Gyroscopy and Navigation, 2014, Vol. 5, No. 1, pp. 1–8. © Pleiades Publishing, Ltd., 2014.Published in Giroskopiya i Navigatsiya, 2013, No. 3, pp. 3–13.

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11. INTRODUCTION

Until now, iXBlue FOG design has always beenable to provide better performance when we tried tosolve the known technological imperfections. iXBluenever found (yet?) any physical limit to improvementof FOG performance. Therefore, with its will of con�tinuous enhancement of performance/cost ratio,iXBlue decided to investigate the capability of FOGtechnology for extremely high performance strapdownnavigation systems. This paper describes results of onestep of this investigation and analyses what furthersteps would be necessary. As a goal and to use roundfigures, we set tests for 1 nautical mile position accu�racy over one month navigation duration.

This level of accuracy requires extremely high per�formance sensors and so far no strapdown technologysucceeded in reaching such accuracy.

2. SENSORS REQUIREMENTS

In an inertial navigation system, most of the sensorerrors generate oscillating navigation errors. Oscilla�tion periods are 84 minutes (known as the Schulerperiod) and 24 hours (the Earth period). Gyro bias

1 The article is published in the original.

along East axis creates, for example, a 24 hour oscillat�ing sine error on latitude and a 24 hour oscillatingcosine error on longitude. Accelerometer bias creates84 minutes error oscillations on latitude and longi�tude. All these oscillating navigation errors are there�fore bound.

However, there is one type of error that creates anunbound longitude error: Earth rotation rate measure�ment error. Such measurement error is due to the biascomponent along earth rotation axis or scale factorerror on the 15.041 degrees per hour rate measure�ment. Figure 1 shows typical latitude error on an iner�tial navigation error. We can see the 24 hour period andthe superimposed 84 minute period.

Figure 2 shows typical longitude error as a functionof time over 60 hours. It can be seen that there is an84 minute oscillating period, a 24 hour period and lin�ear drift. This linear drift leads to unbound longitudeerror.

So the above means that the most importantparameter for long term inertial navigation is gyrobias. Obviously in such a high accuracy navigation sys�tem, all sensor parameters must be under severe con�trol, but gyro bias is the one that must be at the highestlevel.

One Nautical Mile per Month FOG�Based Strapdown Inertial Navigation System: A Dream Already within Reach?1

Y. Paturel, J. Honthaas, H. Lefèvre, and F. NapolitanoiXBlue, Marly le Roi, France

Received May 2, 2013

Abstract—In 2006, we presented at DGON symposium in Stuttgart [2] the design and navigation results ofMARINS, the first FOG�based navigation system within the class of 1 nautical mile per day. This navigationsystem in now in production and has been delivered to numerous navies. Today we are challenged by even better performance and the question is: have we reached the limits of thetechnology or can we still improve the performance of our sensors? One nautical mile in a month means a biasstability of 2 × 10–5 degrees per hour! It may look foolish for a strapdown system with a dynamic range of atleast 100 degrees per second. However, based on tests results, we provide evidence showing that FOG is theright technology to build a fully strapdown INS of this class. In particular we present:• Noise improvement.• Very long term pure inertial navigation (several weeks) of a FOG�based system with temperature controlledenvironment.Of course, the present FOG design is not good enough for the required performance, even in a strictly con�trolled environment. The first way to go about this is obviously to increase the geometry factor (and thereforesensitivity) by increasing both diameter and length of the fiber coils, but this will not be sufficient. It will benecessary to improve detection noise, to control more accurately the light source wavelength, to reduce tem�perature gradient… Clearly there are difficulties on the way to a FOG�based strapdown system able to navi�gate with an accuracy of 1 nautical mile over several weeks; however, we show that FOG technology has notreached its ultimate potential yet and that the dream of even higher performance is within reach.

DOI: 10.1134/S207510871401009X

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GYROSCOPY AND NAVIGATION Vol. 5 No. 1 2014

PATUREL et al.

For a one nautical mile per month navigation per�formance gyro bias must remain below 2 × 10–5 degreeper hour. But also, the scale factor error on Earth ratemeasurement must not generate an error larger than2 × 10⎯5 degree per hour. Therefore the scale factorerror of gyros must be within 1 ppm performancerange.

