Introduction to integration and estimation theory

In this study, the integrated navigation system, consisting of radio and inertial navigation system (INS) altimeters, is presented. INS and the radio altimeter have different benefits and drawbacks. The integration is achieved by using an indirect Kalman filter. Hereby, the error models of the navigators are used by the Kalman filter to estimate vertical channel parameters of the navigation system. In the open loop system, INS is the main source of information, and radio altimeter provides discrete aiding data to support the estimations. At the next step of the study, in case of abrupt faults, the performance of the integrated system is examined. The optimal Kalman filter reacts with abnormal estimates to this situation as expected. To recover such a possible malfunctioning, the robust Kalman filter algorithm is suggested.

How to achieve continuous, reliable and accurate positioning performance using low-cost sensors is one of the main challenges for aviation navigation system. Global Positioning System (GPS) can provide the primary means of navigation in a number of aviation navigation applications (e.g., manned and unmanned aircraft vehicle, airport ground vehicle). However, GPS signal deteriorations typically occur due to aircraft itself during maneuvering, ionospheric scintillation, Doppler shift, multipath and so on. Thus, there is a need to research GPS augmentation strategies which can be used in the Communication, Navigation, Surveillance/Air Traffic Management. GPS integration with Inertial Navigation system (INS) is one of the key strategies. But once GPS signal outages, the integrated navigation system works in pure INS, and positioning accuracy deteriorates with time. When using low cost GPS/INS integration, a primary problem is the rapid performance deteriorate during GPS outages. To provide continuous, accurate and reliable positioning information in aviation, discrete grey prediction model (DGPM) aided fusion methodology is proposed. The DGPM provides pseudo-GPS position information for INS during GPS outages. The mathematical model of integrated navigation system is established, including INS error equations, Kalman filter and DGPM. The model works in the update mode when there is no GPS failure, whereas it switches to the prediction mode in case of GPS outages. To verify the feasibility and effectiveness of the proposed methodology, real road test is performed. The comparison results show that accuracy of longitude and latitude are improved by more than 80% and 70%, respectively. The DGPM can effectively provide position corrections for standalone INS during GPS outages.

Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) are very practical method to get high precision navigation. GPS/INS data Fusion in navigation has been a research topic for decades. Usually the update time of GPS an INS is different. The update time of GPS is 20HZ, and the time of INS is 100HZ or higher. Since GPS and INS are mainly methods in navigation system. Techniques of fusing GPS and INS data are in high demand in navigation industry. Usually the Karman filter is used to fuse the data from GPS and INS. But the Kalman filter is model-dependent and a priori the model parameters need to be known. In this work, a generic and intelligent approach of GPS and INS data fuse using fuzzy interpolation before Kalman algorithm is proposed. First a simplified interpolation model is introduced in a ordinary GPS and INS data fusion. Second a fuzzy rule-based system is established to fuzzy interpolation with objective fuzzy method. Then the parameters of objective fuzzy system are identified, the best n-rule is determinate and the optimal rule base system is found. Finally this approach is applied on an example for a car GPS and INS data fusion, and the results are calculated with computer system to demonstrate the advantages of this approach.

A multi-sensor integrated solution that combine complementary features of the Global Positioning System (GPS), inertial navigation system (INS), and magnetometer is presented due to GPS-aided inertial navigation system (INS) provides poor observability of heading angle. In addition, Based on the principle of federated Kalman filtering and Adaptive Extended Kalman Filter, the algorithm is presented also for accuracy of positioning and attitude, rapidity, and error tolerance of the navigation system. The algorithm is implemented in the integrated navigation system. Experimental results show that the observability issue is solved and improvement in accuracy.

