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原文作者: | David J. Allerton | |

发布时间: | 2020-04-15 | |

来 源: | THE JOURNAL OF NAVIGATION (2005) | |

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摘要：

本文综述了目前飞机综合导航系统设计与开发中使用的容错导航系统体系结构和数据融合方法，并比较了它们的优缺点。回顾了四种容错导航系统的体系结构，讨论了相关的卡尔曼滤波体系结构和算法。这些技术已在大多数综合飞机导航系统中得到应用。本综述的目的是为导航系统设计者开发未来的飞机多传感器导航系统提供指导。

Aircraft navigation systems are a flflight-critical system and must be designed to meet the required navigation performance (RNP) require ments for safety, in terms of accuracy, integrity, continuity and availability. In the past decade, various forms of fault-tolerant aircraft navigation systems have beendeveloped to achieve these requirements. This paper reviews the methodologies used in the design and development of fault-tolerant aircraft navigation systemsfrom the perspective of system design. In Section 2, conventional fault-tolerant navigation system architectures are outlined and brieflfly compared. Section 3reviews the development of several Kalman fifilter architectures and fifiltering algor ithms. The methods summarised in this paper have been widely applied in many integrated aircraft navigation systems and enable navigation system developers to design and develop future aircraft multisensor navigation systems.

Fault-tolerant navigation systems have been in use for over 30 years. The design methods incorporate both fault-tolerant strategies and data fusion techniques to enhance reliability and safety and also to improve the performance of aircraft navigation system in terms of the RNP parameters. During this development, three redundancy strategies have been proposed: hardware redundancy, software redundancy and analytical redundancy. Hardware redundancy uses multiple navigation sensors/ systems to achieve fault tolerance and improve the performance of an aircraft navigation system. This approach is based on the principle that measurements from various sensor systems are independent, redundant, complementary or cooperative.These different types of measurements can be combined by means of data fusion algorithms, so that the overall system performance is better than that of each individual system. Hardware redundancy techniques have been widely applied to many avionics systems1,2,3 . Software redundancy uses different software versions to increase the safety and integrity of navigation solutions by avoiding possible errors caused by software and computing failures. However, software redundancy cannot increase the accuracy of navigation solutions. Analytical redundancy is based on the knowledge of rotational kinematics and translational dynamics of an aircraft to enhance hardware redundancy4 . Analytical redundancy is generally used to generate additional redundant information for the diagnosis of system failures rather than the improvement of accuracy of navigation systems5 . For that reason, analytical redundancy is considered as a failure detection method in most practical systems. Figure 1 outlines the fault-tolerant design methods used for aircraft navigation systems. Hardware redundancy plays an essential role in the design of fault-tolerant navigation systems and the level of fault tolerance depends on both the architecture of hardware redundant systems and the data fusion methods implemented. Three types of hardware redundancy have been developed for the design of fault-tolerant aircraft navigation systems: system-level redundancy, sensor-level redundancy and distributed redundancy.

**2.1. System-Level Redundancy Architecture. **

A typical system-level redundancyarchitecture is shown in Figure 2, where each Inertial Navigation System (INS) operates independently and there is no data communication between these systems. This is generally known as an independent system architecture. Each INS can also be integrated with other navaid systems to improve the navigation accuracy and to control the growth of inertial sensor errors with time. Fault-tolerant methods used to check the consistency and failures of all the INSs are typically majority-voting methods or weighted-mean methods. In order to achieve fail-operational/fail-safe operation, at least three INSs are needed in this configuration. In other words, at least nine pairs of inertial sensors (accelerometers and gyros) are needed, where each INS is a conventional orthogonal configuration. The main advantage of this architecture is that the design and integration is simple and does not require complex fault-tolerant methods for the diagnosis of system failures. However, if any sensor in one INS fails, then this INS has to be removed from the fault-tolerant architecture. Consequently, this architecture cannot exploit the benefits of redundant inertial sensors to dynamically reconfigure an aircraft navigation system when one INS fails. This traditional redundant architecture is still used in many existing avionic systems6 , although these systems are expensive and the duplication of INS modules can result in a significant increase in mass.

