modern inertial sensors and systems pdf

Modern inertial sensors and systems pdf

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1. Introduction

Inertial sensors technologies for navigation applications: state of the art and future trends

Modern Inertial Technology - Ebook

Automatic navigation makes ocean-going and flying safer and less expensive: Safer because machines are tireless and always vigilant; inexpensive because it does not use human navigators who are, unavoidably, highly trained and thus expensive people. What is more, unmanned deep space travel would be impossible without automatic navigation.


1. Introduction

Metrics details. Inertial navigation represents a unique method of navigation, in which there is no dependency on external sources of information. As opposed to other position fixing navigation techniques, inertial navigation performs the navigation in a relative sense with respect to the initial navigation state of the moving platform. Hence, inertial navigation systems are not prone to jamming, or spoofing.

Inertial navigation systems have developed vastly, from their occurrence in the s up to date. The accuracy of the inertial sensors has improved over time, making inertial sensors sufficient in terms of size, weight, cost, and accuracy for navigation and guidance applications. Within the past few years, inertial sensors have developed from being purely mechanical into incorporating various technologies and taking advantage of numerous physical phenomena, from which the dynamic forces exerted on a moving body could be computed accurately.

Besides, the evolution of inertial navigation scheme involved the evolution from stable-platform inertial navigation system, which were mechanically complicated, to computationally demanding strap-down inertial navigation systems.

Optical sensory technologies have provided highly accurate inertial sensors, at smaller sizes. Besides, the vibratory inertial navigation technologies enabled the production of Micro-electro-machined inertial sensors that are extremely low-cost, and offer extremely low size, weight and power consumption, making them suitable for a wide range of day-to-day navigation applications. Recently, advanced inertial sensor technologies have been introduced to the industry such as nuclear magnetic resonance technology, cold-atom technology, and the re-introduction of fluid-based inertial sensors.

On another note, inertial sensor errors constitute a huge research aspect in which it is intended for inertial sensors to reach level in which they could operate for substantially long operation times in the absence of updates from aiding sensors, which would be a huge leap. Inertial sensors error modeling techniques have been developing rapidly trying to ensure higher levels of navigation accuracy using lower-cost inertial sensors.

Besides, this review covers a brief overview on the inertial error modeling techniques used to enhance the performance of low-cost sensors.

The state of motion of any moving platform could be determined through a process known as Navigation. Whereas, navigation is done by determining the navigation states of the moving platform. The navigation states represent the position, velocity, and orientation of the platform in either two-dimensional 2-D or three-dimensional 3-D space [ 1 ]. Navigation techniques are classified into two major categories. Namely, position fixing and dead reckoning.

Position fixing is performed by determining the navigation states with respect to a set of well-known positions. An example of position fixing technique is the global navigation satellite systems GNSS.

On the other hand, dead reckoning determines the navigation states of a moving platform by measuring recursively the progression of such navigation states with respect to their initial values. Inertial navigation is an example of the dead reckoning navigation technique [ 1 ].

The need for dead-reckoning navigation arises from the limitations of typical position fixing techniques which require a direct line of sight between the platform, to be navigated, and the well-known fixed positions. To clarify, navigation using GNSS requires a direct line of sight between the GNSS receiver and at least four satellites to acquire the navigation states of the navigated platform. Such condition is not usually met practically, especially when navigation takes place in urban or indoor environments.

Consequently, GNSS-denied environments require the use of dead-reckoning, especially inertial navigation, to provide a navigation solution for periods in which position fixing solution is not possible [ 2 ]. Hence, inertial sensors emerge. Inertial sensors are classified into two main categories: accelerometers and gyroscopes.

Broadly, accelerometers measure specific forces or accelerations, while, gyroscopes measure angular velocities. When fitted into specific geometric forms that guarantees capturing the motion of any given platform, the inertial sensors assembly is referred to as an inertial measurement unit IMU. Whereas, IMUs are usually coupled with some form of basic on-board data processing to convert the raw measurements to sensible specific forces or angular velocities.

A typical IMU comprises a triad of accelerometers and a triad of gyroscopes mounted along three mutually orthogonal axis to capture the 3-D motion of any given platform to which it is mounted.

Nevertheless, inertial navigation is done by processing the inertial measurements that are acquired from IMUs. The inertial measurements are mathematically reduced into variations in position, velocity, and orientation for the moving platform.

Consequently, the navigation states could be accumulated over time to identify the position, velocity, and orientation of the platform at any given instant. Therefore, a system that utilizes the measurements of IMUs to acquire the navigation states of any moving platform to which it is mounted is known as an inertial navigation system INS. An INS is a system that would include an IMU along with some means to process the inertial measurements into a full navigation solution.

