State transformation extended Kalman filter for GPS/SINS tightly coupled integration

The extended Kalman filter (EKF) has been used widely in Global Position System (GPS) and Strapdown Inertial Navigation Systems (SINS) integrated navigation systems,which simply linearizes all nonlinear models.However, careful treatment of the nonlinearity of the system models is particularly critical when the integrated systems use low cost micro-electro-mechanical (MEMS) inertial sensors. Hence application of the EKF in MEMS inertial sensor-based integrated navigation systems will likely lead to inaccurate results. To overcome the shortcomings of the EKF, the unscented Kalman filter (UKF) has been proposed.The UKF does not require the linearization of the system models. Alternatively it uses a set of deterministically selected "sigma-points",which completely capture the true mean and covariance of the original random vector. Then these sigma-points are propagated through the nonlinear models.This captures the mean and covariance to second order accuracy for arbitrary nonlinear functions. In this paper the EKF and UKF are applied in GPS/SINS integrated systems respectively. Simulation result demonstrates that the performance of the UKF is better than the EKF in MEMS inertial sensor-based SINS/GPS integrated systems.

High dynamic aircraft is a very attractive new generation vehicles, in which provides near space aviation with large flight envelope both speed and altitude, for example the hypersonic vehicles. The complex flight environments for high dynamic vehicles require high accuracy and stability navigation scheme. Since the conventional Strapdown Inertial Navigation System (SINS) and Global Position System (GPS) federal integrated scheme based on EKF (Extended Kalman Filter) is invalidation in GPS single blackout situation because of high speed flight, a new high precision and stability integrated navigation approach is presented in this paper, in which the SINS, GPS and Celestial Navigation System (CNS) is combined as a federal information fusion configuration based on nonlinear Unscented Kalman Filter (UKF) algorithm. Firstly, the new integrated system state error is modeled. According to this error model, the SINS system is used as the navigation solution mathematic platform. The SINS combine with GPS constitute one error estimation filter subsystem based on UKF to obtain local optimal estimation, and the SINS combine with CNS constitute another error estimation subsystem. A non-reset federated configuration filter based on partial information is proposed to fuse two local optimal estimations to get global optimal error estimation, and the global optimal estimation is used to correct the SINS navigation solution. The χ 2 fault detection method is used to detect the subsystem fault, and the fault subsystem is isolation through fault interval to protect system away from the divergence. The integrated system takes advantages of SINS, GPS and CNS to an immense improvement for high accuracy and reliably high dynamic navigation application. Simulation result shows that federated fusion of using GPS and CNS to revise SINS solution is reasonable and availably with good estimation performance, which are satisfied with the demands of high dynamic flight navigation. The UKF is superior than EKF based integrated scheme, in which has smaller estimation error and quickly convergence rate.

Unscented Kalman filter for SINS alignment

SINS/ANS integration for augmented performance navigation solution using unscented Kalman filtering

The integrated navigation system of strapdown inertial navigation system (SINS) and odometer (OD) is a commonly used vehicle positioning system. The installation errors caused by the difference between the installation positions of SINS and OD mainly include the installation deflection angle and lever arm, which will reduce the positioning accuracy. The traditional calibration method is to expand the installation deflection angle error and lever arm error into state variables, the velocity difference under nonholonomic constraint (NHC) is taken as the measurement to establish the Kalman filter model for online calibration, but this method seriously depends on the sensor accuracy. In order to calibrate the installation errors of low-precision SINS, this paper improves NHC, adds the difference between the centripetal acceleration measured by odometer and calculated by SINS as measurement on the basis of the original measurement, and introduces a low-pass filter to reduce the interference of vehicle vibration on the accelerometer.The experimental results show that the proposed algorithm has better convergence of the installation deflection angle, and the error between the estimation results of the forward lever arm and the actual measurement results is less than 0.1m; After compensating the installation errors of the improved NHC, the maximum positioning errors in the east and north directions are reduced by 63.19% and 43.51% respectively, the height error is also greatly reduced, and the positioning accuracy of the integrated navigation system is significantly improved.

In this paper, we investigate the problem of autonomous integrated navigation of strapdown inertial navigation system (SINS)/ celestial navigation system (CNS) for a ballistic missile. To handle the nonlinear missile dynamic model, three filtering methods including extended Kalman filter (EKF), extended Kalman particle filter (EKPF) and unscented particle filter (UPF) are utilized to fusion the integrated navigation system and improve the navigation accuracy. The performance of the navigation system based on the three methods is analyzed and compared. Simulation results indicate that the UPF can provide the highest navigation accuracy with the price of highest computation burden.