**2.2. Sensor-Level Redundancy Architectures.**

Sensor-level redundant architectures were developed with the advent of high-speed, large memory embedded microprocessors and low-cost, small-size and low-mass inertial measurement units (IMU). Several redundant schemes have been proposed, including IMU-level and multisensor redundancies.

**2.2.1. IMU-Level Redundancy.**

An IMU-level redundant architecture used inmany aircraft navigation systems is shown in Figure 3, where duplex or triplexconventional IMUs are configured in a federated architecture to obtain fault tolerance. Each IMU can be skewed with respect to the aircraft body axes when it ismounted in the aircraft in order to reduce the number of IMUs7. Theoretically, a fault-tolerant navigation system consisting of two IMUs affords fail-operational/failoperational/fail-safe operation if one of these IMUs is skewed relative to the aircraft body axes, or is a non-orthogonal IMU. In this configuration, six pairs of inertial sensors can achieve a higher level of fault tolerance in comparison with three independent INSs. Each navigation processor can combine the outputs of all IMUs with data from aiding systems to estimate the aircraft motion states and to perform sensor failure detection and isolation and system reconfiguration. Compared with the INSlevel redundancy, this architecture significantly increases the level of fault tolerance and makes effective use of existing IMU equipment.

However, resultant fault-tolerant systems still share some of the disadvantages of system-level redundant architectures and considerable efforts are being made to reduce volume, weight and cost. 2.2.2. Multisensor RedundancyAn alternative development is to integrate multiple inertial sensors in a single suite in the form of non-orthogonal configurations3, known as skewed redundant IMU (SRIMU) configurations. One multisensor suite can thus replace multiple IMUs to reduce the volume, weight and power required for an aircraft navigation system. A representative architecture of multisensor faulttolerant systems is shown in Figure 4, where the multisensor suite is a dodecahedron configuration. Six pairs of inertial sensors are installed perpendicular to the parallel faces of a regular dodecahedron. The SRIMU outputs are sent to redundant navigation processors, each individually performing the navigation and attitude computations, sensor FDI functions and navigation system reconfiguration. The multisensor redundancy is a cost-effective approach that exploits the benefits of emerging inertial sensor technologies and high-speed embedded microprocessor systems. Multisensor technology will provide the basis for the future generations of fault- tolerant navigation systems.

**2.3. Distributed Redundant Architectures. **

Distributed redundant architectures is a new fault-tolerant concept which has been developed with the introduction of distributed and integrated modular avionics architectures. A current combat platform may have a total of twelve traditional IMUs of various quality, providing the state vector information required by avionic systems and weapon systems8 . In this architecture, inertial sensor systems are mounted at several locations in an aircraft, not only to meet the fault tolerance requirements of navigation systems, but also to provide accurate local inertial vector states for other systems, for example, weapon control systems and imaging sensors and to provide radar stabilization and motion compensation. The concept of using an inertial network for aircraft avionics was initially proposed by Kelley, Carlson and Berning8 in 1994. However, no research has been published describing a systematic study of inertial network architectures for fault tolerant aircraft navigation systems, in terms of combining data fusion methods,dynamic alignment and correction of distributed inertial sensor systems and distributed sensor failure detection and isolation techniques.

**3. DATA FU S ION F ILTER AR CH ITE CTURE S.**

Kalman filtering techniques have been developed for applications in aircraft navigation, control and guidance since the 1970s. During this period, many Kalman filter architectures and filtering algorithms have been proposed as prime data fusion methods, to combine multiple navigation sensors/systems to achieve the required navigation performance. Data fusion filter architectures currently used in aircraft integrated navigation systems can be categorised as four types: centralised, cascaded, federated and distributed data fusion architectures.