About the Author. Preface . Glossary . 1 Introduction . 1.1 Historical Perspective. 1.2 The Case for Simulation. 1.3 The Changing Role of Simulation. 1.4 The Organization of a Flight Simulator. 1.5 The Concept of Real-time Simulation. 1.6 Pilot Cues. 1.7 Training versus Simulation. 1.8 Examples of Simulation. References. 2 Principles of Modelling . 2.1 Modelling Concepts. 2.2 Newtonian Mechanics. 2.3 Axes Systems. 2.4 Differential Equations. 2.5 Numerical Integration. 2.6 Real-time Computing. 2.7 Data Acquisition. 2.8 Flight Data. 2.9 Interpolation. 2.10 Distributed Systems. 2.11 A Real-time Protocol. 2.12 Problems in Modelling. References. 3 Aircraft Dynamics . 3.1 Principles of Flight Modelling. 3.2 The Atmosphere. 3.3 Forces. 3.4 Moments. 3.5 Axes Systems. 3.6 Quaternions. 3.7 Equations of Motion. 3.8 Propulsion. 3.9 The Landing Gear. 3.10 The Equations Collected. 3.11 The Equations Revisited - Long Range Navigation. References. 4 Simulation of Flight Control Systems . 4.1 The Laplace Transform. 4.2 Simulation of Transfer Functions. 4.3 PID Control Systems. 4.4 Trimming. 4.5 Aircraft Flight Control Systems. 4.6 The Turn Coordinator and the Yaw Damper. 4.7 The Auto-throttle. 4.8 Vertical Speed Management. 4.9 Altitude Hold. 4.10 Heading Hold. 4.11 Localizer Tracking. 4.12 Auto-land Systems. 4.13 Flight Management Systems. References. 5 Aircraft Displays . 5.1 Principles of Display Systems. 5.2 Line Drawing. 5.3 Character Generation. 5.4 D Graphics Operations. 5.5 Textures. 5.6 OpenGL (R) . 5.7 Simulation of Aircraft Instruments. 5.8 Simulation of EFIS Displays. 5.9 Head-up Displays. References. 6 Simulation of Aircraft Navigation Systems . 6.1 Principles of Navigation. 6.2 Navigation Computations. 6.3 Map Projections. 6.4 Primary Flight Information. 6.5 Automatic Direction Finding (ADF). 6.6 VHF Omnidirectional Range (VOR). 6.7 Distance Measuring Equipment (DME). 6.8 Instrument Landing Systems (ILS). 6.9 The Flight Director. 6.10 Inertial Navigation Systems. 6.11 Global Positioning Systems. References. Further Reading. 7 Model Validation . 7.1 Simulator Qualification and Approval. 7.2 Model Validation Methods. 7.3 Latency. 7.4 Performance Analysis. 7.5 Longitudinal Dynamics. 7.6 Lateral Dynamics. 7.7 Model Validation in Perspective. References. 8 Visual Systems . 8.1 Background. 8.2 The Visual System Pipeline. 8.3 3D Graphics Operations. 8.4 Real-time Image Generation. 8.5 Visual Database Management. 8.6 Projection Systems. 8.7 Problems in Visual Systems. References. 9 The Instructor Station . 9.1 Education, Training and Instruction. 9.2 Part-task Training and Computer-based Training. 9.3 The Role of the Instructor. 9.4 Designing the User Interface. 9.5 Real-time Interaction. 9.6 Map Displays. 9.7 Flight Data Recording. 9.8 Scripting. References. 10 Motion Systems . 10.1 Motion or No Motion? 10.2 Physiological Aspects of Motion. 10.3 Actuator Configurations. 10.4 Equations of Motion. 10.5 Implementation of a Motion System. 10.6 Hydraulic Actuation. 10.7 Modelling Hydraulic Actuators. 10.8 Limitations of Motion Systems. 10.9 Future Motion Systems. References. Index.