Celestial navigation system (CNS) is a completely autonomous navigation technology with strong anti-interference ability and high navigation accuracy, which has a great application prospect. Aim at defect of traditional integrated navigation system using attitude angle measurement celestial navigation system and strapdown inertial navigation system (SINS), which can only correct of strapdown inertial navigation system’s gyro drift. This paper proposes an improved integrated navigation system that add double-star positioning celestial navigation to traditional SINS/CNS integrated navigation system, meanwhile, introduces the fault detection technology based on statistical distance to solve the problem that inaccuracy of measurement information leads to the integrated navigation system’s performance degradation. By analyzing the simulation results, the improved navigation system can inhibit divergence of system and obtain high accurate and stable navigation information.

There are the scale factor error of LDV (laser Doppler velocimeter) and the misalignment between the SINS (Strapdown inertial navigation system) and the vehicle in a SINS/LDV integrated navigation system. In this paper, the effects of these errors on the attitude, velocity and position of dead reckoning are derived, and a new online calibration method aiming to calibrate the scale factor of LDV and the misalignment between the SINS and the vehicle for the integrated system is put forward. This method, which is utilize the velocity and position of the Global Position System (GPS) as references, use the velocity error and position error of dead reckoning to estimate these errors. Through simulation and experiment, the validity and feasibility of the method are verified. The results show that the scale factor and the misalignment can be calibrated with satisfying accuracy, and the related research can provide technical support for high precision navigation of SINS/LDV integrated navigation systems.

To improve the performance of strapdown inertial navigation system (SINS)/ Doppler velocity logs (DVL) integrated navigation system, a new Interacting Multiple Model Feedback Particle Filter (IMMFPF) approach is proposed under the condition of complex and changeable underwater environment. In this scheme, the Interacting Multiple Model uses to deal with the model switch, while FPF approach takes each particle as a controllable stochastic system. By finding the solution about the Euler-Lagrange boundary value, the optimal feedback control law of Kullback-Leibler distance is obtained, and then the state of the particle itself is corrected and updated. Both simulations and field test illustrate that proposed IMMFPF approach can achieve a more accurate solution and make a more correct and effective response for SINS/DVL integrated navigation system.

To solve the problem of information fusion in the strapdown inertial navigation system (SINS)/celestial navigation system (CNS)/global positioning system (GPS) integrated navigation system described by the nonlinear/non-Gaussian error models, a new algorithm called the federated unscented particle filtering (FUPF) algorithm was introduced. In this algorithm, the unscented particle filter (UPF) served as the local filter, the federated filter was used to fuse outputs of all local filters, and the global filter result was obtained. Because the algorithm was not confined to the assumption of Gaussian noise, it was of great significance to integrated navigation systems described by the non-Gaussian noise. The proposed algorithm was tested in a vehicle’s maneuvering trajectory, which included six flight phases: climbing, level flight, left turning, level flight, right turning and level flight. Simulation results are presented to demonstrate the improved performance of the FUPF over conventional federated unscented Kalman filter (FUKF). For instance, the mean of position-error decreases from (0.640×10−6 rad, 0.667×10−6 rad, 4.25 m) of FUKF to (0.403×10−6 rad, 0.251×10−6 rad, 1.36 m) of FUPF. In comparison of the FUKF, the FUPF performs more accurate in the SINS/CNS/GPS system described by the nonlinear/non-Gaussian error models.

Recently, the Strapdown Inertial Navigation System (SDINS) has been successfully integrated with Global Positioning System (GPS) to obtain reliable navigation solutions. SDINS is based on Micro-Electro Mechanical System (MEMS) sensors such as accelerometer and gyroscope sensors. To improve the overall performance of the integrated navigation system, the Inertial Measurement Unit (IMU) readings is treated through effectively band-limiting the high frequency noise using the Discrete Wavelet Multi-resolution Algorithm (DWMRA) as a first step, while the second step is to enhance the navigation position and velocity through utilizing the Nonlinear Autoregressive model with eXogenous inputs (NARX) to fuse GPS and INS systems. The performance of the proposed integrated navigation system is validated through comparison with other systems. Finally, the obtained results suggest a promising and superior prospect for NARX in the field of navigation for low-cost IMU’s during GPS denied signals, since it outperforms the Conventional Neural Network (CNN) and Extended Kalman Filter (EKF) by 84% and 92%, respectively.

