Divergence in the Kalman filter.

Land vehicle positioning relies mostly on satellite navigation systems such as the Global Positioning System (GPS). However, GPS signals may be degraded or suffer from blockage in urban canyons and tunnels, and the positioning information provided is interrupted. One solution for such a problem is to integrate GPS with an inertial measurement unit (IMU) and the navigation solution is achieved using an estimation technique which is traditionally based on a Kalman filter (KF). In order to have a low cost navigation solution for land vehicles, MEMS-based inertial sensors are used. To further reduce the cost a reduced inertial sensor system (RISS) which consists of only one gyroscope and a speed sensor is integrated with GPS. The position and velocity errors can be estimated by a KF relying on RISS dynamic error model and GPS position and velocity updates. However, low-cost MEMS sensors suffer from complex error characteristics, which are difficult to model by the linearized KF models. The positional accuracy of the integrated system can be improved using Parallel Cascade Identification (PCI) that is cascaded with the KF. The proposed augmented KF-PCI method can handle both linear and nonlinear system errors as the linear parts of the errors are modeled inside the KF and the nonlinear residual RISS errors are modeled by PCI. The performance of this method is examined by road test trajectories in a land vehicle and compared to KF.

One of the most common methods of navigation data integration is the use of a Kalman filter. The paper presents a computer application facilitating testing of the properties of a Kalman filter, designed for a pedestrian or a robot positioning system using range measurements to several base stations. The description of the system is composed of a linear dynamics model and a non-linear observation model. Due to the non-linearity of the observation model, an extended Kalman filter (EKF) was chosen for the position estimation. A computer application was developed in the MATLAB® environment to test the filter properties and to support the process of choosing its parameters. The application gives an insight into the EKF operation and enables an assessment of its accuracy, depending on the assumed shape of the object trajectory, an assumed motion model, a number and locations of the base stations and the filter parameters. Chosen results of simulations are presented in the paper in the same form as they are seen in the GUI of our application. The application enables displaying the assumed trajectory of motion, its estimates from the EKF, as well as the components of estimated position and velocity errors. Additionally, it calculates and presents root-mean-squared (RMS) and maximal estimation errors. The application proved useful for testing the filter efficiency in various configurations. Due to its comfortable GUI, intuitive handling and wide range of possible tests, it can find its applications both in the research and the teaching.

This paper presents a novel technique to estimate DCBs from GPS transmitters and receivers on-board Low Earth Orbit (LEO) satellites. The technique consists of obtaining the DCBs as residuals from the difference between the ionospheric combination of the code and the associated ionospheric delay. The ionospheric delay is computed with TOMION, a background-model-free ionospheric tomographic technique based on dual-frequency GPS carrier phase data only, and solved with a Kalman filter. Thus, DCBs are also estimated epoch-wise from the LEO Precise Orbit Determination (POD) GPS receiver as a secondary product. The results for GPS satellite DCBs, obtained exclusively from the three MetOp LEO POD GPS receivers over four consecutive weeks, are in full agreement (i.e., at the level of a few tenths of ns) with those reported independently with other techniques from hundreds of ground-based receivers exclusively, by JPL and CODE analysis centers.

: This paper represents orbit propagation and determination of Low Earth Orbit(LEO) satellites, which is immediate orbit satellite positioning. Beiseds, satellite global positioning system (GPS) configured satellite receiver provides position and velocity measures by navigating the filter to get the coordinates of the orbit propagation (OP), while the satellite orbit coordinates is an important basis for the task operation. The main contradictions in real time orbit which is determined by the problem are: orbit positioning accuracy and the amount of calculating two indicators; how to balance these two indicators. This article is dedicated to solving the problem of tradeoffs. To plan to use a non-linear filtering method for immediate orbit tasks requires more precise satellite orbit state parameters in a short time. Although the traditional extended Kalman filter (Extended Kalman Filter, EKF) method is widely used, its linear approximation of the drawbacks in dealing with nonlinear problems was especially evident, without compromising Kalman filter (Unsented Kalman Filter, UKF). As a new non-linear estimation method, it is measured at the estimated measurements on more and more applications. This paper will be the first study to UKF microsatellites in LEO orbit in real time, trying to explore the real-time precision orbit determination techniques.

This paper addresses the integration of a subordinate Kalman filter processing terrain data into a Kalman filter integrating Global Positioning System (GPS) data and Inertial Navigation System (INS) data with limited computing resources. The study shows that modeling the difference between the horizontal position estimates supplied by the Digital Terrain System (DTS) and the integrating Kalman filter is sufficient for accurate solution integration. The two new error states required to model this difference are modeled as random walks driven by variable process noise. Augmenting the GPS/INS integrating Kalman Filter with the horizontal position offset states requires minute changes to the existing filter mechanization. Performance measurements of position, velocity and platform tilt error using Monte Carlo simulations show stable and acceptable navigation accuracy. An alternative integration of subordinate solutions scheme is also suggested and presented.

