Giroux, Richard
(2004).
*Capteurs bas de gamme et systèmes de navigation inertielle : nouveaux paradigmes d'application.*
Thèse de doctorat électronique, Montréal, École de technologie supérieure.

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## Résumé

L'objectif global de la thèse concerne l'utilisation des capteurs bas de gamme dans les systèmes de navigation inertielle. Les véhicules terrestres possédant une faible dynamique constituent le cadre de développement des algorithmes.

Premièrement, un nouveau modèle d'erreur pour l'intégration des SNI a été développé en utilisant une démarche claire. Le modèle générique en découlant est de nature non-linéaire, où aucune hypothèse d'approximation est impliquée. Comparativement au modèle linéaire, le modèle non-linéaire permet une convergence de l'erreur d'azimut beaucoup plus rapide. Cet aspect est important surtout lorsque la dynamique du véhicule est lente, d'où une faible observabilité de l'erreur d'azimut.

Deuxièmement, il est prouvé dans cette thèse que pour un nombre de capteurs donné, le placement orthogonal de capteurs est également optimal et équivalent au placement non-orthogonal de ces capteurs, lorsque l'on optimise le volume d'information disponible au système. De plus, en prenant en ligne de compte la complexité de la structure, et la diminution des coûts des capteurs, l'approche de redondance orthogonale devient économiquement intéressante.

D'un autre côté, la calibration en-ligne des capteurs bas de gamme est nécessaire à cause de la grande variabilité des erreurs des capteurs bas de gamme. Deux structures d'identification ont été implantées: une première où les erreurs résultantes sur les axes du repère mobile sont identifiées; et une deuxième dite indirecte avec mesure du vecteur de parité, où les erreurs des capteurs sont spécifiquement identifiées. Cette deuxième structure s'avère nécessaire si un algorithme de détection et d'isolation de fautes est implanté.

L'intérêt et le marché pour les SNI bas de gamme sont vastes et prometteurs. Les contributions élaborées dans cette thèse ajoutent une pièce supplémentaire dans le concert de la recherche mondiale qui permettra d'intégrer de façon efficace les capteurs bas de gamme dans des systèmes de navigation inertielle à bas coût hybridés avec un récepteur GNSS.

## Résumé traduit

The exploration of the world has always relied on navigation breakthroughs. From the Polynesian experimental voyaging by use of sea landmarks and stars, to borderless space exploration, techniques of positioning were and still are of primary importance. Radio-navigation started around the beginning of the 20th century, as onboard sea ship dock bias was estimated with a standard clock reading sent from the nearby coast by wireless transmission, discovered earlier by Marconi. The Germans were first to successfully demonstrate the use of gyroscopes as a means of guidance for their V2 missiles. By doing so, they have paved the way to what has been called stabilized-platform Inertial Navigation System (INS), designed by Charles S. Draper and his team of the Instrumentation Laboratory (now called the Charles Stark Draper Laboratory, Inc.) at the MIT.

Stabilized-platform INS is a mechanical moving structure, implying significant costs in maintenance and overhaul. The advent of numerical computers has changed the way INS is implemented. Instead of having a mechanized moving platform ensuring a known orientation of the sensor frame, the orientation could then be virtually computed. Hence, it allowed the sensors to be fixed to the vehicle frame, which led to the name: Strap-down INS. Despite its attractive advantages (no external moving parts, cheaper and operational under any kind of trajectory), this new configuration soon showed its constraints : errors in the navigation solution were tightly coupled with the dynamics of the vehicle and were more sensitive to internal errors of the sensors (bias, drift, etc.). To cope with these problems, the Strap-down INS solution is combined with an external navigation aid. The Global Positioning System (GPS) is the most well-known navigation aid these days, whereas it was fully operational only in 1996. However, GPS is not a perfect system. lts main problems reside in its availability, its integrity and its risk of being jammed. Consequently, any applications requiring continuous updates of position will need to merge both systems.

During the late 80's and 90's, the integration of Strap-down INS and GPS (or other kind of navigation aid) was well established. However, the choice of sensors was limited to varying grades of quality depending on the application. For precise navigation, the use of expensive sensors was mandatory, which restricted the application of INS mainly to the military sector (airplanes, submarines, missiles) and for the mass transportation civilian airplanes.

