Generalized SSPRT for Fault Identification and Estimation of Linear Dynamic Systems Based on Multiple Model Algorithm

This research aims at improving Detect and Avoid (DAA) functions in Unmanned Aircraft Systems (UAS) using a Multiple Model Estimation algorithm to track maneuvering intruders. This research builds on previous work that used predefined aircraft encounter trajectories. An established encounter model generates the intruder trajectories while a multiple model algorithm is introduced to improve intruder dynamics estimation. A new method based on the Kalman prediction phase inside the Interactive Multiple Model (IMM) algorithm is presented to estimate time to closest point of approach, horizontal miss distance, and vertical separation. An analysis of the sensor error on the algorithm estimation and the sensor field of regard requirement from the Air-to-Air Radar Minimum Operational Performance Standards (MOPS) is performed. The efficiency of the trajectory estimation has direct implication on the estimation of the intruder trajectory in relation to the own aircraft. The methods described in this research can aid a certification authority in determining if a DAA system is sufficient for safely integration of UAS into the National Airspace System.

The behavior of the model probability is closely related to the performance of multiple model algorithm. A clear view about the behavior of model probability will benefit the performance analysis and the model set design for multiple model algorithm. We investigate the behavior of the model probability of multiple model algorithm for parameter estimation and filtering. It turns out that the Kullback-Leibler information between the true model and the model in the model set plays an important role to determine the evolution of model probability. Most importantly, we draw a connection between multiple model algorithm and the comparison of multiple estimation algorithms through the view of multiple hypotheses. The behavior of the model probability suggests a feasible way to combine multiple algorithms to obtain a new method of better performance. An illustrative example is also presented.

In this paper, the multiple model algorithm is used in deriving recursive algorithms for the identification of nonlinear systems. The radial basis function (RBF) networks with only linear weights requiring estimation combined with the Kalman filter algorithm forms the essence of the identification algorithm. Multiple networks are used to identify the multi-modes of the system under a Markovian assumption, the model estimation and selection being carried out on-line. Both, 'hard' and 'soft' competition based estimation schemes are developed where in the former, the most probable network is adapted by the Kalman filter and in the latter all networks are adapted by appropriate weighting of the observation.

In order to solve the problem of an uncertain initial state and big errors for hypersonic glide vehicle (HGV) tracking, a hybrid model algorithm is proposed by combining a single model algorithm with a multiple model algorithm. To develop the tracking algorithm with the Cubature Kalman filter, in every model filter the process equation is established based on the HGV aerodynamic model and the measurement equation is established based on the radar measurement principle. The proposed hybrid model algorithm is developed by using the multiple model algorithm in the initial tracking stage and using the single model algorithm in the stable tracking stage, and they are divided by a proposed parameter. The former can avoid divergence and reduce the errors caused by the uncertain initial state. The latter can track the HGV at higher accuracy. The simulation indicates that the proposed hybrid model has high speed accuracy in the whole tracking stage and high position accuracy in the stable tracking stage. The average position root mean square error (RMSE) using the hybrid model algorithm is almost the same as that using the single model algorithm but the average speed RMSE using the single model algorithm is about 30% greater than that using the hybrid model algorithm. In a system for defending the HGV, the speed accuracy has more effect on the trajectory prediction as time goes on. Thus, the hybrid model algorithm is an engineering algorithm for HGVs with high accuracy. In future research, the hybrid model algorithm will be studied for general maneuvering target tracking.

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Detection and identification of induction machine faults through the stator current signal using higher-order spectra analysis is presented. This research proposes two types of engine failures that are broken rotor bars, and rotor unbalance. Several conventional vibration and current analysis techniques exist by which certain faults in rotating machinery can be identified; however, they generally deal with a single fault only. Instead, in real induction machines, the case of multiple faults is common. When multiple faults exist, vibration and current are excited by several fault-related frequencies combined with each other, linearly or nonlinearly. The contribution of this paper is the development of a condition-monitoring strategy that can make accurate and reliable assessments of the presence of specific fault conditions in induction motors with single or multiple faults present.