Inertial sensors suffer from errors, which are either systematic errors or random errors. Systematic errors can be modeled mathematically and can be mitigated through calibration. Systematic errors, in inertial sensors, include biases scale factor, scale-factor non-linearity, and cross-coupling of sensitive axes measurements.

A bias in an inertial sensor is a constant shift in the measured quantity from the actual input to the sensor. Whereas, a scale factor is an error that represents the mismatch between the input quantity to an inertial sensor, and the reported output quantity of the sensor. Typically, one should expect an inertial sensor to report an output value equivalent to whichever input value imposed upon the sensor.

Hence, the expected input—output ratio should be equal to one. However, a scale factor would manifest as deviation of the input—output relation of an inertial sensor from being equal to one. Another form of the systematic errors is the scale-factor non-linearity. Typically, the input—output relation of a sensor is expected be a linear relation. However, due to environmental impacts and some sensors designs, the input—output relation ship of the inertial sensor might not be a linear relation, which is a systematic error that should be accounted for.

Due to improper mounting of inertial sensors within a geometric assembly of an IMU, cross-coupling error occurs. Cross-coupling is caused by the non-orthogonality of the sensitive axes of inertial sensors. Consequently, the inertia sensors either accelerometers or gyroscopes measure residual inertial measurements from another axis that is supposed to be orthogonal to its sensitive axis [ 3 ]. Evidently, inertial sensors endure random errors that would manifest as noises within the inertial measurement signals acquired from inertial sensors.

The random errors can be attributed to electrical or mechanical sources, depending on the design and manufacturing of the inertial sensors. Nonetheless, the order of magnitude and impact of such random errors on the inertial navigation solution is dependent upon the technology, design, and manufacturing techniques of the inertial sensors. Consequently, the performance of any given IMU in terms of providing an accurate navigation solution is defined by the order of magnitude of the systematic and random errors included in its measurements.

Hence, IMUs are classified into grades as per their performance and accuracy. However, it is understandable that there exists a high correlation between the performance of any given IMU, its underlying technology, and its cost.

Whereas, IMUs are classified into: strategic, navigation, tactical, and consumer grades. It is noted that performance parameters upon which the IMUs are classified are discussed afterwards. The differentiation between the two categories of INSs resides in the mechanical system mounts, and mathematical process implemented to acquire a full navigation solution and their differences.

Another form of classifying the INSs is depending on their mechanical operation scheme. An argument can be made that this classification is a chronological one. However, stable platform INSs are not being entirely replaced, and are still used for some navigation applications.

Shows a schematic of the difference between stable-platform and a strapdown INSs, from [ 1 ]. This type of INSs require mounting the inertial sensors on a stable platform that is mechanically isolated from the rotational motion of the vehicle. Such requirement could be achieved by utilizing mechanical inertial sensors, specifically gyroscopes. Within its internal structure and mechanism, a typical mechanical gyroscope comprises a rotating rotor means, with high moment of inertia about a given spin axis, which is rotated by mechanical means, and are presumed to maintain high rotational speeds.

These conditions lead such rotor to maintain spatial rigidity in space, as per the law of conservation of momentum. Such spatial rigidity of the rotor allows it to maintain a stable direction in space. A gimbal connection is connected to said rotor means, which typically constitute three free rings connected through pure hinged connections and are free to rotate in 3D. Consequently, the rotation rate of the moving platform can be detected by utilizing a pick-off means to determine the rotation of the gimbal tings with respect to the spatially rigid rotor [ 4 ].

Nonetheless, mechanical gyroscopes were the means to provide a mechanically stable platform that helped realize inertial navigation in the first place. It is noted that such theoretical assumption of having a stable spin axis direction for the mechanical gyroscope rotor was not entirely satisfied practically.

Whereas, mechanical INSs suffered from various sources of errors. Chief among those errors, is the precession error caused by externally applied torques to the spinning rotor which would in turn affect its spatial rigidity in space and would lead the rotor to deviate from its assumed direction [ 4 ].

Such external torques could be caused by improper balance of masses within the gyroscope design, or under the impact of external shocks. Despite that, stable platform INSs are considered very accurate and reliable. Whereas, stable platform INSs are still used for applications that require very accurate estimates of navigation data such as ships and submarines. However, the downsides of such systems are being large in size, being of high cost, and having high mechanical complexity.

From the nomenclature, strap-down INSs imply that the inertial sensors are strapped down rigidly to the vehicle to which they are mounted. Generally, it is noted that the concept of inertial navigation depends of acquiring inertial measurements of the moving vehicle with respect to an inertial non-rotating non accelerating reference coordinate system, or frame.

