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This paper proposes a dynamic aided inertial navigation method to improve the attitude accuracy for ocean vehicles. The proposed method includes a dynamic identification algorithm and the utilisation of dynamic constraints to derive additional observations. The derived additional observations are used to update the filters and limit the attitude error based on the dynamic knowledge. In this paper, two dynamic conditions, constant speed cruise and quasi-static, are identified and corresponding additional velocity and position observations are derived. Simulation and experimental results show that the proposed method can improve and guarantee the accuracy of the attitude. The method can be used as a backup method to bridge external information outages or unavailability. Both the features of independence of external support and integrity of the Inertial Navigation System (INS) are enhanced.
This paper proposes a simplified algorithm for reducing the computational load of the conventional underwater integrated navigation system. The system usually comprises a three-dimensional accelerometer, a three-dimensional gyroscope, a three-dimensional Doppler Velocity Log (DVL) and a data fusion algorithm, such as a Kalman Filter (KF). Since the expected variations of roll, pitch and depth are small, these quantities are assumed to be constant, and the proposed system is designed in a two-dimensional form. Due to the low speed of the vehicle, the nonlinear dynamic equation of the velocity can be simplified in a linear form. We also simplify the conventional KF in order to avoid matrix multiplications and matrix inversions. The performance of the designed system is evaluated in a sea trial by an Autonomous Underwater Vehicle (AUV). The results show that the proposed system can significantly reduce the computational load of the conventional integrated navigation system without a significant reduction in position and velocity accuracy.
A novel synthetic air data estimation method without using air data sensors is presented, and the method only relies on the information from the Navigation System (NS) and Flight Control System (FCS). The aircraft's aerodynamic model is also required to make a connection between the FCS control parameters and the NS measurements. The airspeed, angle of attack and sideslip, angular velocity and wind speed are defined as state vectors, and state equations are established through the aircraft's aerodynamic model and dynamics. Linear velocity and angular velocity provided by the navigation system are considered as the measurement vector. To deal with variable wind fields, a novel Initialised Three-step Extended Kalman Filter (ITEKF), which considers the wind speed as an unknown input, is developed to track the variation of wind speed. Simulation results based on a Generic Hypersonic Vehicle (GHV) model are presented and compared with an existing method. Factors affecting the method's accuracy include the navigation system accuracy and the aerodynamic model error, are also discussed.
The paper presents a laser guided bomb guidance law based on the linear quadratic differential game theory, where a case of two perpendicular planes with two state variables in each plane has been considered. The Kalman filtering method has been used for noise removal from the measured signals and for estimation of the missing state variable values needed for the optimal guidance law. Optimisation has been conducted with respect to minimisation of the performance index. Comparative analysis of different guidance laws is done. A statistical analysis is performed to obtain the terminal miss distance in dependence on total flight time.
A Position and Orientation System (POS) integrating an Inertial Navigation Systems (INS) and the Global Positioning System (GPS) is a key component of remote sensing motion compensation. It can provide reliable and high-frequency high-precision motion information using a Kalman Filter (KF) during GPS availability. However, the performance of a POS significantly degrades during GPS outages. To maintain reliable POS outputs, this paper proposes a new hybrid predictor based on modelling the nonlinear time-series data-driven INS-errors using Noisy Input Gaussian Process Regression (NIGPR), which takes the input noise into account. The proposed approach is used to learn the nonlinear INS-errors model when GPS signals are available. When GPS outages occur, it starts to predict the observation measurement, and then feeds it to a KF as a virtual update to estimate all the INS errors. The proposed approach is verified in a real airplane, which combines a POS and Synthetic Aperture Radar (SAR). Experimental results show that the proposed approach significantly improves the performance of the POS, with improvements more than 90% better than a KF and 10% better than a Gaussian Process Regression (GPR/KF) combination during various GPS outages.
The hierarchical credibility model was introduced, and extended, in the 70s and early 80s. It deals with the estimation of parameters that characterize the nodes of a tree structure. That model is limited, however, by the fact that its parameters are assumed fixed over time. This causes the model's parameter estimates to track the parameters poorly when the latter are subject to variation over time. This paper seeks to remove this limitation by assuming the parameters in question to follow a process akin to a random walk over time, producing an evolutionary hierarchical model. The specific form of the model is compatible with the use of the Kalman filter for parameter estimation and forecasting. The application of the Kalman filter is conceptually straightforward, but the tree structure of the model parameters can be extensive, and some effort is required to retain organization of the updating algorithm. This is achieved by suitable manipulation of the graph associated with the tree. The graph matrix then appears in the matrix calculations inherent in the Kalman filter. A numerical example is included to illustrate the application of the filter to the model.