The high precision positioning and navigation of underwater vehicles is one of the key technologies for deep-sea exploration and ocean exploration, the underwater localization systems can be categorized into two main types: Inertial Navigation System (INS) and acoustic positioning system. INS is widely used in underwater navigation on account of its autonomy, however, without the information aiding from additional sensors, the errors of inertial measurement units accumulate with time passes. The acoustic positioning system can be divided into three types: Long Base Line (LBL), Short Base Line (SBL) and Ultra Short Base Line (USBL). They are defined according to the distance between transponders. The short baseline (SBL) positioning system includes more than 3 transponders to form an acoustic array, and the formation of the array is normally triangle or quadrilateral. The distance between the transponder is accurately measured and generally more than 10m. The acoustic array coordinate system is built based on the transponder and its relationship with the carrier coordinate system of the vehicle is determined by conventional method, the main disadvantage of the SBL positioning system is that the baseline length is relatively large in order to achieve high accuracy in deep-water measurement. However, as the lateral length of the vehicles is small, it is difficult to make sure the transponders be placed way from each other, meanwhile it is difficult to calibrate multiple transponders and avoid noise. To solve this problem, this paper present an inertial navigation system and single range navigation system (SRNS) based on one acoustic transponder, the navigation system consist of an acoustic transponder, a pressure transponder and inertial sensors mounted on the vehicle and an answering device transponder which is laoid out at tens of meters deep straight under the buoy. This paper studies the measurement equation's nonlinearity effect of the INS/SRNS, establishes state equation and measurement equation of the INS/SRNS integrated system. To deal with the nonlinear noise problems of transponders, meanwhile, in view that fault detection based on traditional state chi-square hypothesis testing cannot determine the specific cause of the fault, and could only determine the validity of measure information, a new fault detection algorithm based on dual-state method is adopted. The application of this method on underwater integrated navigation system demonstrates that the algorithm can rapidly and accurately detecting and identify the faults in the system. Experiments on QIANDAO Lake show that the proposed method restrains the divergence trend error of the integrated system's navigation, which verify the effectiveness of the single range integrated navigation.

In this article, a prediction method based on a radial basis function neural network and an improved unscented Kalman filter, is proposed to improve the accuracy of position and velocity of the Global Positioning System/Strapdown Inertial Navigation System (GPS/SINS) integrated navigation system, especially in the presence of GPS signal outages. The improved unscented Kalman filter based on the adaptive theory is adopted to enhance the positioning accuracy of the GPS/SINS integrated navigation system when a GPS signal is available. A radial basis function neural network and a non-stationary time series analysis are used to predict and compensate for the positioning error of the GPS/SINS integration in the presence of GPS signal outages to improve the reliability of the navigation system. The effectiveness of the proposed method is verified by the simulation experiment and vehicle test. The simulation and test results show that the proposed method can improve the position accuracy and velocity accuracy in different GPS outage time periods.

With the development of the vehicle industry, controlling stability has become more and more important. Techniques of evaluating vehicle stability are in high demand. Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is a very practical method to get high-precision measurement data. Usually, the Kalman filter is used to fuse the data from GPS and INS. In this paper, a robust method is used to measure vehicle sideslip angle and yaw rate, which are two important parameters for vehicle stability. First, a four-wheel vehicle dynamic model is introduced, based on sideslip angle and yaw rate. Second, a double level Kalman filter is established to fuse the data from Global Positioning System and Inertial Navigation System. Then, this method is simulated on a sample vehicle, using Carsim software to test the sideslip angle and yaw rate. Finally, a real experiment is made to verify the advantage of this approach. The experimental results showed the merits of this method of measurement and estimation, and the approach can meet the design requirements of the vehicle stability controller.

