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This paper aims to propose a constant-gain Kalman Filter algorithm based on the projection method and constant dimension projection, which ensures that the dimension of the observation matrix obtained is maintained when there is a satellite with multiple sensors.

First, a time-invariant observation matrix is determined with the projection method, which does not require the Jacobi matrix to be calculated. Second, the constant-gain matrix replaces the EKF (extended Kalman filter) gain matrix, which requires online computation, considerably improving the stability and real-time properties of the algorithm.

The simulation results indicate that compared to the EKF algorithm, the constant-gain Kalman filter algorithm has a considerably lower computational burden and improved real-time properties and stability without a significant loss of accuracy. The algorithm based on the constant dimension projection has better real-time properties, simpler computations and greater fault tolerance than the conventional EKF algorithm when handling an attitude determination system with three or more star trackers.

In satellite attitude determination systems, the constant-gain Kalman Filter algorithm based on the projection method reduces the large computational burden and improve the real-time properties of the EKF algorithm.

The successful use of the standard extended Kalman filter (EKF) is restricted by the requirement on the statistics information of the measurement noise. The covariance of the measurement noise may deviate from its nominal value in practical environment, and the filtering performance may decline because of the statistical uncertainty. Although the adaptive EKF (AEKF) is available for recursive covariance estimation, it is often less accurate than the EKF with accurate noise statistics.

Aiming at this problem, this paper develops a parallel adaptive EKF (PAEKF) by combining the EKF and the AEKF with an adaptive law, such that the final state estimate is dominated by the EKF when the prior noise covariance is accurate, while the AEKF is activated when the actual noise covariance deviates from its nominal value.

The PAEKF can reduce the sensitivity of the algorithm to the model uncertainty and ensure the estimation accuracy in the normal case. The simulation results demonstrate that the PAEKF has the advantage of both the AEKF and the EKF.

The presented algorithm is applicable for spacecraft relative attitude and position estimation.

The PAEKF is presented for a kind of nonlinear uncertain systems. Stability analysis is provided to show that the error of the estimator is bounded under certain assumptions.

The purpose of the paper is to present an approach to detect and isolate the sensor failures, using a bank of extended Kalman filters (EKF) using an innovative initialization of covariance matrix using system dynamics.

The EKF is developed for nonlinear flight dynamic estimation of a spacecraft and the effects of the sensor failures using a bank of Kalman filters is investigated. The approach is to develop a fast convergence Kalman filter algorithm based on covariance matrix computation for rapid sensor fault detection. The proposed nonlinear filter has been tested and compared with the classical Kalman filter schemes via simulations performed on the model of a space vehicle; this simulation activity has shown the benefits of the novel approach.

In the simulations, the rotational dynamics of a spacecraft dynamic model are considered, and the sensor failures are detected and isolated.

A novel fast convergence Kalman filter for detection and isolation of faulty sensors applied to the three‐axis spacecraft attitude control problem is examined and an effective approach to isolate the faulty sensor measurements is proposed. Advantages of using innovative initialization of covariance matrix are presented in the paper. The proposed scheme enhances the improvement in estimation accuracy. The proposed method takes advantage of both the fast convergence capability and the robustness of numerical stability. Quaternion‐based initialization of the covariance matrix is not considered in this paper.

A new fast converging Kalman filter for sensor fault detection and isolation by innovative initialization of covariance matrix applied to a nonlinear spacecraft dynamic model is examined and an effective approach to isolate the measurements from failed sensors is proposed. An EKF is developed for the nonlinear dynamic estimation of an orbiting spacecraft. The proposed methodology detects and decides if and where a sensor fault has occurred, isolates the faulty sensor, and outputs the corresponding healthy sensor measurement.

The purpose of this paper is to propose an extended Kalman particle filter (EPF) approach for dynamic state estimation of synchronous machine using the phasor measurement unit’s measurements.

EPF combines the extended Kalman filter (EKF) with the particle filter (PF) to accurately estimate the dynamic states of synchronous machine. EKF is used to make particles of PF transfer to the likelihood distribution from the previous distribution. Therefore, the sample impoverishment in the implementation of PF is able to be avoided.

The proposed method is capable of estimating the dynamic states of synchronous machine with high accuracy. The real-time capability of this method is also acceptable.

The effectiveness of the proposed approach is tested on IEEE 30-bus system.

Introducing EKF into PF, EPF is proposed to estimate the dynamic states of synchronous machine. The accuracy of a dynamic state estimation is increased.

Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion.

This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model.

While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination.

The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models.

The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.

The purpose of this paper is to explore a multi-innovation with forgetting factor-based EKF-SLAM (FMI-EKF-SLAM) algorithm to solve the error increasing problem, caused by the Extended Kalman filtering (EKF) violating the local linear assumption in simultaneous localization and mapping (SLAM) for mobile robots because of strong nonlinearity.

A multi-innovation with forgetting factor-based EKF-SLAM (FMI-EKF-SLAM) algorithm is investigated. At each filtering step, the FMI-EKF-SLAM algorithm expands the single innovation at current step to an extended multi-innovation containing current and previous steps and introduces the forgetting factor to reduce the effect of old innovations.