A new integration of the acquisition and tracking modes is proposed for the integration of a Celestial Navigation System (CNS) and a Strapdown Inertial Navigation System (SINS). After the integration converges in the acquisition mode, it switches to the tracking mode. In the tracking mode, star pattern recognition is unnecessary and the integration is implemented in a cascaded filter scheme. A pre-filter is designed for each identified star and the output of the pre-filter is fused with the attitude of the SINS in the cascaded navigation filter. Both the pre-filter and the navigation filter are designed in detail. The measurements of the pre-filter are the positions on the image plane of one identified star. Both the starlight direction and its error are estimated in the pre-filter. The estimated starlight directions of all identified stars are the measurements of the navigation filter. The simulation results show that both the reliability and accuracy of the integration are improved and the integration is effective when only one star is identified in a period.
It is desirable for complex engineered systems to be resilient to various sources of uncertainty throughout their life cycle. Such systems are high in cost and complexity, and often incorporate highly sophisticated materials, components, design, and other technologies. There are many uncertainties such systems will face throughout their life cycles due to changes in internal and external conditions, or states of interest, to the designer, such as technology readiness, market conditions, or system health. These states of interest affect the success of the system design with respect to the main objectives and application of the system, and are generally uncertain over the life cycle of the system. To address such uncertainties, we propose a resilient design approach for engineering systems. We utilize a Kalman filter approach to model the uncertain future states of interest. Then, based upon the modeled states, the optimal change in the design of the system is achieved to respond to the new states. This resilient method is applicable in systems when the ability to change is embedded in the system design. A design framework is proposed encompassing a set of definitions, metrics, and methodologies. A case study of a communication satellite system is presented to illustrate the features of the approach.
In Strapdown Inertial Navigation System (SINS)/Odometer (OD) integrated navigation systems, OD scale factor errors change with roadways and vehicle loads. In addition, the random noises of gyros and accelerometers tend to vary with time. These factors may cause the Kalman filter to be degraded or even diverge. To address this problem and reduce the computation load, an Adaptive Two-stage Kalman Filter (ATKF) for SINS/OD integrated navigation systems is proposed. In the Two-stage Kalman Filter (TKF), only the innovation in the bias estimator is a white noise sequence with zero-mean while the innovation in the bias-free estimator is not zero-mean. Based on this fact, a novel algorithm for computing adaptive factors is presented. The proposed ATKF is evaluated in a SINS/OD integrated navigation system, and the simulation results show that it is effective in estimating the change of the OD scale factor error and robust to the varying process noises. A real experiment is carried out to further validate the performance of the proposed algorithm.
Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.
Regression analysis with stationary errors is extended to the case when observations are not equally spaced. The errors are modelled as either a discrete-time ARMA process with missing observations, or as a continuous-time autoregression with observational error observed at arbitrary times. Using a state-space representation, a Kalman filter is used to calculate the exact likelihood. The linear regression coefficients are separated out of the likelihood so non-linear optimization is required only with respect to the parameters modelling the error structure.
Numerous applications, not only Earth-based, but also space-based, have strengthened the interest of the international scientific community in using Global Navigation Satellite Systems (GNSSs) as navigation systems for space missions that require good accuracy and low operating costs. Indeed, already successfully used in Low Earth Orbits (LEOs), GNSS-based navigation systems can maximise the autonomy of a spacecraft while reducing the burden and the costs of ground operations. That is why GNSS is also attractive for applications in higher Earth orbits up to the Moon, such as in Moon Transfer Orbits (MTOs). However, the higher the altitude the receiver is above the GNSS constellations, the poorer and the weaker are the relative geometry and the received signal powers, respectively, leading to a significant navigation accuracy reduction. In order to improve the achievable GNSS performance in MTOs, we consider in this paper an adaptive orbital filter that fuses the GNSS observations with an orbital forces model. Simulation results show a navigation accuracy significantly higher than that attainable individually by a standalone GNSS receiver or by means of a pure orbital propagation.
In various applications of land vehicle navigation and automatic guidance systems, Global Navigation Satellite System/Inertial Measurement Unit (GNSS/IMU) positioning performance crucially depends on the attitude determination accuracy affected by gyro and accelerometer bias instabilities. Traditional bias estimation approaches based on the Kalman filter suffer from implementation complexity and require non-intuitive tuning procedures. In this paper we propose, as an alternative, a simple observer that estimates inertial sensor biases exclusively in terms of quantities with obvious geometrical meaning. By this, any multidimensional vector-matrix operations are avoided and observer tuning is substantially simplified. The observer has been successfully tested in a farming vehicle navigation system.