Standard implementation of INS

The implementation of a standard INS is done in two steps. First, the solution of the rigid body equations of motion in a rotating frame is computed to give inertial position, velocity and attitude information, based on accelerometer and rate gyros measurements. However, inherent sensor errors cause position and velocity inaccuracies to build up in the inertial solution. To cope with this misleading information, an error model is used. The error model is deducted from the equations of motion and the sensor errors, the latest being composed of bias, drift, random bias, and any other relevant error sources. The GPS is then used to compute the error, based on the GPS position and velocity information, and serve as the measurement vector for the Kalman filter. Finally, the estimated error from the Kalman filter solution is subtracted from the inertial solution to improve position, velocity and attitude information.

Low-cost sensors

A novel sensor design technique has brought to the market cheap and interestingly performing sensors. Indeed, from the classical macroscopic mechanical design and the microscopic integrated circuit fabrication technology emerged Micro-Electro-Mechanical Systems (MEMS). The first commercially-available MEMS sensor was the ADXL202, of Analog Devices Inc., which came on the market at the beginning of the 90's. This accelerometer was designed to be part of automotive air bags. Since that time, many improvements have enhanced the capabilities of those MEMS sensors and many other kinds of sensor have appeared. Also, because of the batch process nature of the fabrication technique, the cost of a single sensor is dramatically reduced. Then, a mosaic of yet-to-mature applications has seen a huge opportunity to improve their potential. Navigation systems are of course part of this challenge.

As one might expect, the impact of a new major technology implies a change of paradigm. The Strap-down INS was made possible due to the breakthrough of numerical computers because more complex algorithms (like the Kalman filter) have to be implemented to compensate for the deterioration in performance of the inertial sensors used ( compared to the ones used in the platform version). So, the performance of Strap-down INS is due to the use of more sophisticated algorithms compared to the Stabilized-platform INS. Hence, it is expected that the use of MEMS sensors in INS will imply a similar increase in complexity and innovation.

First, errors from low-cost sensors make them less suitable for using the standard linear error model for the Kalman filter. Also, low-cost rate gyros cannot sense the earth rate, which is a way of initializing the heading of the vehicle.

On another hand, the small size and low cost of these sensors make them suitable for using many of them, implying redundancy of measurements. Hence, the old paradigm where the minimisation of the number of sensors that performs a fault detection and isolation task can be challenged. In theory, redundant measurements of the same signal will give a better estimation of the real signal. However, due to the level of errors in low-cost sensors, and especially the "turn-on to turn-on" or slowly varying ones, it is not clear how redundancy can improve the solution in low-cost systems.

So, from all the areas of research in this field, two specific ones have not been thoroughly looked at in the literature, and are analyzed in this thesis : non-linear error model and redundancy of low-cost sensors. The algorithms that will be developed are applied to terrestrial vehicles with low dynamics.

Non-linear error model

Few researchers have investigated the area of error models applied to low-cost systems, where the heading error cannot be statically estimated. Hence, the heading error at the start of the navigation phase might be big enough so that the hypothesis of small error in the Kalman filter is no longer valid. The models developed so far addressed only this issue, and are based on the extension of the linear error model.

The error model developed in this thesis is based on a clear and sound demonstration. A generic non-linear error model is constructed, where no approximation hypothesis are used. Then, the model is compared to the known error models, and is proved to be equivalent under their respective hypothesis.

Compared to the linear error model, the rate of convergence of the heading error for the nonlinear error model is much better. This fact is very important when used with a low

dynamic vehicle or equivalently when following a trajectory that has poor dynamics. However, for the general navigation phase, the use of the non-linear error model does not seem to improve the overall performance.

The real-time implementation of the non-linear model is feasible, although it necessitates more computational power than its linear counterpart.

Redundancy analysis of Iow-cost sensors

lt seems logical to think that many measurements of the same signal lead to a better estimation of that signal, and this implies a better overall performance of the system. At first, redundancy was used for fault detection and isolation. While maintaining the ability of isolating a fault, the number of redundant sensors was minimized to reduce the cost of the system. Hence, a complex non-orthogonal structure of sensors was used.

lt is shown in this thesis that an orthogonal redundant structure has the same amount of information than its skewed counterpart with the same number of sensors, and is still optimal. Indeed, for fault detection and isolation, the number of sensors in the orthogonal configuration increases (especially for the worst case scenario). However, taking into account the complexity of mechanical structure, and the decrease in sensor cost, it is shown that the orthogonal structure of redundant sensors is effective.

