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At present, smartphones are embedded with accelerometers, gyroscopes, magnetometers and WiFi sensors. Most researchers have delved into the use of these sensors for localization. However, there are still many problems in reducing fingerprint mismatching and fusing these positioning data. The purpose of this paper is to improve positioning accuracy by reducing fingerprint mismatching and designing a weighted fusion algorithm.

For the problem of magnetic mismatching caused by singularity fingerprint, derivative Euclidean distance uses adjacent fingerprints to eliminate the influence of singularity fingerprint. To improve the positioning accuracy and robustness of the indoor navigation system, a weighted extended Kalman filter uses a weighted factor to fuse multisensor data.

The scenes of the teaching building, study room and office building are selected to collect data to test the algorithm’s performance. Experiments show that the average positioning accuracies of the teaching building, study room and office building are 1.41 m, 1.17 m, and 1.77 m, respectively.

The algorithm proposed in this paper effectively reduces fingerprint mismatching and improve positioning accuracy by adding a weighted factor. It provides a feasible solution for indoor positioning.

Recent studies have shown that low-volatility shares outperform high-volatility shares. Given the conventional finance theory that risk drives return, this study aims to investigate and attempt to explain the presence of the low-risk anomaly (LRA) in South Africa.

Using share prices from 1990 to 2016, various buy-and-hold strategies are constructed to determine the return to an investor attempting to capitalise on such an anomaly. These strategies involve combinations relating to a price filter, the calculation of risk and volatility, value-weighting or equal-weighting of portfolios and the window period to construct said portfolios.

It was found that the LRA exists on the Johannesburg Stock Exchange (JSE_=) when using univariate sorts, without controlling for the size or value effect. When using multivariate portfolio sorts (size and volatility or value and volatility), it was found that the LRA does not exist on the JSE under the majority of risk proxies, but particularly prevalent when downside risk is used. This loosely points towards a potential “inverse momentum” effect where low-return portfolios outperform their counterparts.

In general, it is established that the risk–return relationship is non-linear and deterministic under traditional proxies, but improves to being somewhat, but not completely, linear under a Kalman filter. The Kalman filter, which can be considered a proxy for learning, does not remove the anomaly in its entirety, indicating that behavioural approaches are needed to explain such phenomena.

The purpose of this paper is to examine the possibility of creating hedge funds “clones” using liquid exchange traded instruments.

Authors analyze the performance of fixed weight and extended Kalman filter generated clone portfolios (EKF) for 14 hedge fund strategies from February 2004 to September 2009. EKF approach does not indeed impose any normality constraints on the error terms which allow the filter to find the optimal recursive process by itself. Such models could adjust even faster to sudden shifts in market conditions vs a standard Kalman filter.

For five strategies out of 14, this work finds that EKF clones outperform their corresponding indices. Thus, for certain strategies, the possibility of cloning hedge fund returns is indeed real. Results should be however considered with caution.

This paper suggests that the most important benefits of clones are to serve as benchmarks and to help investors to better understand the various risk factors that impact hedge fund returns.

Rather than using fixed‐weight and rolling windows approaches (as Hasanhodzic and Lo), this work considers an extended version of the Kalman filter, a computational algorithm that better captures the time changing dynamics of hedge fund returns. Also, in order to be practical, this research considers investable factors and that the models themselves could not be constant over time.

The purpose of this paper is to introduce an artificial bee colony-based Kalman filter algorithm along with an extended objective function to ensure the optimality of the estimator of the quadrotor in the presence of unknown measurement noise statistics.

Six degree-of-freedom mathematical model of the quadrotor is derived. Position controller for the quadrotor is designed. Kalman filter-based estimation algorithm is implemented in the sensor feedback loop. Artificial bee colony-based hybrid algorithm is used as an optimization method to handle the unknown noise statistics. Existing objective function is extended with a penalty term. Mathematical proof of the extended objective function is derived. Results of the proposed algorithm is compared with de facto genetic algorithm-based Kalman filter.