**3.1. Centralised Filter Architecture.**

The centralised filter architecture is illustrated in Figure 5, where measurements or data from all navigation sensors/systems are processed in a central data fusion filter to obtain the accurate estimates of aircraft motion states. This architecture is the most common filter design implemented in current integrated navigation systems, including INS/GPS/Doppler integrated systems9, GPS/Doppler integrated systems10 and tightly-coupled GPS/inertial systems11,12. In these systems, INS outputs and raw GPS measurements are combined in a centralised filter to estimate the navigation state errors and sensor errors, including GPS receiver clock errors, inertial sensor errors and baro-altimeter errors. Numerous covariance analysis methods and numerical computations of the standard and extended Kalman fifilters have been reported in the literature. Theoretically, the cen tralised fifilter can obtain optimal estimates of the aircraft motion states. However, with the increasing number of sensor systems in aircraft, the fifiltering algorithms can be quite complex and the centralised fifilter computation can be time-consuming as a result of the large number of states in the dynamic models of the fifilter. Accordingly, the centralised fifilter is not necessarily an appropriate methodology in the develop ment of fault tolerant multisensor navigation systems20,29,31. To overcome the limitations of the centralised fifilter, other fifilter architectures have been developed.

**3.2. Cascaded Filter Architecture. **

The cascaded fifilter architecture is shown inFigure 6, where the outputs of one fifilter are used as inputs to a subsequent fifilter stage.The fifilter outputs include the estimates of the system states and their error covari ances. This fifilter architecture has been proposed for the integration of existing navi gation systems which contain their own Kalman fifilters. The cascaded fifilter can improve the accuracy of integrated navigation systems and also perform in-flflight calibration or transfer alignment between an INS/GNSS integrated system and a slave INS or attitude heading reference system (AHRS). This architecture has been used in GPS/INS/terrain-aided navigation systems13 and loosely-coupled GPS/INS integrated navigation systems, where the GPS navigation solutions, derived by an GPS internal fifilter and INS data, are combined in a separate cascaded fifilter external to the GPS receiver to estimate the navigation state errors and the inertial sensor errors. The GPS fifilter estimates the GPS receiver clock errors. However, the GPS fifilter is generally based on a simplifified model and may not output the computed error covariances. Consequently, the cascaded fifilter may not have access to covariance information. Schlee et al14 developed a cascaded fifiltering algorithm to improve the accuracy of an existing GPS/inertial system, known as a master INS, which utilises an internal fifilter to estimate the master INS navigation solutions and the GPS clock errors. This cascaded algorithm also provides transfer alignment between the master INS and a second inertial system. Their study showed that improvement in the accuracy of the master INS and the accuracy of the transfer alignment depend on the update rate of the cascaded fifilter. However, correlations of the state errors caused by the internal fifilter are ignored in the measurement noise matrix of the cascaded fifilter. From Kalman fifilter theory, the non-diagonal elements of the state error covariance matrix of the fifilter (which represent the correlations) can only be ignored if the fifilter offffers highly accurate estimates of the navigation states and the magnitudes of the off-diagonal elements are far less than the diagonal elements. Otherwise, the per formance of the cascaded fifilter may be degraded as a result of the correlation. Wade and Grewal15 analysed the effffect of this correlation on the accuracy of cascaded GPS/INS systems; their results show that the accuracy of cascaded systems depends on the correlation matrix. When the state errors estimated by the internal fifilter are closely correlated, the cascaded fifilter may incorrectly estimate the navigation state errors and the inertial sensor errors. Wade and Grewal suggest adjusting the measurement noise matrix by using adaptive process noise in the cascaded fifilter.