In order to get the best performance during longterm navigation without aiding, it is useful to estimategyro biases and accelerometer biases during alignmentphase. During this alignment phase, position aiding(satellite positioning systems (GNSS)) is available and

this estimation is possible. In order to minimize thealignment time, it is necessary that noise on gyro sen�sors be as low as possible. If we want noise influence tobe within the required bias accuracy (2 × 10–5 deg/h)in one hour, angular random walk must be less than 2 ×

10–5 deg/ .

3. PREVIOUS TECHNOLOGIES FOR SUCH ACCURACY

So far, navigation systems for this class of perfor�mance have used the following technologies:

√h

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Fig. 1. Latitude vs. time (pure inertial mode).

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Fig. 2. Longitude vs. time (pure inertial mode).


ONE NAUTICAL MILE PER MONTH 3

• Electrically Suspended Gyro (ESG): gimbaledplatforms using ESG. The performance of this gyro isexcellent. But it is very complex. It uses a spinningberyllium sphere supported by electrical field in vac�uum. The number of complex mechanical and electri�cal parts and the gimbaled architecture make this sys�tem very expensive and not as reliable as necessary.

• Carouseling of Ring Laser Gyro IMU: a RLGIMU is mounted on 2�axis carousel. This slewingmethod allows reducing gyro and accelerometer biaseffect by averaging each axis to be pointing in all direc�tions for an equal amount of time. This techniqueleads to very good long term navigation performancebut has some drawbacks on accuracy and noise of rolland pitch and accuracy of instantaneous velocity.

These two products are not real strapdown systems,since both use gimbals.

4. WHY IS FOG TECHNOLOGY A GOOD CANDIDATE FOR SUCH A STRAPDOWN

NAVIGATION SYSTEM?

For space applications, our partner EADS�Astrium compared results of Allan variance measure�ments over a long period of time for different gyrotechnologies: Hemispheric Resonating Gyro (HRG),Ring Laser Gyro (RLG) and Fiber�Optic Gyro(FOG) (ASTRIX 120 and ASTRIX 200, two differentFOG products).

These measurements were performed by EADS�Astrium for internal purpose. This study was not pub�lished but results were shared with iXBlue. They mea�sured the Allan variance up to 300 hours for gyrosplaced in a temperature controlled environment.

HRG reaches a minimum bias stability of 1.5 ×10⎯3 deg/h after 10 hours while RLG reaches 2 ×10⎯3 deg/h after 60 hours. Both FOG models did notreach a minimum value after 300 hours. A FOG with200 mm diameter coil provided standard deviation of4 × 10–5 deg/√h after averaging of 300 hours, withoutreaching yet a minimum value.

Angular random walk on FOG technology reaches2 × 10–4 deg/√h while RLG noise is 4 × 10–3 deg/√h.

These long�term Allan variance measurementshave given iXBlue confidence for long term navigationperformance using FOG technology.

5. TECHNICAL CHALLENGES

The two first parameters that we wanted to improveor check on FOG technology are noise reduction andlong term bias stability.

5.1. Noise Reduction

iXBlue FOG 200, used in the satellite navigationsystems has a noise performance of 2 × 10–4 deg/√h. Asdiscussed above, we want to achieve a goal ten times

better. We started analyzing the influence of differenttypes of noise in FOG technology.

5.1.1. FOG Modulation

As extensively described in literature, the interfer�ence signal from a FOG is a cosine function. Since thisfunction has no sensitivity around zero and does notdifferentiate rotation sign, a square�wave modulationis applied to the FOG signal. This biased signal is thenmeasured by demodulating the detector signal. Thesignal becomes therefore a sine wave function of thephase shift between the two contra�propagating opti�cal beams.

5.1.2. Noise Sources

(a) Shot Noise

Shot noise is due to the particle nature of light: it isproportional to the square root of the actual power.Figure 6 shows:

• The signal, a sine function of the modulationdepth (or the phase shift).

• The actual optical power on detector, cosinefunction of modulation depth (or the phase shift).

• The shot noise, proportional to square root ofpower.

• The noise to signal ratio, which is therefore pro�portional to 1/√P.

• The noise to signal ratio decreases as the modu�lation depth increases.

Shot noise is the ultimate theoretical noise reduc�tion limit.

