Observability analysis of four-position alignment for laser gyroscope strap-down inertial navigation system

This paper presents detailed derivations and further explanations of the state transformation extended Kalman filter (ST-EKF) from the common frame error definition perspective. Both the system error and measurement models of strapdown inertial navigation system (SINS)/Odometer (OD) tightly-coupled navigation are derived based on the ST-EKF. Both theoretical analysis and test results indicate the effectiveness of the proposed velocity error definition on mitigating the covariance-inconsistency problem that is caused by the specific force calculation error in the EKF state transition matrix. The excellent covariance-consistency of the ST-EKF makes it not necessary to remove gyro and accelerometer bias errors from the initial alignment Kalman filter states. This phenomenon can ensure the subsequent integrated navigation performance. Single-position ground SINS alignment experiments by using a navigation grade inertial measurement unit (IMU) showed that the estimated yaw angle from the conventional 15-state EKF slowly diverged over time. Furthermore, this phenomenon became more distinct when the initial yaw angle error was larger. In contrast, the estimated yaw angle from the proposed 15-state ST-EKF was significantly more stable and less degraded by large initial yaw angle errors. Long- distance land-vehicle SINS/OD integrated navigation tests also exhibited the ST-EKF's higher positioning and heading accuracy than the EKF.

Unscented Kalman filter for SINS alignment

The strapdown inertial navigation system can provide the navigation information for the boom-type roadheader in the unmanned roadway tunneling working face of the coal mine. However, the complex vibration caused by the cutting process of the boom-type roadheader may result in significant errors of its attitude and position measured by the strapdown inertial navigation system. Thus, an error compensation method based on the vibration characteristics of the roadheader is proposed in this paper. In order to further analyze the angular and linear vibration of the fuselage, as the main vibration sources of the roadheader, the dynamic model of the roadheader is formulated based on the cutting load. Following that, multiple sub-samples compensation algorithms for the coning and sculling errors are constructed. Simulation experiments were carried out under different subsample compensation algorithms, different coal and rock characteristics, and different types of roadheader. The experimental results show that the proposed error compensation algorithm can eliminate the effect of the angular and linear vibration on the measurement accuracy. The coning and sculling error of the strapdown inertial navigation system can reduce at least 52.21% and 42.89%, respectively. Finally, a strapdown inertial navigation error compensation accuracy experiment system is built, and the validity and superiority of the method proposed in this paper are verified through calculation and analysis of the data collected on the actual tunneling work face.

Noncommutativity error of a strapdown inertial navigation system (SINS) in an unmanned aerial vehicle's (UAV) vibration environment is analysed. The traditional analysis of noncommutativity errors is based on a coning motion model, which is inconsistent with a UAV's vibration environment. In this paper the UAV's vibration form is discussed and is modelled as a sinusoidal angular vibration and a random angular vibration. Then, SINS motion models under these two forms of vibration are built up and the formulas for the noncommutativity errors are derived separately. In addition, the effect of a multi-sample algorithm is explored, which is an effective method for compensating for noncommutativity errors in cases of coning motion. Finally, the UAV's vibration environment is simulated and it is indicated that the simulation results of the SINS's noncommutativity errors are consistent with theoretical analysis.

Extended Kalman filter (EKF) is a widely used estimator for integrated navigation systems, and it works well in general situations. However, in adverse conditions such as partially observable environments and highly dynamic maneuvers, the performance of the traditional EKF-based strap-down inertial navigation system (SINS)/GPS integrated navigation system is easily to be affected by the dynamic changes of the specific force, thus leading to the problem of error covariance inconsistency. Though the inconsistency problem can be overcome to some extent if the system matrix, the states and the error covariance matrix are propagated as fast as possible in the SINS calculation rate, the problem cannot be fully solved. State transformation extended Kalman filter (ST-EKF) mechanization, with a new converted velocity error model for the SINS, is proposed, which can also be used to solve the inconsistency problem. In the ST-EKF, the specific force vector in the system error model is replaced by the nearly constant gravity vector for local navigation. Since the propagation and the updating of the ST-EKF can be executed simultaneously in the updating interval, the computation cost is greatly reduced compared with the traditional EKF. Experiments for the GPS/SINS tightly coupled navigation, including linear vibration Monte Carlo test and an unmanned aerial vehicle flight test, are implemented to evaluate the performance of the proposed ST-EKF. The results show that the proposed ST-EKF has superior performance to the traditional EKF, especially in partially observable situations.