However, the average effect of redundant measurements is cancelled by deterministic errors. Hence, in addition to the calibration of the sensors prior to their use in the field, an on-line calibration has to be performed (at least for low-cost sensors). Two approaches for on-line identification have been proposed: one where only the resulting error on the axes of the body frame are identified; and a second one, where each sensor error is identified, using the parity vector of the measurements. The first method is applicable only to obtain the average effect of redundant measurements. When fault detection and isolation is needed, the second method has to be used to minimise false alarms created by sensor errors (that are not faults).

A third approach has been investigated, although the results are not conclusive. It uses a direct version of the Kalman filter, where the integration of the equation of motion, along with sensor measurements, are integrated in the Kalman filter model, instead of the error model. The theory and preliminary results are shown in an appendix.

The real-time implementation of these approaches has been verified. The indirect redundancy with parity vector measurements is more demanding than the estimation of the resulting error on the body frame. If more than 9 sensors (3 per axis) are used, an upgrade in the embedded computer used in this thesis should be required, since the computation burden is a function of the number of sensors. The real-time computation effort for the standard redundancy is not a function of the number of sensors and is easily implemented.

Development tools

In order to simulate, test and validate the algorithms presented in the thesis, a generic simulator has been designed in the Simulink environment. It can be used to simulate any desired trajectory, or post-process real inertial data.

The Simulink environment has been chosen because it permits real-time testing through its fast-prototyping capability. This approach has been used to gather real-time inertial data from a redundant inertial measurement unit designed during the thesis and has greatly fast-tracked the design process.

Experimental setup

To obtain real inertial data, an inertial measurement unit has been overhaul. This unit is composed of four accelerometers and four gyros, placed on the sides of a tetrahedron. These sensors are not typical low-cost sensors (average unit cost of 1500$ CND), but still are of commercial accuracy. The acquisition board has been bought off-the-shelf and is based on the PC104 standard for embedded computers. The vehicle used to gather the data is a utility vehicle. Hence, the developed algorithms will be applied to terrestrial vehicle navigation with low dynamics.

Contributions

The main scientific/technical contributions brought by this thesis can be summarized as following:

• Derivation of a generic non-linear model for the propagation of INS solution errors (NL error model);

• Proof of equivalency between the NL error model and known linear error models under their respective assumptions (usually the small error assumption);

• Qualitative and quantitative comparison between orthogonal and non-orthogonal redundancy, and proof that both structure are optimal;

• Study of redundant sensor error identification, which is crucial for sensor fault detection and isolation of low-cost sensors;

• Design of an INS simulator based on Simulink and its performance assessment;

• Heuristic proof of the equivalency between high-order integration method and the standard two-stage integration method introduced by Savage;

• Overhaul of a skewed-redundant inertial measurement unit;

• Implementation of a fast-prototyping approach for the design of INS algorithms.

Growing areas of application

Low-cost sensors modify the way INS was designed in two areas : the error model and the redundancy management. lt has been theoretically proven and results show in this thesis that these sensors imply changes in the integration of inertial systems. The original contributions of this thesis are part of a global effort to efficiently integrate low-cost sensors in inertial systems fused with GPS.

As it happens quite often, a technology breakthrough creates a demand, and this demand stimulates the research and technology development and so on. Low-cost sensors applied to navigation systems have opened a broad perspective of applications, and new applications have emerged that require the development of better technology and algorithms.

Type de document: | Mémoire ou thèse (Thèse de doctorat électronique) |
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Renseignements supplémentaires: | "Thèse présentée à l'École de technologie supérieure comme exigence partielle à l'obtention du doctorat en génie". Bibliogr.: f. [235]-242. |

Mots-clés libres: | Algorithme, Application, Bas, Capteur, Erreur, Gamme, GPS, Inertiel, Lineaire, Modele, Navigation, Non, Non-Lineaire, Redondance, SNI, Systeme |

Directeur de mémoire/thèse: | Directeur de mémoire/thèse Landry, René Jr. |

Codirecteur: | Codirecteur Gourdeau, Richard |

Programme: | Doctorat en génie > Génie |

Date de dépôt: | 26 avr. 2011 15:48 |

Dernière modification: | 21 oct. 2016 01:04 |

URI: | https://espace.etsmtl.ca/id/eprint/701 |

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