However, development of this adaptive process and identifification of the measure ment noise matrix are not reported in detail. In order to improve the robustness of the cascaded fifilter to input conditions and adverse environments, Karatsinides16 proposes two methods for dealing with the GPS position bias and identifying the statistical values of measurement noise for the cascaded fifilter. The GPS positioning solution contains biases resulting from satellite clock errors, ephemeris errors, ranging signal propagation delay and geometries of visible satellites. Although GPS position bias is unobservable and cannot be esti mated in the GPS fifilter, it can inflfluence the accuracy of cascaded GPS/INS systems through the error covariance matrix. The fifirst method models GPS position bias as a fifirst-order Gauss-Markov process and then uses these biases as the consider-states of a Schmidt-Kalman fifilter. The part of the Schmidt-Kalman gain matrix related to the consider-states is set to zero in order to ignore the estimated consider-states. The second method computes the variances and covariances of the errors of the navi gation states derived by the GPS fifilter, using conventional computation equations of variance and covariance, provided that the update rate of the cascaded fifilter is less than the GPS fifilter. The cascaded fifilter architecture can be used to integrate existing navigation systems into a fully integrated system and may only require minimal modififications to existing navigation systems. In practice, most existing navigation systems do not output covariance data of the navigation state errors. Consequently, the cascaded fifilter is extremely dependent upon the methods that are used to estimate the covari ances of the primary fifilter and the performance of the primary fifilter. Moreover, tuning of the primary fifilter is of critical importance to the performance of the cascaded fifilter15.

**3.3. Federated Filter Architecture.**

The federated fifilter architecture was initially recommended by Carlson17 for integrating multiple navigation sensor systems in order to provide a high level of fault tolerance and accuracy. This is a two-stage fifiltering architecture, as shown in Figure 7, where all the parallel local fifilters combine their own sensor systems with a common reference system, usually an inertial system, to obtain the local estimates of the system states. These local estimates are sub sequently fused in a master fifilter to achieve the global estimations. By using a common reference system, all parallel fifilters have a common state vector. The federated fifilter is generally designed on the basis of two difffferent strategies17,18. In the fifirst method, the local fifilters are designed independent of the global performance of the federated fifilter and estimate n sets of local state vectors and their associated covariances by using their own local measurements. These n sets of the local state estimates are then weighted by their error covariances to obtain the global state estimates. The second method is based on the global optimality of the federated fifilter; the local fifilters are derived from the global model of the federated fifilter and estimate n versions of the global states from local sensor measurements. These n versions of estimates are weighted by their error covariances to obtain the global optimality. The master fifilter is a weighted least-squares estimator. Carlson19 developed a square-root form of the federated fifiltering algorithm to increase the computational precision and the numerical stability of the federated fifilter.

A signifificant feature of the federated fifiltering process is that a reference INS must be used to create the common system states in the local and master fifilters, which are the navigation states. Therefore, each local fifilter can obtain the suboptimal navi gation states. A comparison of the federated and centralised fifilters has shown that the federated architecture offffers improvements in failure detection, isolation and recov ery (FDIR) and fault tolerance over the centralised fifilter20. Levy21 uses dual state suboptimal analysis to model the true world state vector and develops covariance analysis algorithms for assessing the sub optimality of both the cascaded and the federated fifilters. The dual state contains the states of the fifirst and second fifilters in the case of the cascaded fifilter (or the states of all parallel fifilters and the master fifilter in the case of the federated fifilter). Levy’s results have shown that the cascaded and federated fifilters are seldom optimal in comparison with the centralised Kalman fifilter. As the master fifilter updates become sparser, the actual performance of the federated fifilter degrades in comparison with the centralised fifilter. The federated fifilter is only optimal (or equivalent to the centralised fifilter) when the full global state is modelled in each local fifilter and the master fifilter is run at the update rate of the local fifilters. Tupysev22 develops a federated fifiltering algorithm based on the principles of state vector augmentation and the rejection of partial information. Unlike Carlson’s fifilter, the global state model that is used to derive the parallel local fifilters contains a com mon state vector plus individual local bias state vectors instead of all the states of the local fifilters. However, the use of a reference navigation system as a common informationsource of all local fifilters in the federated fifilter architecture means that common mode failures in the reference system can corrupt the performance of these fifilters. This inflfluence can further degrade the level of fault tolerance and FDIR functions.

