Uniform Nonlinear Error Model Based on Gibbs Parameter for the INS

This paper presents new algorithmic methods for accuracy improvement of autonomous inertial navigation systems of aircrafts. Firstly, an inertial navigation system platform and its nonlinear error model are considered, and the correction schemes are presented for autonomous inertial navigation systems using internal information. Next, a correction algorithm is proposed based on signals from precession angle sensors. A vector of reduced measurements for the estimation algorithm is formulated using the information about the angles of precession. Finally, the accuracy of the developed correction algorithms for autonomous inertial navigation systems of aircrafts is studied. Numerical solutions for the correction algorithm are presented by the adaptive Kalman filter for the measurement data from the sensors. Real data of navigation system Ts-060K are obtained in laboratory experiments, which validates the proposed algorithms.

In this paper, a robust unscented Kalman filter (UKF) based on the generalized maximum likelihood estimation (M-estimation) is proposed to improve the robustness of the integrated navigation system of Global Navigation Satellite System and Inertial Measurement Unit. The UKF is a variation of Kalman filter by which the Jacobian matrix calculation in a nonlinear system state model is not necessary. The proposed robust M–M unscented Kalman filter (RMUKF) applies the M-estimation principle to both functional model errors and measurement errors. Hence, this robust filter attenuates the influences of disturbances in the dynamic model and of measurement outliers without linearizing the nonlinear state space model. In addition, an equivalent weight matrix, composed of the bi-factor shrink elements, is proposed in order to keep the original correlation coefficients of the predicted state unchanged. Furthermore, a nonlinear error model is used as the dynamic equation to verify the performance of the proposed RMUKF with a simulation and field test. Compared with the conventional UKF, the impacts of measurement outliers and system disturbances on the state estimation are both controlled by RMUKF.

A novel nonlinear attitude error model based on square root cubature information filter (SR-CIF) is proposed aiming to speed up the convergence rate of DVL-aided strapdown inertial navigation system (SINS) in-motion initial alignment for autonomous underwater vehicle (AUV) when both large initial heading error and large initial level attitude errors exist The new nonlinear attitude error model and measurement model are applicable for initial alignment after a short-time coarse alignment with large attitude errors exist. The SR-CIF embeds the whole iterative process into the data structure framework of the information filtering, replacing the covariance matrix in the square root cubature Kalman filter (SR-CKF) with an information matrix which simplifies the filter initialization. The square root technology ensures the symmetry and positive definiteness of the information matrix with enhanced stability of the filter. The simulation and experimental results indicate that the proposed DVL-aided alignment filter is effective with large initial attitude errors. The rate of convergence and estimation accuracy of the SR-CIF is higher than that of the conventional SR-CKF with large attitude misalignments.

This paper proposes a twice rapid transfer alignment algorithm based on dual models in order to solve the problems such as long convergence time, poor accuracy, and heavy computation burden resulting from the traditional nonlinear error models. The quaternion matching method based on quaternion error model along with the extended Kalman filter (EKF) is applied to deal with the large misalignment in the first phase. Then in the second transfer alignment phase, velocity plus attitude matching method as well as classical Kalman filter is adopted. The simulation and the results of vehicle tests demonstrate that this method combines the advantages of both nonlinear and linear error models with the guarantee of accuracy and fastness.

We consider the assessment of outliers and influential observation in non-linear measurement error models. Residuals, leverage measures and case-deletiondiagonostics are examined. The method of local influence is also applied to the models. In particular, the perturbation of measurement error variances has been found useful in assessing the adequancy of the model assumptions. A numerical example is given to illustrate the application of the diagonostics.

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.

Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) are the most commonly used navigation systems. They both have unique advantages and disadvantages. GNSS is capable of generating precise navigation solutions while enough satellites are in view. However, the GNSS signals are sensitive to the environment. While the signals is attenuated, the GNSS receiver will fail to provide reliable navigation solutions. INS is an advanced navigation system built based on Newton's law. Due to the random noises contained in the Inertial Measurement Unit (IMU), the INS navigation solutions errors diverge over time. Therefore, effective integration of the two common systems can obtain better navigation results than any individual system. In this paper, for enhancing the GNSS/INS tightly integration system with low cost, multiple receivers were employed in the tight integration. Pseudo-range and Pseudo-range rates from the multiple receivers were employed to compose the measurement vector of the integration filter. In order to reduce the computation load, a measurement difference method was proposed. The state vector dimension could be reduced with the measurement difference scheme. Both simulation and field test were carried out for evaluating the performance of the proposed method. Since it was hard to obtain GNSS raw measurements from commercial receivers, self-developed DSP+FPGA (Digital Signal Processor, DSP; Field Programmable Gate Array, FPGA) based GNSS receivers were employed in the field test. The statistical analysis of the results showed that the positioning errors decreased with the receiver's amount increasing. In addition, a measurement difference method was proposed to reduce the state vector dimension for saving the computation load with the identical navigation solutions accuracy.

In recent years, quantum computing has been applied in optimizing different challenging systems in the domains of science and engineering. This work reflects the identification of the input nonlinear output error (I-NOE) model by using the Quantum-based avian navigation optimizer algorithm (QANA). QANA is an evolutionary method inspired by the precision navigation of migratory birds. The assessment of QANA is achieved on various iterations, population, and noise levels. The complexity, statistical, and convergence investigation of QANA with arithmetic optimization algorithm (AOA), coati optimization algorithm (COA), grey wolf optimizer (GWO), particle swarm optimization (PSO), synergistic swarm optimization algorithm (SSOA), and velocity pausing particle swarm optimization (VPPSO) approves the robustness of QANA for I-NOE model identification.

In modern navigation applications, Inertial Navigation System (INS) is attractive for integrating with Global Positioning System (GPS). Although traditional GPS/INS integrated systems can bridge the GPS gaps, the navigation capability is strongly dependent on the performances of standalone INS. As an important complementary, a new terrestrial, Radio-Frequency (RF) based, distance measurement technology “Locata” can provide continuously time-synchronised ranging signals even in many GPS challenged environments e.g. poor satellite geometry, signal blockage in suburban, tunnels, high rise buildings canyon. This paper investigates the integration of Locata, GPS, and INS with a focus on the loosely-coupled triple integration algorithm. Firstly, the Conventional Kalman Filtering (CKF) based triple integration of Locata/GPS/INS architecture is described and briefly discussed. Secondly, to overcome the pitfalls of conventional Locata/GPS/INS integration algorithm, an Adaptive Dual Kalman Filtering (ADKF) algorithm is proposed and developed in three stages: (1) To enhance the reliability of position and velocity (PV) quantities generated from Locata/GPS integrated sensors, the 1st KF is additionally constructed to reliably estimate the PV solution before fusing INS sensor. (2) Combining the 15-state INS error model and the measurements which are the differences between PV solution from the 1st KF and INS sensor, the 2nd KF is subsequently employed to correct the INS navigation errors. (3) The final integration solution is reversely used as the feedback for precisely estimating the stochastic model (i.e. variance of dynamic and observation model noise) of the 1st KF. Finally, the real flight experiment is carried out to demonstrate the efficiency and validity of Locata/GPS/INS integration algorithms. The results show that: (1) Conventional GPS/INS integration performs well but its accuracy dramatically decreases when GPS signals are unavailable for a short period. (2) Augmented by Locata, GPS/INS produces tolerable results in whole experiment even without aiding of GPS. (3) By additionally operation of the 1st KF and adaptively estimating its stochastic model with feedback of integration solution, ADKF achieves more accurate and reliable position, velocity and attitude (PVA) solution than CKF.KeywordsINS errorLocata/GPS/INS integrationAdaptive Kalman filteringStochastic model

ABSTRACT: This paper compares the use of an inertial navigation system (INS) and a multiple GPS antenna system for attitude determination of an off-road vehicle. The INS system currently provides a less expensive attitude solution than the multiple GPS antenna system. Additionally, the INS system does not suffer from GPS errors resulting from multipath and antenna blockages. A Kalman filter incorporates the INS measurements with centimeter-level carrier-phase differential GPS (DGPS) measurements from one position antenna for complete position and attitude estimation of an off-road vehicle. The centimeter-level accuracy of DGPS allows for precise calibrations of the INS system for accurate attitude estimation. The paper shows that a low-cost INS system is capable of providing the attitude accuracy necessary for centimeter-level control of an off-road vehicle. Results of using the INS system in conjunction with DGPS position measurements to autonomously control a farm tractor are presented.