However, the navigation states should be represented with respect to a navigation frame. However, for strap-down INSs, the mechanical stabilization that was provided within stable-platform systems are replaced by a computational model to achieve the same output navigation states.

Since, the computational model of strap-down INSs is a mathematical realization of the mechanical stabilization in mechanical systems, it is referred to as INS mechanization [ 4 ].

The navigation states include the position, velocity, and attitude of the moving platform. INS Mechanization in general can be realized using any set of sensors that would be able to provide the raw measurements, that when processed can give the navigation states within the chosen reference frame dimensions i. Consequently, the mechanization process transforms the measurements to the navigation frame as a basic component of the process.

Then, the mechanization process includes an integration over time to acquire the navigation states from the raw measurements of the IMU. Such measurements include the rotation rates from the gyroscopes that are integrated to acquire the attitude angles, and the specific forces from the accelerometers that are integrated to acquire the velocities and the positions [ 1 ].

Strap-down INSs provide optimal alternative for the stable-platform INSs, because strap-down systems provide lower cost, smaller size INSs, that have comparable reliability to the stable-platform systems.

Besides, strap-down INSs remove most of the mechanical complexity associated with the stable-platform systems. Such advantages enable the strap-down INSs to be utilized for a wider range of applications, that demand high performance and light weight.

On the other hand, strap-down systems endure some drawbacks that include the substantial increase in computational complexity and high demand for on-board processing power. However, due to recent advances in computer technology with the development of suitable sensors, such strap-down systems have been successfully realized, and dominate the major aspects in the state-of -the-art inertial navigation.

There are numerous technologies that comprise the state-of-the-art commercialized inertial sensors that are utilized to build strapdown INSs. However, there are basic technologies which dominate the market of inertial navigation. In this section, the dominant state-of-the-art technologies in inertial navigation are discussed in terms of sensor basic operation principles and expected performances.

This section highlights the main technologies for angular rate sensors, and accelerometers, as well.


IMUs represent a complete hardware solution for a variety of applications including human machine interfaces, robotics, platform stabilization, and virtual and augmented reality. For example, since its first appearance on the market, multisensorial platforms have changed the way of playing with the game consoles in a new dynamic mode. This has been possible thanks to the data fusion among the different sensors of the IMU used to implement the game controllers. Data fusion among several sensors is also important for navigation system solutions either in automotive applications or in pedestrian navigation systems used as handheld devices [ 1 ]. In both cases, the IMU provides measurements for controlling the three-dimensional position and orientation, as well as acceleration and angular rate measurement that can be useful to recognize linear movement of the vehicle in case of loss of GPS signal, if the platform is GPS assisted [ 2 ]. The personal navigation systems performed with Pedestrian Dead Reckoning PDR systems are well-suited solutions for indoor use or in urban environments where GPS signals are degraded or not available [ 3 ]. Moreover the integration of a pressure sensor in these units provides further information in terms of altitude.

If you wish to contribute or participate in the discussions about articles you are invited to join SKYbrary as a registered user. On the one hand the term INS is used as a blanket description for a wide variety of navigation sensors and systems of different design; and on the other hand, it is also used to describe a specific version of these sensors and systems! The term has also changed over the years as the technology has improved. What can be said with confidence is that all these systems work on a similar principle and for the same purpose. Below is a list of commonly used terms that are used colloquially and interchangeably by pilots if not by all designers, manufacturers and engineers to mean very much the same thing, with differences in some of the detail. Where necessary two or more definitions are provided. For the purposes of this Article, the definition of INS what it is and what it does that is likely to be most commonly used in the aviation community is as follows:.

Nowadays one of the most common problems for science is the answer for the question how to improve our tools. Each year there are more attempts to solve the problem. In XXI century there is a trend to design tools that require as little human interaction as possible to fulfill their tasks. Unmanned flying objects used for military, mobile robots, space ships, exoskeletons or intelligent clothing monitoring body signals. These are only a few examples of useful devices that are being developed at the moment. In order to navigate the object it is required to know the exact position and orientation of the object in relation to the known environment.

Modern Inertial Technology - Ebook


The proliferation of powerful microcomputers and the development of modern machine learning tools have enabled human daily activity monitoring systems using wearable inertial sensor like accelerometers and gyroscopes. For most current activity monitoring systems, there exists an assumption that the sensors are always securely and correctly mounted by the users. Unfortunately, such assumptions do not hold as the scale of studies increase. And it is especially challenging for subjects with neurological diseases to follow instructions about how to mount the sensors everyday, because some of the elderlies tend to be technophobic and neurological diseases are often accompanied with cognitive difficulties. Errors in sensor mounting pose can cause large amount of data loss and distortion and will affect the robustness of the systems severely.


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