This problem seems to have been ignored in current designs of federated integrated navigation systems. The federated fifilter has been applied to several multisensor navigation systems, for example, GPS/INS/SAR/terrain aided navigation and tracking systems23. It should be noted that the federated fifilter is sometimes referred to as the decentralised fifilter27.

**3.4. Distributed Filter Architectures.**

Distributed fifilter architectures were orig inally developed for target tracking and identifification where distributed sensor sys tems (possibly in difffferent platforms) are combined in order to estimate and identify various moving targets in military applications. Liggins et al24 gives a comprehensive survey of distributed fusion architectures for target tracking. Distributed fifiltering techniques used for the design and development of fault-tolerant navigation systems have appeared since 199027. The cascaded and federated fifilter algorithms are special cases of the distributed fifilter architectures. Unlike the fifilter architectures described above, distributed fifilter architectures have no standard models. In general, there are two main data fusion approaches to the design of distributed fifilters, known as measurement fusion and state fusion. In state fusion, the local states estimated by the local fifilters are fused in a central fifilter to obtain global estimations. By contrast, in measurement fusion, various subsets of all the sensor measurements are fused by means of a bank of Kalman fifilters to obtain multiple state estimation versions of the global system states, which are combined to obtain the more accurate global state estimation and to detect system failures. However, there may be no central data fusion in a fully distributed multisensor data fusion system. In fact, the distributed fifilter architecture offffers the most flflexible scheme in the design of multisensor navi gation systems. Several distributed fifiltering algorithms have been developed since 1980 for the design of various distributed control systems, target tracking systems and integrated navigation systems. Speyer25 describes a distributed fifiltering algorithm in which each of K local fifilters has its own local sensor measurements and the same state model. Each local fifilter computes the global estimate of the system state vector. The infor mation shared between these local fifilters consists of the local estimates and error covariances and an additional (locally computed) data-dependent term, which is a dynamic compensation to account for the correlation between the local estimates. Speyer’s fifilter is a fully distributed fifiltering architecture and has a high level of fault tolerance. However, by using the same state model, this fifiltering algorithm cannot be used in a distributed inertial sensor system where the local state vector is needed for a specifific application, for example, local motion compensation. Willsky et al26 consider a problem where two local fifilters have models which diffffer from the global model. Each local fifilter processes its local measurements and a fusion algorithm (based on the global model) computes a dynamic correlation correction term. The local estimates are then combined to obtain the global estimate. A necessary and suffiffifficient condition for recovering the global state from the local states is that a relationship must exist between the observation matrix of the global state model and that of each local state model. This relationship is formulated as a static matrix transformation. In other words, the local state vector is a subset of the com ponents of the global state vector. This algorithm has been extended to the design of a multisensor navigation system33. However, these algorithms imply that both the local and the global states are represented in the same coordinate system and this is not necessarily true for distributed inertial sensor systems.

Kerr27 proposes a decentralised fifiltering structure but the decentralised fifilter algorithms applicable for this structure are not detailed. However, some fifiltering malgorithms, for example, Speyer’s parallel fifiltering algorithms26, may be used for this decentralised structure. In terms of the fifilter architecture, Kerr’s version is similar to the federated fifilter architecture given by Carlson17. The difffferences between these architectures are the individual methods used for detection and isolation of sub system failures. For example, Kerr’s fifilter uses voter/monitoring methods based on Gaussian confifidence regions of the estimated states whereas Carlson’s fifilter uses fifilter residuals to detect sensor and subsystem failures.

Brumback and Srinath28 describe a distributed fifiltering mechanism that is a hierarchical fifiltering architecture, where the local fifilters fuse difffferent subsets of all measurements for local state estimates and failure detection and isolation. A master fifilter combines the outputs of failure-free local fifilters to yield the global estimation. The local fifilters in the distributed fifilter architecture can have system models, which are difffferent from the global model. Hashemipour et al29 introduce decentralised Kalman fifiltering algorithms for three types of sensor system networks: sensor collected, time sequential measurements and a hybridisation of these two types. In Hashemipour’s fifilter, each local fifilter has the same state model as the central fifilter and the observation matrix of each local model corresponds to one sub-matrix of the observation matrix of the global model. Each local fifilter computes the global estimation and its local error covariance; these are subsequently fused in a central fifilter to obtain the global optimal estimation. Accordingly, this fifiltering algorithm is similar to Speyer’s fifilter, but uses the infor mation form of the Kalman fifilter and does not need feedback from the central fifilter to the local fifilters. Although this algorithm has been applied to target-tracking prob lems, it is not suitable for distributed multisensor navigation systems because feed back control is an important means to correct sensor errors in a distributed inertial sensor system.