(b) Relative Intensity Noise (RIN)

This noise is due to the light source width which isnecessary for “destroying” the parasitic coherent

Fig. 3. Electrically Suspended Gyro.

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PATUREL et al.

effects, but the source width creates beats between thedifferent pulses within the source spectrum.

RIN is proportional to the actual power P. This iswhy power curve and noise curve are superimposed onFig. 7.

The Noise to Signal ratio is therefore independentfrom power. It decreases deeply when modulationdepth increases and reaches zero when modulationdepth is �. However, signal is also zero, which makesmeasurement very complicated!

Relative Intensity Noise is, in practice, the noisethat limits mostly FOG noise performance.

(c) Thermal Noise

This noise is due to the resistance of the transim�pedance: the power detector provides current intensityproportional to optical power. In order to be mea�sured, this intensity must be transformed into voltageusing a resistor. The thermal agitation of the electronsgenerates the thermal noise. Thermal noise is inde�pendent from the actual power P.

The Noise to Signal ratio is therefore proportionalto 1/P. It can be seen on Fig. 8 that noise to signal ratiois minimal for modulation depth π/2 and that itincreases when modulation depth is larger than π/2.

(d) Other Noise Sources

The three noise sources described above are intrin�sic to the Fiber�Optic Gyro. They do not come fromimperfections of the manufacturing but from physics.There are other sources of noise inside the FOG andthey come from optical imperfections or from elec�

Fig. 4. Allan variance comparison.

Interference signal

Detector signal

Sagnaceffect

Digital biasingmodulation ateigenfrequency

t

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Fig. 5. Square�wave biasing modulation.

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Allan Variance

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tronics. These other sources can be reduced by a betterdesign or a better manufacturing process.

5.1.3. Optimization of Global Noise

We have seen above that noise to signal ratiodecreases for shot noise and RIN and increases forthermal noise when modulation depth is over π/2.Therefore it is clear that it is possible to optimize noiselevel by selecting carefully modulation depth.

Hence, we tried to optimize:• the light power generated by the light source,• the power coming back to the detector,• the modulation depth,

• the reduction of other noise sources in the elec�tronics,

• the parasitic reflections inside the optical path.

With such an optimization, we have reached0.13 μrd/√Hz with a light source power of 160 μW asthe phase noise. This phase noise translates into angu�lar random walk on the FOG according to the FOGsensitivity (depending on length of fiber and mean coildiameter).

For a FOG 120 (about 1 km of fiber), this phasenoise is equivalent to 3.4 × 10–4 deg/√h.

For a FOG 200 (several km of fiber), this phasenoise is equivalent to 7 × 10–5 deg/√h.

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Power

Shot noise

Signal

Noise toSignal ratio

Fig. 6. Shot noise.

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Fig. 7. Relative Intensity Noise.

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It can be seen on Fig. 9 the noise improvementusing the same coil but with optimized parameters.Noise is improved by a threefold factor.

5.2. Long Term Bias Stability

In order to measure what is the potential long termnavigation capability of our sensors, we tested a mod�ified version of our highest performance navigationsystem. The test that was performed was performed ona navigation system and Inertial Measurements datawere not logged. Nevertheless, it was possible toobserve gyroscopes bias stability through latitude andlongitude drift over long period of time. In particular,

the linear drift of longitude provides a good estimate ofthe gyro bias stability.

This demonstrator unit has been mounted in anoven where the temperature was stabilized at 40°C.The accuracy of temperature stabilization is about0.2°C. After a two position alignment phase in order tomeasure accelerometers and gyroscopes biases usingthe navigation Kalman filter, we let the system navi�gate in pure inertial mode during 38 days. Results ofthis navigation on latitude and longitude are shown onFigs. 10 and 11.

On latitude, it can be noticed that there is abso�lutely no linear drift component. The Schuler periodmodulates the 24 hour period. This corresponds to the

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Thermal noise

Signal


Fig. 8. Thermal noise.

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Fig. 9. Noise reduction on same coil.



theory, when gyro and accelerometer biases are stableover time.

On longitude, one can also see the 24�hour and the84�minute oscillation components. A linear driftoccurs, as also expected from theory. This linear driftis less than 0.4 nautical miles over 38 days, which is lessthan 0.01 nautical miles or 18 meters per day! It isequivalent to linear drift of 550 meters per month.