Now a day navigation system has been receiving a high demand for numerous applications. Among these systems global positioning system (GPS) is more popular which is frequently using for the aircraft for navigation and autonomous navigation purposes. However GPS suffers because of continuity and reliability problems in many applications. In this proposed model a novel architecture of kalman filter has been selected to integrate with GPS to overcome above problem. A software defined radio (SDR) is used for the GPS data extraction which is nothing but an analog to digital converter. The integrated GPS with kalman filter system can be able reduce velocity, position and attitude errors compared to the many conventional algorithms. To verify this technique a real time model is created using Simulink/Matlab. The simulated outcomes confirm the advantages of assimilated system in both urban and open areas and suitable for real time implementations.

Fault detection and isolation algorithms for LEO satellite attitude determination and control system using an approach for checking the statistical characteristics of EKF innovation sequence are proposed. The fault detection algorithm is based on statistic for the mathematical expectation of the spectral norm of the normalized innovation matrix of the EKF. This approach permits simultaneous real-time checking of the mathematical expectation and the variance of the innovation sequence and does not require a priori information about the faults and statistical characteristics of the system in fault cases. In this study an attitude estimation and control system for LEO satellite is proposed. To determine the attitude of the satellite, this system use algebraic method (two-vector algorithm). As a reference direction, the unit vectors toward the Sun, the Earth’s center, and the Earth magnetic field are used. Thus, it includes three different two-vector algorithms based on using the Earth’s magnetic field – the Sun vector, the Earth’s magnetic field – nadir vector, and nadir vector – the Sun vector couples. In order to increase the attitude determination accuracy, the redundant data processing algorithm, based on the Maximum Likelihood Method, is used. An extended Kalman filter has been developed for nonlinear rotational dynamics estimation of LEO satellite. Failures in the sensors affect the characteristics of the innovation sequence of the EKF. The failures that affect the mean and variance of the innovation sequence have been considered. The application of the proposed fault detection algorithm to the LEO satellite attitude determination and control system has shown that, sensor fault detection by the presented algorithm is possible in real time. Assuming that the effect of the faulty sensor on its channel is more significant than on the other channels, a sensor isolation method is presented by transforming n-dimensional innovation process to n one-dimensional processes. The simulations, carried out on a nonlinear dynamic model of the rotational motion of LEO satellite, confirm the theoretical results. The future work is to investigate the faults affecting the attitude dynamics e.g., actuator faults and to perform the integrated sensor/actuator FDI via innovation approach.

The object of research is the onboard subsystems of Unmanned Aerial Vehicles (UAVs). The research is aimed at analyzing UAVs, specifically the integration and enhancement of satellite-based positioning systems, including Global Navigation Satellite Systems (GNSS) and Inertial Navigation Systems (INS). The problem concerns traditional satellite-based positioning services, especially those relying solely on medium earth orbit (MEO) satellites, which are insufficient for specific requirements. The study aims to address the limitations of these systems on onboard subsystems of UAVs, especially in challenging environments laden with jammers and interference, and to provide a more accurate, robust, and continuous positioning solution. The research proposes a «multilayer system of systems» approach that integrates signals from various sources, including low Earth orbit (LEO) satellites, ground-based positioning, navigation, and timing (PNT) systems, and user-centric sensors. The combined approach, termed LeGNSS/INS, leverages the strengths of each component, providing redundancy and enhanced accuracy. The system's performance was evaluated using pseudo-real output data, demonstrating its ability to generate quasi-real dynamic trajectories for UAV flight. The error analysis showed that the proposed method consistently outperforms traditional GNSS systems, especially in challenging environments. The enhanced performance of the LeGNSS/INS system can be attributed to integrating multiple satellite systems with INS and applying optimal filtering techniques. The research also employed mathematical modeling to represent the dependencies and interactions when combining data from different sources, such as GPS, LEO, and INS. The Kalman filter is a mechanism to fuse data from multiple sources optimally. The insights from this study apply to various sectors, including aviation, maritime navigation, autonomous drones, and defense. The enhanced positioning accuracy can significantly improve safety, navigation precision, and operational efficiency. However, the study assumes idealized conditions for satellite signal reception, which might not always be accurate in real-world scenarios. Challenges, such as the martial law conditions in Ukraine affecting data collection and potential satellite signal restrictions, were also highlighted. Further research can delve into the impact of more complex environmental factors and the integration of additional satellite systems or sensors to enhance accuracy further.

Almanac is an elegant design to help Global Navigation Satellite Systems (GNSS) signal acquisition, which has been adopted by all global satellite navigation systems. For the future low Earth orbit (LEO) navigation constellation, the almanac will be more critical due to larger constellation and signal Doppler variation, while the LEO orbit prediction is more challenging due to complex perturbation forces, especially atmospheric drag. This study introduces a novel 9-parameter almanac model for LEO constellation, leveraging the Empirical Mode Decomposition (EMD) method. Our innovative approach uniquely balances almanac accuracy and simplicity by considering the atmosphere drag effects, addressing a critical gap in existing models. The proposed almanac model is validated with four in-orbit LEO satellites at various altitudes. For the LEO with a 600 km orbit or lower, our model achieves a 50% improvement in 23-day orbit prediction accuracy compared to the classical GPS almanac model. This significant enhancement extends to visibility prediction and signal acquisition performance. Our design limits the maximum elevation angle error to less than 1.5 degrees, efficiently excluding invisible satellites during LEO navigation signal acquisition. Furthermore, for visible satellite, the proposed LEO almanac reduces the signal frequency searching range by about 20 times during acquisition, with Doppler prediction errors better than 0.5 kHz/0.3 kHz for 95% of cases. These advancements represent a substantial leap in LEO navigation technology, offering improved efficiency and accuracy for future satellite systems.