An expanded form of the third-order Markov undulation model is developed which includes undulation of the geoid, vertical deflections, gravity anomaly, and the anomalous gravity gradients. First, the complete set of autocorrelation and cross-correlation functions, as specified by the autocorrelation of undulation, is obtained. Then, a time-domain approach is used to synthesize the corresponding linear system driven by white noise that represents the anomalous gravity field behavior along a straight horizontal track. The resulting nine-state Markov model provides a shaping filter for applying covariance analysis and optimal estimation techniques to inertial navigation and gravity gradiometry systems analysis. ONTINUED mechanical refinement has brought inertial navigation technology to the stage where unmodeled variations in the Earth's gravity field have become significant and sometimes dominant error sources.1 At the same time, inertial navigation system analysts have been facing the task of developing error models to evaluate the impact of gravity uncertainties on navigation system performance. Ad- ditionally, the development of gravity gradiometers has made it necessary to model gravity-gradient signals to specify sensor requirements and analyze gradiometer-aided inertial navigation or gradiometry survey performance. To apply the powerful tools of linear system theory and Kalman filtering, it has become common to consider gravity uncertainties random variables, and to model them as Markov processes. Following the first treatment of vertical deflections as a first-order Markov process,2 a succession of higher order Markov models was proposed culminating with the third- order Markov undulation model3'4 which is fully self- consistent; that is, the auto- and cross-correlation functions of undulation, vertical deflections, and gravity anomaly obey and are derived according to the mathematical relationships of physical geodesy. The motivation for using Markov models for gravity un- certainties is that they can be cast in the form of linear dif- ferential equations driven by white noise. This allows use of the model as a shaping filter in covariance analysis of linear dynamic systems, Kalman filters, and optimal smoothing algorithms. The expanded third-order Markov undulation model described in this paper is derived from the original version, but it has three differences. First, it was found that the original model could easily be extended to include all the anomalous gravity gradients by continued differentiation of auto- and cross-correlation functions. Second, the exact cross-correlation function between undulation and gravity anomaly contains modified Bessel functions.4 Modified Bessel functions are solutions to a class of differential equations whose coefficients are functions of the independent variable. To obtain a Markov shaping filter, it is necessary to substitute an approximate function which is the solution to a linear differential equation with constant coefficients. While the chosen exponential form did not approximate the exact Bessel function as well as at first hoped possible, it provides a suitable representation of the un- dulation-gravity anomaly cross-correlation.

The sidewalk is often located in complex environments such as buildings or covered by dense trees. Satellite navigation systems are susceptible to the surrounding environment, resulting in multipath effects, resulting in reduced positioning accuracy. Therefore, the global satellite navigation system (GNSS) and inertial navigation system (INS) based on kalman filter (KF) algorithm are studied, and the navigation algorithm and system model suitable for pedestrians are given. Considering that the pedestrian speed is low, the satellite navigation system obtains the carrier orientation information (heading angle), which also produces a large error. Therefore, the pedestrian dead reckoning (PDR) correction method is adopted to make the positional accuracy of the integrated navigation continuously stable. This paper proposes a pedestrian navigation system solution based on a single navigation device.

The introduction of automated flight control and management systems have made possible aircraft designs that sacrifice arodynamic stability in order to incorporate stealth technology intro their shape, operate more efficiently, and are highly maneuverable. Therefore, modern flight management systems are reliant on multiple redundant sensors to monitor and control the rotations of the aircraft. To this end, a novel distributed quaternion Kalman filtering algorithm is developed for tracking the rotation and orientation of an aircraft in the three-dimensional space. The algorithm is developed to distribute computation among the sensors in a manner that forces them to consent to a unique solution while being robust to sensor and link failure, a desirable characteristic for flight management systems. In addition, the underlying quaternion-valued state space model allows to avoid problems associated with gimbal lock. The performance of the developed algorithm is verified through simulations.

This paper proposes an in-coordinate interval adaptive Kalman filter for INS/GPS/SMNS (Inertial Navigation System/Global Position System/Scene Matching Navigation System) integrated navigation system in which SMNS has the characteristics of randomness and in-coordinate interval when it outputs the reliable positioning information. The proposed filter sets the period of the INS parameters analysis as reference, the periods of parameters output of GPS and SMNS are adjusted to be integral multiple of the INS analysis period by interpolation or extrapolation method; The system is updated only based on INS information when the observation information don't reach, it is updated based on all navigation information when the observation information reach; In addition, this method can overcome the drawbacks of the traditional Kalman filtering method when the system measurement noise is unknown. The proposed algorithm and the method proposed by reference [8] are applied to INS/GPS/SMNS integrated navigation system. Simulation results show that the in-coordinate interval adaptive Kalman filter outperforms the traditional Kalman filter.