Hong30 presents a distributed multisensor integration algorithm in which the local measurements, together with previous global estimates obtained via the communi cation network, are locally processed to obtain the local state estimate and the local error covariance. These local estimates (state and covariance) are fused in a central fifilter to obtain the global estimate. Because the local state and covariance predictions are derived from the previous global estimates, the local fifilters have no state models. However, rotation matrices and translation transformations are introduced to defifine the relationships between the local states and the global (central) state. Moreover, this algorithm was designed to minimise the uncertainties of these transformations. It should be noted that the same relationships are also used for the measurement transformations from the local nodes to the central node. This is not necessarily true in distributed inertial sensor systems, especially when a nonlinear relationship exists between the measurements and the states. Compared with Speyer’s fifiltering algor ithm, this method simplififies the complexity of the distributed fifiltering algorithms. However, the local states greatly depend on the global states because this method lacks local dynamic models. Roy et al31 propose a square root fifiltering structure where parallel local fifilters have a smaller dimension than the global fifilter. Paik et al32 develops a gain fusion algor ithm for decentralised parallel Kalman fifilters to obtain computation-effiffifficient suboptimal estimation results. Raol et al33 describe a decentralised square-rootinformation fifiltering scheme where all information fusion is processed locally at each node and there is no central fusion. These algorithms can improve the computational precision and numerical stability of existing distributed fifiltering algorithms. Fully distributed fifiltering architecture and information fusion algorithm are developed, where no central data fusion centre is needed34. Each local fifilter has its own local system model and processes the local measurements and information assimilated from other fifilters to obtain a global estimate of the system state. However, there is still a key problem to be considered; the dynamic relationship between the local states must be determined, especially if the local state models are difffferent. Berg et al35 describe the static relation between the local states and the global state using an approach similar to Speyer’s method25. For aircraft systems, multisensor data fusion offffers potential improvements in performance in the following areas of navigation:

- Aircraft navigation system RNP parameters;
- Fault tolerance of navigation systems;
- Estimation of local motion states.

The majority of previous applications have focused on meeting RNP and reliability requirements. In other words, existing distributed fifiltering algorithms have preserved the global optimality of the navigation states, which is a desirable feature and serves as a benchmark for other avionic systems. However, these methods rarely consider the dynamics of the local subsystems or the dynamic relationships between the local subsystems. Some algorithms still require extensive computations of local and global inverse covariances. Very few studies have addressed estimation of the local states. In fact, distributed inertial sensor systems consisting of several IMUs mounted in an aircraft affffords both redundant inertial measurement information and distributed inertial state vectors, which can be used for aircraft navigation, guidance and control and also in the implementation of local motion compensation functions. These IMUs measure local motion with reference to specifific coordinate frames defifined by their installation positions and have individual error dynamics. Therefore, the local states must be accurately estimated to determine the local dynamic motion. The develop ment of distributed fifiltering algorithms can also be used to investigate methods for dynamic alignment and calibration of distributed IMUs. To date, these consider ations have not been addressed in the open literature.

This paper has reviewed the developments of fault tolerant aircraft navigation systems based on an extensive literature survey. The methodologies for the design and development of safety-critical aircraft navigation systems have been summarised, including fault-tolerant navigation system archi tectures, data fusion fifilter architectures and corresponding fifiltering algorithms. These methods provide the techniques for navigation system engineers and researchers to design and develop future aircraft multisensor navigation systems.

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