This paper presents a new approach to accurately track a moving vehicle with a multiview setup of red–green–blue depth (RGBD) cameras. We first propose a correction method to eliminate a shift, which occurs in depth sensors when they become worn. This issue could not be otherwise corrected with the ordinary calibration procedure. Next, we present a sensor-wise filtering system to correct for an unknown vehicle motion. A data fusion algorithm is then used to optimally merge the sensor-wise estimated trajectories. We implement most parts of our solution in the graphic processor. Hence, the whole system is able to operate at up to 25 frames per second with a configuration of five cameras. Test results show the accuracy we achieved and the robustness of our solution to overcome uncertainties in the measurements and the modelling.
This paper presents a new type of Global Positioning System/Inertial Navigation System (GPS/INS) providing higher navigation accuracy under large initial heading error. The mechanization introduced is applicable to low cost GPS/INS systems and enhances the performance when the heading error is large. The proposed approach has the capability to decrease large heading errors very quickly and can start the strapdown navigation computations under poor heading accuracy without any special alignment procedure. Although the design is applicable to land, sea and aerial vehicles, a land vehicle is used for the performance tests. The test is conducted around a closed path and the proposed system is compared to a GPS/INS system based on small attitude error assumption. The performance of both systems is given in this paper.
In this paper, a conventional Strapdown Inertial Navigation System (SINS) alignment method on a disturbed base is analysed. A novel method with an attitude tracking idea is proposed for the rocking base alignment. It is considered in this method that the alignment algorithm should track the rocking base attitude real changes in the alignment process, but not excessively restrain disturbance. According to this idea, a rapid alignment algorithm is devised for the rocking base. In the algorithm, coarse alignment is carried out within 30 s in the inertial frame with alignment precision less than 2°, which meets Kalman filter linearization conditions well. Then a Kalman filter with ten state vectors and four measurement vectors is applied for the fine alignment to improve the capability of the algorithm in tracking the vehicle attitude. A turntable rotation experiment is carried out to validate the capability of the fine algorithm in tracing the large magnitude change during alignment. It is shown that the repeated alignment precision is about 0·04° by the alignment experiment on a rocking vehicle, with alignment time of 180 s. The Laser Strapdown Inertial Navigation System (LINS) ground navigation experiment suggests that the algorithm proposed by this paper can be satisfied without the need of high precision SINS alignment.
Nonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.
A loosely coupled Inertial Navigation System (INS) and Global Positioning System (GPS) are studied, particularly considering the constant lever arm effect. A five-element vector, comprising a craft's horizontal velocities in the navigation frame and its position in the earth-centred and earth-fixed frame, is observed by GPS, and in the presence of lever arm effect, the nonlinear observation equation from the state vector to the observation vector is established and addressed by the correction stage of an unscented Kalman filter (UKF). The conditionally linear substructure in the nonlinear observation equation is exploited, and a computationally efficient refinement of the UKF called marginalized UKF (MUKF) is investigated to incorporate this substructure where fewer sigma points are needed, and the computational expense is cut down while the high accuracy and good applicability of the UKF are retained. A performance comparison between UKF and MUKF demonstrates that the MUKF can achieve, if not better, at least a comparable performance to the UKF, but at a lower computational expense.
We study a two-country model with changes in the technological growth rate. Such changes are attributed to transitory and persistent shocks in the growth rate of technology. Cases are considered in which agents in two countries do not have enough information to distinguish between the two types of shocks; gradually, however, the persistence of the shock is recognized through the learning process. Utilizing a set of parameters obtained from U.S. and European productivity growth rates, it is then shown that (i) when persistent shocks affect the two countries identically, there is no consumption-correlation puzzle, and the international comovement puzzle becomes imperceptible; and (ii) even when persistent shocks affect the two countries differently, imperfect information plays an important role in explaining both the consumption-correlation puzzle and the international comovement puzzle (provided transitory shocks are strongly internationally correlated and are relatively larger than persistent shocks).
This paper is devoted to the study and implementation of real-time techniques for the estimation of time-varying, contingently correlated quantities, and relevant uncertainty. An estimation algorithm based on a metrological customization of the Kalman filtering technique is presented, starting from a Bayesian approach. Moreover, a fuzzy-logic routine for real-time treatment of possible outliers is incorporated in the overall software procedure. The system applicability is demonstrated by results of simulations performed on dimensional measurement models.