The Global Navigation Satellite Systems (GNSS) such as Global Positioning System (GPS) are the prime land and autonomous vehicles navigation information source. However, urban canyons high rise buildings block the GPS signal. Therefore, the Inertial Navigation System (INS) or the Reduced Inertial Sensor System (RISS) are utilized as an alternative source of the navigation information. The RISS is able to produce a full navigation solution using less number of sensors and calculations. Dramatically, the RISS solution drifts over time as the INS system. The integration between the GPS and the RISS is mitigating each system drawbacks. However, during the GPS outage periods, the navigation system is only depending on the inertial measurements. The RISS is utilizing the odometer/speedometer to measure the vehicle's forward speed. Many types of error affect the odometer measurements. These errors are either due to the vehicle's specifications as the differences in wheel diameters, and/or inefficient wheelbase or the road nature as wheel slips, uneven road surfaces, and/or skidding. In this paper, a Radar-based RISS system is introduced to take place the traditional RISS or INS systems. The radar unit is an essential part of the adaptive cruise control (ACC) system. Furthermore, it is capable of measuring the relative velocity and distance between the carrying and the in front vehicle to reduce collisions and increase the safety of driving. In addition, the radar measurements are not affected by the error sources that affect the odometer. The idea is to invest the ground reflection and derive the forward speed of the onboard vehicle as the ACC keep a safe distance between the cars. A novel method based on extracting the ground reflection features is introduced to obtain the onboard vehicle's speed. The obtained speed is utilized with two accelerometers and one vertical gyroscope to produce the Radar-based RISS system. The proposed system has been integrated with the GPS producing a Radar-based RISS/GPS integrated navigation system. The system has been tested on a real road trajectory in a downtown area and involved several GPS signal outages. The results show the significant capabilities of the proposed system in keeping the navigation solution drift to a minimum especially when the GPS signal is in outage compared with the traditional RISS/GPS system.

Navigation systems for ships mainly include inertial navigation system (INS), “BeiDou” satellite navigation system, Global Positioning System (GPS), and Doppler navigation system and so on. The characteristics of each system are different. In order to improve the accuracy and fault-tolerant ability of naval-ship navigation system, an integrated navigation algorithm based on Measurement-based adaptive Kalman filtering algorithm (MAKF), improved Suge-Husa algorithm and non-reset federated Kalman filter structure is proposed in this paper. The algorithm uses the short-term high precision of the inertial navigation system and the prior velocity information of the ship to adaptively estimate the measurement noise characteristics of the satellite navigation system. When the satellite navigation system is unable to locate, the INS and the log are combined with the help of the prior velocity information. The simulation results show that the algorithm can effectively exploit the characteristics of each navigation system, and can output high-precision navigation results even when the GPS/BeiDou satellite navigation system fails.

In the integration of Global Positioning System (GPS) and Inertial Navigation System (INS), the commonly used Kalman filter provides satisfactory results if both sources of information are continuously available. However, GPS outages provoke a fast degradation of precision, especially in low dynamic trajectories such as a mobile platform device held by a human operator. To deal with this problem we propose a data-filtering scheme to apply to INS raw data prior to the integration with GPS. The proposed technique proves to be very valuable for mitigating the high short-term instability of raw INS data during the walking movement and is also capable of eliminating the induced undesirable human operator vibrations. Final imposed corrections adapted to the particular dynamical response of the INS sensor provide comparably accurate results and often better than those achieved in similar works with the use of the Kalman filter.