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.

On the error state selection for stationary SINS alignment and calibration Kalman filters – part I: Estimation algorithms

The article presents a method of determining gyro and accelerometer delays during calibration of strapdown inertial navigation systems (SINS) of navigation accuracy. The method uses the Kalman filter in SINS navigation mode and estimates errors in gyro and accelerometer delays and scale factors, sensitivity axes misalignment and drift, coordinates of accelerometer proof masses in the body-fixed frame. Application of SINS navigation mode during calibration reduces the requirements to accuracy of the rate table. The obtained estimates of calibration parameters are self-consistent, minimizing the resulting SINS error. The method was tested during calibration of FOG-based SINS.

The observability of the system states are the key indexes to check the convergence accuracy and convergence speed of designed Kalman filter. First of all, the error dynamic system equation and observation equation of strapdown inertial navigation system (SINS) online calibration are described in this paper, and then the system can be demonstrated to meet the law of piece-wise constant system (PWCS).Finally,the singular value of the system states based on the singlular value decomposition, which provides the necessary foundation of online calibration, are described.

There are periodic oscillation errors in the strapdown inertial navigation system (SINS) when it works in pure inertial navigation mode. It seriously restricts the navigation accuracy of the system. In order to improve the accuracy of the system, the traditional idea of the external horizontal damping in the stabilized inertial navigation system is introduced into SINS. We find that they are equivalent through comparing the damping network of the stabilized inertial navigation system with the compass alignment network. According to the equivalence, the external horizontal damping network of SINS is designed. And the difference between the velocity of the system itself and the velocity of the electromagnetic log are utilized to damp the periodic oscillation. At the same time, a horizontal damping algorithm based on the external velocity is proposed on the basis of the external horizontal damping idea. The effectiveness of the algorithm is verified by the static base of the three-axis turntable, the swing base experiment, and the vehicle simulation experiment. The experiment shows that the external damping network designed in this paper can suppress the system Schuler periodic oscillation error and improve the accuracy of the system.

The article describes an approach to ensuring stability and controllability of unmanned aerial vehicle (UAV) with unknown aerodynamic characteristics by computer simulation of the airplane flight along a given route in the meteorological standard atmosphere. This computer model takes into account the programmed flight of an unmanned aerial vehicle in the meteorological atmosphere along a given route with waypoints. For this purpose the model incorporates 5 feedback systems (FS) with autopilot (AP) that ensure the stability and controllability of an airplane. Besides the autopilot and the airplane glider the control system encompasses the Kalman filter and a strapdown inertial navigation system. The appropriate structure and parameters of the control system of the model were chosen on the basis of practical technical solutions of the de veloped UAVs. The closed control systems of the model are developed according to the equations considering generation of aerodynamic forces and moments, a model of the standard atmosphere, the routing scheme and the feedback system with autopilot. The stability and controllability of the model were analyzed according to the theory of feedback systems with the graphic plotting of Bode magnitude plot and Bode phase plot. With a view to the assessment of dynamic and fluctuation errors of the control systems the model is represented by stochastic differential control system with the Kalman filter and the strapdown inertial navigation system in quaternions. The results of the computer simulation showed that the Kalman filter estimates the measured parameters with the noise reduction under 10 dB. The strapdown inertial navigation system influences the general dynamics of the control system during the assessment of its stability and controllability. Changing the band of the control system at the expense of external perturbations affecting the plane can lead to instability, and in order to avoid it the robust autopilot is recommended.