The Interacting Multiple Model (IMM) algorithm has been used in various applications with good performance. However, to the best of our knowledge, stability conditions of the IMM algorithm have not been shown in the control literature. This technical note presents a sufficient condition for the exponential stability of the IMM algorithm for a class of Markov jump linear systems. We derive a lower bound and an upper bound for the error covariances of the IMM algorithm, and then derive the stability condition by the Lyapunov approach.

The grid points of the Adaptive Grid Interactive Multiple Model (AGIMM) algorithm change slowly at the target high maneuvering and fluctuate when the target is moving at a constant speed. The paper proposes an improved AGIMM algorithm based on maneuverability of target. Firstly, divide the Maneuverability zones by Filter residuals. Secondly, according to different zones, the grid points are updated in different ways to speed up the convergence of the model when the target is high maneuvering, and reduce the fluctuation of the model when the target is low maneuvering. Realize the model update method according to the target maneuverability adaptive adjustment. The simulation shows that the improved algorithm significantly reduces the tracking error regardless of whether the target turns or not.

This paper considers the decline problem of tracking accuracy caused by acceleration estimation inaccuracy in hybrid grid multiple model (HGMM) algorithm. A new improved tracking algorithm of maneuvering targets based on CSHGMM is proposed. Grid partition is performed by estimation of the acceleration mean in current statistic (CS) model, where a fading factor is adopted to improve tracking accuracy by adjusting the gain matrix under the condition of the abrupt change of acceleration. Then possible model sets of the target are generated online, and interactive multiple model algorithm is adopted to estimate the target state. The proposed algorithm performance is tested and compared in general and strong maneuvering scenarios, and simulation results demonstrate that the proposed algorithm not only improves the accuracy for maneuvering target tracking, but also can be applied to most of the tracking scenarios.

The quality of multiple model estimators can be improved with multisensor fusion. This paper contrasts the performance of three multiple model algorithms. It is shown that the simplest is adequate in high signal-to-noise environments. The more sophisticated warrant attention when the observations are ambiguous.

The paper compares the performance of two different configurations of the interacting multiple model (IMM) algorithm in tracking a civil aircraft. The first configuration of the IMM algorithm uses one straight line motion model and different constant turn rate models whereas the other configuration also employs a straight line motion model and a single turn rate model which uses an estimate of the turn rate. In the first algorithm, results have been obtained using different process noise values and different numbers of models. From these results, recommendations are made regarding the choice of both these variable parameters.

In this paper, we offer generalized exponentiated gamma distribution. We consider the maximum likelihood and Bayesian estimators of unknown parameters and propose Markov chain Monte Carlo (MCMC) method to generate samples from the posterior distribution. The mean square error of estimations is computed and comparisons are made using Monte Carlo simulation. Key words: Maximum likelihood estimator, Bayesian estimator, squared error loss function, generalized exponentiated gamma distribution.

The problem of recursive robust identification of linear discrete-time single-input single-output dynamic systems with correlated disturbances is considered. Problems related to the construction of optimal robust stochastic approximation algorithms in the min-max sense are demonstrated. Since the optimal solution cannot be achieved in practice, several robustified stochastic approximation algorithms are derived on the basis of a suitable non-linear transformation of normalized residuals, as well as step-by-step optimization with respect to the weighting matrix of the algorithm. The convergence of the developed algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the proposed algorithms. The results indicate the most suitable algorithms for applications in engineering practice.

An interacting Fuzzy-Fading-Memory-based Augmented Kalman Filtering method for maneuvering target tracking

This study is devoted to the problem of state estimation of discrete-time stochastic systems with Markov switching parameters. Three improved interacting multiple model (IMM) algorithms for manoeuvring target tracking are presented, in which the filter outputs are combined based on three optimal multi-model fusion criterions weighted by scalars, diagonal matrices and general matrices, respectively. The proposed algorithms can receive the optimal state estimations of target in the linear minimum variance sense. It is proved that the traces of variance matrices of tracking errors in three proposed algorithms are less than the trace in the classical IMM algorithm. Extensive Monte Carlo simulations verify that the proposed algorithms are effective and have an absolute advantage in the velocity estimation. In particular, one of the proposed algorithms is obviously better than the IMM algorithm in accuracy and elapsed time and, therefore, can be a competitive alternative to the classical IMM algorithm for the tracking of manoeuvring target in real time.