A three-axis, magnetometer/Kalman filter, attitude-determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve three-axis knowledge using magnetic field measurements only. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Covariance computation and simulation testing are used to evaluate performance. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir-pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as a part of a low-cost, three-axis attitude stabilization system. I. Introduction T HE objective of this work has been to develop a low-cost system for estimation of three-axis, spacecraft-attitude information based solely on three-axis magnetometer measurements from one satellite orbit. Such a system will be useful for missions that operate in an inclined, low-Earth orbit and require only coarse attitude information. It can also serve as the sensor part of a low-cost, three-axis, closed-loop attitude control system or as a backup attitude estimator. A single three-axis magnetometer measurement can give only two-axes worth of attitude information and no attitude rate or disturbance torque information. Therefore, this attitude determination system must use a sequence of magnetometer measurements. It processes these measurements recursively in a Kalman filter. This paper describes the design, development, analysis, and simulation testing of a Kalman filter arid reports its expected peformance. A follow-on, postlaunch paper is planned to report actual performance.

In the past decades, short multipath effect is one of the most important error sources in global navigation satellite systems (GNSS) navigation, and seriously affects the positioning precision. Therefore, some algorithms based on traditional Kalman filtering (KF) have been proposed to overcome the short multipath effect, for example extended KF (EKF), adaptive KF (AKF) and constrained KF (CKF). However, height positioning accuracy of EKF and AKF is lower than that of horizontal. On the other hand, CKF requires additional height information from a barometer or location service system. To overcome the limitations of current algorithms, this paper first proposes an empirical multipath residual model after GNSS baseband processing, which shows that pseudo range error exhibits “rectangular” distribution or “shock” distribution. This paper also demonstrates that GNSS positioning error has the same distribution as the pseudo range error, and the height positioning error is higher than the horizontal positioning error in influence of short multipath effect. To improve the height positioning accuracy and suppress the short multipath effect, we propose a practical climbing motion model to constrain the height estimation in the AKF, which can effectively suppress short multipath effect and achieve an improved positioning result. Field tests illustrate that the proposed height constrained AKF (HCAKF) improves the height positioning accuracy by 85.1% over traditional EKF, 85.4% over AKF, and improves the total positioning accuracy by 56.9% over traditional EKF, 37.8% over AKF. Furthermore, the height estimate from HCAKF is smoother than those from traditional EKF and AKF.

Simulation of microsatellite attitude using Kalman filtering in orbit results

A Generalized Image Navigation and Registration (INR) method is presented using Kalman Filter (KF). The basic method is landmark-based, ‘self- contained’ INR system that estimates orbit in itself or refines the coarse orbit received from the Flight Dynamics System (FDS). Kalman Filter measurements consist of landmarks taken by the imaging instrument, maneuver delta v or orbit from FDS, and attitude from spacecraft telemetry inserted in the imager wideband data. The KF state vector (SV) consists of spacecraft attitude cor-rection angles, constant attitude correction angles biases, spacecraft orbit position and velocity relative to ideal orbit using Euler-Hill equations, imager internal misalignments, and constant misalignment biases. The basic method is then shown how it can be adapted to systems using star and landmark measurements, systems using star only measurements with orbit provided by FDS or GPS, and systems using spacecraft attitude rate inserted in wideband telemetry.

Data fusion algorithms are inevitable in improving the accuracy and reliability of radar target tracking. Considering the shortcomings of target tracking in Cartesian coordinates, all the fusion process are carried out in spherical coordinate system. To fuse data from bidimensional radar and Infrared Search and Track (IRST), five data fusion methods, Bayesian fusion, Signal variance based fusion, Optimal fusion, Error variance based fusion and Extended Kalman Filter (EKF) based fusion are proposed and analyzed. The performances of the methods are analyzed in terms of Root Mean Square Error in Position (RMSPE) and Mean Absolute Error in Position (MAPE) for a wide range of measurement noise variances. It is concluded that EKF based fusion has the best error performance. Kalman Filter State-Vector Fusion (KF-SVF) which is a hierarchical fusion architecture, having first level of fusion with Kalman filter and second level with error variance based fusion method, is available in the literature. In this work it has been expanded to Extended Kalman Filter—State-Vector Fusion (EKF-SVF) with either error variance based fusion, signal variance based fusion or optimal information fusion as second level. All the three EKF-SVF methods have similar error characteristics, but EKF-SVF with signal variance based fusion, unlike the other two, provides less computational cost since it does not involve matrix inversion. While comparing EKF based fusion and EKF-SVF, EKF-SVF offers increased error minimization.

Kalman filtering for GPS/magnetometer integrated navigation system