Artificial bee colony algorithm-based Kalman filter and extended objective function duo are able to optimize the measurement noise covariance matrix with an absolute error as low as 0.001 [m²]. Proposed method and function is capable of reducing the noise from 2 to 0.09 [m] for x-axis, 3.4 to 0.14 [m] for y-axis and 3.7 to 0.2 [m] for z-axis, respectively.

The motivation behind this paper is to bring a novel optimization-based solution for the estimation problem of the quadrotor when the measurement noise statistics are unknown along with an extended objective function to prevent the infeasible solutions with mathematical convergence analysis.

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 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.

This paper aims to develop an adaptive unscented Kalman filter (AUKF) formulation for orientation estimation of aircraft and UAV utilizing low‐cost attitude and heading reference systems (AHRS).

A recursive least‐square algorithm with exponential age weighting in time is utilized for estimation of the unknown inputs. The proposed AUKF tunes its measurement covariance to yield optimal performance. Owing to nonlinear nature of the dynamic model as well as the measurement equations, an unscented Kalman filter (UKF) is chosen against the extended Kalman filter, due to its better performance characteristics. The unscented transformation of the UKF is shown to equivalently capture the effect of nonlinearities up to second order without the need for explicit calculations of the Jacobians.

In most conventional AHRS filters, severe problems can occur once the system suddenly experiences additional acceleration, resulting in erroneous orientation angles. On the contrary in the high dynamic accelerative mode of the new proposed filter the errors would not suddenly increase, since the additional to cruise accelerations are being continuously estimated resulting in substantially more accurate orientation estimation. This feature causes the associated filter errors to gradually increase, in the event of continuous vehicle acceleration, up to a point of zero additional acceleration that subsequently causes a subsidence of the error back to zero.

The proposed filtering methodology can be implemented for orientation estimation of aircraft and UAV that are equipped with low‐cost AHRSs.

Traditional AHRS algorithms utilize the accelerometers output for the computation of roll and pitch angles and magnetometer output for the heading angle. Moreover, these angles are also calculated from the gyroscopes output as well, but with errors that increase with time. Of course for some applications of AHRS system, orientation errors can be damped out with a proportional‐integral controller. In such a case, the filter cut‐off frequency is usually selected experimentally. But, for high accelerating vehicles utilizing AHRS, the system errors can become very large. A possible remedy to this problem could be to use more advanced nonlinear filter algorithms such as the one proposed.

This chapter presents a novel human arm gesture tracking and recognition technique based on fuzzy logic and nonlinear Kalman filtering with applications in crane guidance. A Kinect visual sensor and a Myo armband sensor are jointly utilised to perform data fusion to provide more accurate and reliable information on Euler angles, angular velocity, linear acceleration and electromyography data in real time. Dynamic equations for arm gesture movement are formulated with Newton–Euler equations based on Denavit–Hartenberg parameters. Nonlinear Kalman filtering techniques, including the extended Kalman filter and the unscented Kalman filter, are applied in order to perform reliable sensor fusion, and their tracking accuracies are compared. A Sugeno-type fuzzy inference system is proposed for arm gesture recognition. Hardware experiments have shown the efficacy of the proposed method for crane guidance applications.

To improve sensorless control of induction motor using Kalman filtering family, this paper aims to introduce a new metaheuristic optimizer algorithm for online rotor speed and flux estimation.

The main problem with unscented Kalman filter (UKF) observer is its sensibility to the initial values of Q and R. To solve the optimal solution of these matrices, a novel alternative called ant lion optimization (ALO)-UKF is introduced. It is based on the combination of the classical UKF observer and a nature-inspired metaheuristic algorithm, ALO.

Synthesized ALO-UKF has given good results over the famous extended Kalman filter and the classical UKF observer in terms of accuracy and dynamic performance. A comparison between ALO and particle swarm optimization (PSO) was established. Simulations illustrate that ALO recovers rapidly and accurately while PSO has a slower convergence.

Using the proposed approach, tuning the design matrices Q and R in Kalman filtering becomes an easy task with a high degree of accuracy and the constraints of time cost are surmounted. Also, ALO-UKF is an efficient tool to improve estimation performance of states and parameters’ uncertainties of the induction motor. Related optimization technique can be extended to faults monitoring by online identification of their corresponding signatures.