For the guidance, control and navigation of autonomous vehicles, both positioning and orientation are important for mission success and surveillance. Global positioning system (GPS) and strapdown inertial navigation system (SINS) have complementary characteristics to overcome the demerits of each other and can well perform as integrated navigation system. The observability analysis of low-cost SINS/GPS from many researches shown that the heading and yaw rate gyro bias is unobservable in straight motion and with constant acceleration. This paper presents integration of low-cost SINS/GPS aided with odometer and heading from two antennae GPS receiver to overcome this problem and to control the accuracy degradation during GPS outage. The carrier phase measurements are processed to obtain the heading from two antennae position measurement. The obtained heading and position from GPS and velocity measurement from odometer are used as observation input to extended Kalman filter (EKF) for the heading and positioning accuracy improvement of SINS/odometer/GPS integrated system for land vehicle navigation. When GPS signal is unavailable, the filter switches to SINS/odometer integration to control the position and velocity errors growth during this period. The observation model for heading measurement from two antennae is derived for the designed system. A field test was conducted to check the effectiveness using proposed method for heading and positioning accuracy improvement. The test results showed that Low-cost IMU/Odometer/ Two Antennae GPS integrated systems' accuracy both in position and heading is improved significantly.

For the long-range voyage and light Autonomous Underwater Vehicle (AUV), the high-precision navigation and positioning is the key point in the completion of the task. Therefore, this paper designs an underwater integrated navigation system, including the strapdown inertial navigation system (SINS), Doppler velocity loci (DVL), magnetometers and depth sensor. Based on the principle of each navigation sensor and the corresponding error model, the mathematic model of each sub-filter of the integrated navigation system is firstly established. Secondly, combining the combination filter and federated filtering theory, the integrated navigation system based on federated filtering is designed. Finally, to eliminate the influence of unknown or time-varying statistical characteristics on the Kalman filter (KF), a new federated filtering algorithm based on Sage-Husa adaptive KF is proposed to estimate each local filter. And the corresponding simulation results will show the performance of the research.

The ring laser gyro (RLG) dither axis will bend and exhibit errors due to the specific forces acting on the instrument, which are known as g-sensitive misalignments of the gyros. The g-sensitive misalignments of the RLG triad will cause severe attitude error in vibration or maneuver environments where large-amplitude specific forces and angular rates coexist. However, g-sensitive misalignments are usually ignored when calibrating the strapdown inertial navigation system (SINS). This paper proposes a novel method to calibrate the g-sensitive misalignments of an RLG triad in linear vibration environments. With the SINS is attached to a linear vibration bench through outer rubber dampers, rocking of the SINS can occur when the linear vibration is performed on the SINS. Therefore, linear vibration environments can be created to simulate the harsh environment during aircraft flight. By analyzing the mathematical model of g-sensitive misalignments, the relationship between attitude errors and specific forces as well as angular rates is established, whereby a calibration scheme with approximately optimal observations is designed. Vibration experiments are conducted to calibrate g-sensitive misalignments of the RLG triad. Vibration tests also show that SINS velocity error decreases significantly after g-sensitive misalignments compensation.

In this paper, we propose a systematic framework for the autonomous navigation system based on distributed filtering for an Unmanned Aerial Vehicle (UAV). The proposed framework consists of the design and algorithm of the autonomous navigation. Therein, the camera mounted on the UAV functions as a navigation sensor targeted for navigation and positioning. In order to reduce the computational complexity and exclude the risk caused by Global Positioning System (GPS) outage, an autonomous navigation system based on distributed filtering is designed and realized. When GPS is available by monitoring the GPS integrity, sensor information from Strapdown Inertial Navigation System (SINS) and GPS is fused using a 7-state Conventional Kalman Filter (CKF) to estimate the full UAV state (position, velocity and attitude); when GPS is unavailable, sensor information from gyroscopes, accelerometers and magnetometer is fused using a 4-state Extended Kalman Filter (EKF) to estimate the attitude and heading of the UAV, and sensor information from SINS and vision positioning system is fused using a 7-state Incoordinate Interval Kalman Filter (IIKF) to estimate the position and velocity of the UAV. In addition, the second-order vertical channel damping loop is adopted to fuse measurements from a barometer with those of SINS, which suppresses the divergence of the vertical channel error and makes the altitude information calculated by SINS trustable. Both ground and flight experiments of the autonomous navigation system have been carried out. The test results show that the system can provide stabilized attitude information in long durations, and can realize the automatic flight control of UAV.