Initial alignment is one of the key technologies of the inertial navigation. The initial alignment precision affects the navigation result. Researches show that the result of initial alignment depends on the observability of the system state variables. So it's necessary to enhance the system states observability to improve the accuracy and speed. A positioning method based on dual-axis rotating strapdown initial navigation system (SINS) is introduced in this paper which enhances the system states observability and improves the observability degree by changing the system error model matrix periodically. The PWCS (Piece-Wise Constant System) and SVD (Singular Value Decomposition) are used to analyse the observability. The results show that the system observability is improved; the misalignment angles and the gyroscope constant drifts are estimated in 1 hour, and accelerometers bias are estimated in 0.8 hour with the new dual-axis rotating inertial alignment and self-calibration method.

The accuracy and rate of convergence are two important performance factors for initial ground alignment of a strapdown inertial navigation system (SINS). For navigation-grade SINS, gyro biases and accelerometer offsets can be modeled as constant values during the alignment period, and they can be calibrated through two-position ground alignment schemes. In many situations for SINS ground alignment, the azimuth of the vehicle remains nearly constant. This quasi-stationary alignment information can be used as an augmented measurement. In this paper, a piecewise combined Kalman filter utilizing relative azimuth constraint (RATP) is proposed to improve the alignment precision and to reduce the time consumption for error convergence. It is presented that a piecewise time-invariant linear system can be combined into a whole extended time-invariant linear system so that a piecewise combined Kalman filter can be designed for state estimation. A two-position ground alignment algorithm for SINS is designed based on the proposed piecewise combined Kalman filter. Numerical simulations and experimental results show its superiority to the conventional algorithms in terms of accuracy and the rate of convergence.

Alignment accuracy and alignment time are two important indexes of the initial alignment procedure of a strapdown inertial navigation system (SINS). However, large misalignment angles will bring nonlinear problems of SINS error models and prolong the convergence time of the initial alignment procedure. In this paper, an innovative control scheme is proposed for the initial alignment of SINS on stationary base, which is implemented by active disturbance rejection control (ADRC). Compared with the conventional compass method, the proposed method has a lower requirement on high accuracy of the coarse alignment. Therefore, the total alignment time is decreased, meanwhile the interferences caused by the system errors are decreased and the stability of the closed-loop system is enhanced. Simulations and experiments show that the alignment procedure has been greatly hastened and the accuracy has been improved.

Strapdown inertial navigation systems (SINS) are widely used in modern air transport. The service life of such systems is decades. During this time, the characteristics of such systems may deteriorate due to the degradation of inertial sensors - gyroscopes and accelerometers. Under these conditions, in order to maintain the required accuracy of the SINS during the entire period of operation, it is necessary either to periodically carry out routine maintenance with the onboard system, or to continuously adapt the used sensor measurement model in terms of compensating for errors that arise. The second direction, which we will call calibration, has the advantage over the first one that it is carried out automatically by the system itself and does not require any additional equipment or additional maintenance work. The known method of SINS recalibration is based on the integration of information from the SINS and from the receiver of satellite radio navigation signals (SRNS). Such calibration, firstly, significantly depends on the availability and quality of satellite information, and secondly, it is possible only for integrated navigation systems in which the inertial subsystem is supplemented by a SRNS receiver. In contrast to the known method, this article solves the problem of autonomous SINS calibration, which is carried out after each flight. The solution is based on a linearized inertial navigation error model based on the boundary conditions of the state vector (at the beginning and end of the flight). The external information used consists only of the initial values of the coordinates and the current measurements of the baroaltimeter. As a result of the decision at the end of the flight, the errors of gyroscopes and accelerometers are determined, as well as the error in determining the final values of latitude and longitude in the SINS. Sensor errors can be used in subsequent system activations, which improves the accuracy of its operation as a whole. The analysis of the suitability and effectiveness of the developed methodology was carried out on a typical flight simulation program.