This longitude linear drift is equivalent to less than4.7 × 10–6 degree per hour. This result is absolutelyexcellent for two reasons:

• it means that during alignment phase, the gyrobiases were measured extremely accurately, at leastwithin this very same accuracy (4.7 × 10–6 degree perhour),

• the bias stability since the alignment is alsowithin this accuracy range.

No specific improvements were done on the FOGfor bias stability improvements. The present design isperforming so well that bias is extremely stable overtime. Only remaining sensitivity could be then tem�perature dependant.

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Fig. 10. Latitude error vs. time.

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Fig. 11. Longitude error vs. time.

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It can be seen that the overall error includingSchuler and 24�hour period oscillations is close to±1 nautical mile over the whole 38�day duration.

6. WHAT REMAINS TO BE DONE?

The above results are very encouraging. We havedemonstrated that:

• under some favorable conditions, our demon�strator unit long term navigation accuracy is muchbetter than 1 nautical mile per month,

• gyro noise and algorithm performance enablegyro biases to be measured with great accuracy duringalignment.

However, it would be foolish to consider that wehave already reached our goal (or our dream, as thepaper title may suggest). It is clear that these results areobtained in very stable temperature conditions and instatic mode.

So we need to improve some features of our sensors:• Gyro angular random walk: we do have to gain

another 3�fold factor on ARW, in order to reduce thealignment time. For this purpose we are working oninnovative solution to further reduce the RIN. At thesame time, in order to increase light power at thedetector level, we are working on improvement on thePM coil fiber itself to further reduce its attenuationmaking 10 km long coils usable: this development isperformed by iXFiber, an iXBlue company.

• Gyro bias stability: • Geometry factor: increase the L × D (fiber

length × coil dia.).• Temperature control accuracy must be suffi�

ciently easy to implement: reduction of temperaturesensitivity of FOGs: winding method, …

• IOC: further improvement of polarization rejec�tion with Photline, an iXBlue partner.

• Scale factor: we have to gain one order of magni�tude.

• To be honest, this is the parameter on whichFOG has some drawbacks with respect to RLG. Nev�ertheless, linearity is already 1 ppm, which is the proofof the performance of the processing electronics.

• Present 10 ppm stability is obtained with simpletemperature modeling but there are solutions for bet�ter control of the geometrical stability of the coil andimproved mean wavelength stability of the lightsource.

7. CONCLUSIONS

The dream for a strapdown navigation system withone�nautical mile accuracy over one month has notyet come true. But we think that we have demonstratedthat it is be possible using Fiber�Optic Gyro technol�ogy. There are clearly some improvements to be imple�mented in iXBlue products for reaching such accuracy,but in static mode it has been demonstrated bias esti�mation accuracy and bias stability over 38 days betterthan 4.7 × 10–6 degree per hour.

Such bias accuracy is equivalent to 4 degrees percentury! Maybe this new unit will become standard inthe future for high precision navigation systems.

REFERENCES

1. Post, E.J., Sagnac effect, Review of Modern Physics,1967, vol. 39, pp. 475⎯494.

2. Arditty, H.J., Graindorge, P., Lefèvre, H.C., Martin, P.,Morisse, J., and Simonpiétri, P., Fiber�Optic Gyro�scope with All�Digital Processing, OFS 6, Springer�Verlag Proceedings in Physics, 1989, pp. 131⎯136.

3. 30th FOG Anniversary Session, OFS 18 Conference,Cancun, 2006

4. Aronowitz, F., Fundamentals of the Ring LaserGyro, Optical Gyros and their Application, RTOAGARDograph 339, 1999, pp. 3�1⎯3�45.

5. Rozelle, D.M., The Hemispherical Resonator Gyro:from Wineglass to the Planets, Proceedings of the19th AAS/AIAA Space Flight Mechanics Meeting, 2009,pp. 1157⎯1178.

6. Lefèvre, H., The Fiber�Optic Gyroscope, Boston−Lon�don: Artech House, 1992.

7. Savage, P.G., Strapdown Analytics, Maple Plain: Strap�down Associates, 2007.

8. Paturel, Y., et al., MARINS, the First FOG NavigationSystem for Submarines, Proceedings of Symposium GyroTechnology, 2006.

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One nautical mile per month fog-based strapdown inertial navigation system: A dream already within reach?