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The purpose of this paper is to provide an analysis on using two non‐conventional nonlinear estimating filters compared to the traditional linearized extended Kalman filter (EKF). This analysis will look at two state‐of‐the‐art applications and will provide insight to the problems associated with these applications.

The approach taken was to simulate both applications with three different filter designs: EKF, unscented Kalman filter, and particle filter. After results and explanations are given for both applications, then there is a comparison of results between the two applications to compare and contrast their findings.

This research shows how critical it is when selecting a filter for different applications. Not only is tuning the filter properly a necessity, but choosing a filter that is optimum for the application also greatly affects the accuracy and precision of the results.

As these filter methods are proven feasible for these applications, testing can move beyond simulation. Further research could compare other nonlinear filters to these results to determine if a better estimation technique exists.

This paper shows a lot of the issues one must face when choosing an estimation technique for their application as well as the impact the technique can have on the outcome.

This paper clearly describes the decision‐making criteria in regards to these two specific applications. These two applications are current technological problems that many are trying to solve. This paper shows where and why errors in calculations occur. It also offers insight into different ways to solve these problems when the specific application is taken into account.

Doppler-Bearing Tracking (DBT) is commonly used in target tracking applications for the underwater environment using the Hull-Mounted Sensor (HMS). It is an important and challenging problem in an underwater environment.

The system nonlinearity in an underwater environment increases due to several reasons such as the type of measurements taken, the speeds of target and observer, environmental conditions, number of sensors considered for measurements and so on. Degrees of nonlinearity (DoNL) for these problems are analyzed using a proposed measure of nonlinearity (MoNL) for state estimation.

In this research, the authors analyzed MoNL for state estimation and computed the conditional MoNL (normalized) using different filtering algorithms where measurements are obtained from a single sensor array (i.e. HMS). MoNL is implemented to find out the system nonlinearity for different filtering algorithms and identified how much nonlinear the system is, that is, to measure nonlinearity of a problem.

Algorithms are evaluated for various scenarios with different angles on the target bow (ATB) in Monte-Carlo simulation. Computation of root mean squared (RMS) errors in position and velocity is carried out to assess the state estimation accuracy using MATLAB.

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.

From many decades, bearings-only tracking (BOT) is the interested problem for researchers. This utilises nonlinear filtering methods for state estimation as there is only information about the target, i.e. bearing is a nonlinear measurement. The measurement bearing is tangentially related to the target state vector. There are many nonlinear filtering algorithms developed so far in the literature.

In this research work, the recently developed nonlinear filtering algorithm, i.e. shifted Rayleigh filter (SRF), is applied to BOT.

The SRF is tested for two-dimensional BOT against various scenarios. The simulation results emphasise that the SRF performs well when compared to the standard nonlinear filtering algorithm, unscented Kalman filter (UKF).

SRF utilises the nonlinearities present in the bearing measurement through the use of moment matching. The SRF is able to produce the solution in highly noisy environment, long ranges and high dimension tracking.

The time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM.

According to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update.

Under the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm.

In this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm.

In this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

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.

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 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.

This paper aims to focus on the sensor fault-tolerant control (FTC) for civil aircraft under exterior disturbance.

First, a three-step cubature Kalman filter (TSCKF) is designed to detect and isolate the sensor fault and to reconstruct the sensor signal. Meanwhile, a nonlinear disturbance observer (NDO) is designed for disturbance estimation. The NDO and the TSCKF are combined together and an NDO-TSCKF is proposed to solve the problem of sensor faults and bounded disturbances simultaneously. Furthermore, an FTC scheme is designed based on the nonlinear dynamic inversion (NDI) and the NDO-TSCKF.

The method is verified by a Cessna 172 aircraft model under bias gyro fault and constant angular rate disturbance. The proposed NDO-TSCKF has the ability of signal reconstruction and disturbance estimation. The proposed FTC scheme is also able to solve the sensor fault and disturbance simultaneously.

NDO-TSCKF is the novel algorithm used in sensor signal reconstruction for aircraft. Then, disturbance observer-based FTC can improve the flight control system performances when the system with faults.

The NDO-TSCKF-based FTC scheme can be used to solve the sensor fault and exterior disturbance in flight control. For example, the bias gyro fault with constant angular rate disturbance of a civil aircraft is studied.

Signal reconstruction for critical sensor faults and disturbance observer-based FTC for civil aircraft are useful in modern civil aircraft design and development.

This is the research paper studies on the signal reconstruction and FTC scheme for civil aircraft. The proposed NDO-TSCKF is better than the current reconstruction filter because the failed sensor signal can be reconstructed under disturbances. This control scheme has a better fault-tolerant capability for sensor faults and bounded disturbances than using regular NDI control.

The purpose of this paper is to estimate aerodynamic parameters accurately from flight data in the presence of unknown noise characteristics.

The introduced adaptive filter scheme is composed of two parallel UKFs. At every time‐step, the master UKF estimates the states and parameters using the noise covariance obtained by the slave UKF, while the slave UKF estimates the noise covariance using the innovations generated by the master UKF. This real time innovation‐based adaptive unscented Kalman filter (UKF) is used to estimate aerodynamic parameters of aircraft in uncertain environment where noise characteristics are drastically changing.

The investigations are initially made on simulated flight data with moderate to high level of process noise and it is shown that all the aerodynamic parameter estimates are accurate. Results are analyzed based on Monte Carlo simulation with 4000 realizations. The efficacy of adaptive UKF in comparison with the other standard Kalman filters on the estimation of accurate flight stability and control derivatives from flight test data in the presence of noise, are also evaluated. It is found that adaptive UKF successfully attains better aerodynamic parameter estimation under the same condition of process noise intensity changes.

The presence of process noise complicates parameter estimation severely. Since the non‐measurable process noise makes the system stochastic, consequently, it requires a suitable state estimator to propagate the states for online estimation of aircraft aerodynamic parameters from flight data.

This is the first paper highlighting the process noise intensity change on real time estimation of flight stability and control parameters using adaptive unscented Kalman filter.