This paper presents a new method for in-field calibration of accelerometers to address the problems of low efficiency and high cost associated with traditional calibration methods. A nonlinear mathematical model of the accelerometer is established, and the cost function is analysed and deduced the cost function. Then, an adaptive Northern Goshawk Optimisation (NGO) algorithm based on prior knowledge enhancement is introduced. A method of collecting multi-position data with a hand-held accelerometer is introduced, and the proposed algorithm is used to in-field calibrate nine parameters of the accelerometer’s nonlinear error model. In addition, simulation is used to compare the results of calibrating the accelerometer using the proposed algorithm and the original algorithm, demonstrating the superiority of the proposed algorithm. Finally, experimental results confirm that the proposed method can rapidly calibrate accelerometer error parameters without relying on complex equipment and with greater accuracy than traditional methods.

When the vehicle passes through the tunnel or bridge, Global Positioning System (GPS) will fail due to signal occlusion or interference. In order to improve the positioning accuracy of vehicle-carried inertial navigation system (INS) in GPS rejection environment, the lateral constraint method based on vehicle-carried INS is studied in this article. According to the characteristics of lateral constraint, in the area with good GPS signal, installation errors between the INS body coordinate frame and the vehicle coordinate frame are estimated at the same time of integrated navigation. In the GPS-denied area, the estimated installation errors are compensated to calculate the reference velocity at first. After compensation, the difference between INS velocity and reference velocity is taken as the measurement. Finally, the Kalman filter model is established to correct the inertial navigation position. In addition, the simulation and experimental verification of the proposed lateral constraint method are carried out. The results show that the INS positioning accuracy can be improved above 50% by using the lateral constraint method in GPS-denied environment, which verifies the effectiveness of the proposed lateral constraint method.

Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) integration requires accurate modelling of both INS deterministic and stochastic errors. The Allan Variance (AV) analysis on INS static data is one method of determining INS stochastic errors. However, it is known that INS errors can vary depending on a vehicle’s motion and environment, and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic. In order to overcome this limitation, this paper proposes the use of Dynamic Allan Variance (DAV). The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV. The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV, applied on a kinematic dataset compared to the AV, applied on a static laboratory dataset.

Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a nonlinear system. We describe how a nonlinear model error model can be developed, that allows a complete linear design process that results in a closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) against the nonlinear error. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of ‘practical stability’ for robust control design, with possible non‐linear model errors. We use affine norms for that purpose. Copyright © 2004 John Wiley & Sons, Ltd.

In present days, real time navigation depends on Kalman filter to fuse data from Global Positioning System (GPS) and Inertial Navigation System (INS). But there exist drawbacks like long design time, requirement of prior knowledge in fusing data from GPS and INS using Kalman Filter. In order to overcome the drawbacks of Kalman filter, GPS and INS integration are done using Artificial Neural Networks (ANN) like FFNNs. But still there exists certain drawbacks like less accuracy in FFNNs for GPS and INS data integration. Therefore, this paper introduces Higher Order Neural Networks (HONNs) approach for INS and GPS data integration to overcome the drawback. A higher order feed forward neural network architecture with optimum number of nodes is used. In the given architectures, the replacement of summation at each node by multiplication results in more powerful mapping, because of its capability of processing higher-order information from training data. Performance comparison of HONNs with FFNNs shows that the proposed architecture provides satisfactory results in terms of error rate and number of epochs. The HONNs like Multiplicative Neural Network (MNN) module and Sigma-Pi-ANN module and Traditional Feed Forward Neural Networks(FFNNs) like Radial Basis Function Neural Network (RBF) module and Back propagation Neural Network (BPN) module are trained to predict the INS position error and provide accurate position of the moving aircrafts. Sigma-Pi ANN is found to be the best in terms of accuracy, number of epochs and execution time among the two HONNs.