The simulation results show that the explored FMI-EKF-SLAM method reduces the state estimation errors, obtains the ideal filtering effect and achieves higher accuracy in positioning and mapping.

The method proposed in this paper improves the positioning accuracy of SLAM and improves the EKF, so that the EKF has higher accuracy and wider application range.

The main reason for the low accuracy of magnetometer-based autonomous orbit determination is the coarse accuracy of the geomagnetic field model. Furthermore, the geomagnetic field model error increases obviously during geomagnetic storms, which can still further reduce the navigation accuracy. The purpose of this paper is to improve the accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms.

In this paper, magnetometer-based autonomous orbit determination via a measurement differencing extended Kalman filter (MDEKF) is studied. The MDEKF algorithm can effectively remove the time-correlated portion of the measurement error and thus can evidently improve the accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms. Real flight data from Swarm A are used to evaluate the performance of the MDEKF algorithm presented in this study. A performance comparison between the MDEKF algorithm and an extended Kalman filter (EKF) algorithm is investigated for different geomagnetic storms and sampling intervals.

The simulation results show that the MDEKF algorithm is superior to the EKF algorithm in terms of estimation accuracy and stability with a short sampling interval during geomagnetic storms. In addition, as the size of the geomagnetic storm increases, the advantages of the MDEKF algorithm over the EKF algorithm become more obvious.

The algorithm in this paper can improve the real-time accuracy of magnetometer-based autonomous orbit determination during geomagnetic storms with a low computational burden and is very suitable for low-orbit micro- and nano-satellites.

The purpose of this paper is to present research in the area of the signal processing and application into pedestrian tracking in the video scene.

The paper describes the design of a new extended Kalman filter (EKF) in the high‐dimensional space (HDS) and studies of mean square error and variance analysis of error. A design algorithm is implemented in MATLAB software and tested. The data set includes many hours of captured films.

This paper includes a new derivation of the EKF and its implementation into the video scene.

The proposed algorithm can be used to track each video application.

The Kalman filter in the HDS is presented for the first time. Also, the application of the proposed method is applied in pedestrian tracking and counting.

The purpose of the paper is to present an approach to detect and isolate the aircraft sensor and control surface/actuator failures affecting the mean of the Kalman filter innovation sequence.

The extended Kalman filter (EKF) is developed for nonlinear flight dynamic estimation of an F‐16 fighter and the effects of the sensor and control surface/actuator failures in the innovation sequence of the designed EKF are investigated. A robust Kalman filter (RKF) is very useful to isolate the control surface/actuator failures and sensor failures. The technique for control surface detection and identification is applied to an unstable multi‐input multi‐output model of a nonlinear AFTI/F‐16 fighter. The fighter is stabilized by means of a linear quadratic optimal controller. The control gain brings all the eigenvalues that are outside the unit circle, inside the unit circle. It also keeps the mechanical limits on the deflections of control surfaces. The fighter has nine state variables and six control inputs.

In the simulations, the longitudinal and lateral dynamics of an F‐16 aircraft dynamic model are considered, and the sensor and control surface/actuator failures are detected and isolated.

A real‐time detection of sensor and control surface/actuator failures affecting the mean of the innovation process applied to the linearized F‐16 fighter flight dynamic is examined and an effective approach to isolate the sensor and control surface/actuator failures is proposed. The nonlinear F‐16 model is linearized. Failures affecting the covariance of the innovation sequence is not considered in the paper.

An approach has been proposed to detect and isolate the aircraft sensor and control surface/actuator failures occurred in the aircraft control system. An extended Kalman filter has been developed for the nonlinear flight dynamic estimation of an F‐16 fighter. Failures in the sensors and control surfaces/actuators affect the characteristics of the innovation sequence of the EKF. The failures that affect the mean of the innovation sequence have been considered. When the EKF is used, the decision statistics changes regardless the fault is in the sensors or in the control surfaces/actuators, while a RKF is used, it is easy to distinguish the sensor and control surface/actuator faults.

The purpose of this paper is to present a small UAV system with autonomous formation flight capability, the Swallow UAV system, and the application of an extended Kalman filter (EKF) based augmentation method to reduce the impact of data link loss, which will fail the formation flight algorithm of the system.

The hardware of the Swallow UAV system is composed of two aircraft and a set of ground control station for leader‐wingman formation flight. A hardware‐in‐the‐loop simulation environment is build to support the system development. Fuzzy logic control method is applied to the guidance, navigation, and control system of leader and wingman aircraft. The leader system is designed with waypoint navigation and circle trajectory tracking functions to make the aircraft stay in visual range autonomously for safety. The wingman system is designed with formation flight functionality. However, the relative position and velocity are derived from the wireless data link transmitted leader navigation information. It is vulnerable to the data link loss. The EKF based leader motion estimator (LME) is developed to estimates the leader position when the data link broke, and corrects the estimation when the data link is available.

The designed LME is flight tested, and the results show that it woks properly with sound performance that the estimation error of relative position within 3 meters, relative velocity within 1.3 meters, and leader attitude within 1.6 degrees in standard deviation.

The research implements the autonomous formation flight capability with the EKF based LME on a small UAV system.