Aircraft Trajectory Prediction Based on Modified Interacting Multiple Model Algorithm

In order to realize the aircraft trajectory prediction,a modified interacting multiple model(M-IMM) algorithm is proposed,which is based on the performance analysis of the standard interacting multiple model(IMM) algorithm.In the proposed M-IMM algorithm,a new likelihood function is defined for the sake of updating flight mode probabilities,in which the influences of interacting to residual's mean error are taken into account and the assumption of likelihood function being a zero mean Gaussian function is discarded.Finally,the proposed M-IMM algorithm is applied to the simulation of the aircraft trajectory prediction,and the comparative studies are conducted to existing algorithms.The simulation results indicate the proposed M-IMM algorithm can predict aircraft trajectory more quickly and accurately.

Efficient Graph-based Genetic Programming Representation with Multiple Outputs

In this work, we explore and study the implication of having more than one output on a genetic programming （GP） graph-representation. This approach, called multiple interactive outputs in a single tree （MIOST）, is based on two ideas. First, we defined an approach, called interactivity within an individual （IWI）, which is based on a graph-GP representation. Second, we add to the individuals created with the IWI approach multiple outputs in their structures and as a result of this, we have MIOST. As a first step, we analyze the effects of IWI by using only mutations and analyze its implications （i.e., presence of neutrality）. Then, we continue testing the effectiveness of IWI by allowing mutations and the standard GP crossover in the evolutionary process. Finally, we tested the effectiveness of MIOST by using mutations and crossover and conducted extensive empirical results on different evolvable problems of different complexity taken from the literature. The results reported in this paper indicate that the proposed approach has a better overall performance in terms of consistency reaching feasible solutions.

ADAPTIVE MULTIPLE MODEL FILTER USING IMM AND STF

In fault identification, the Strong Tracking Filter (STF) has strong ability to track the change of some parameters by whitening filtering innovation. In this paper, the authors give out a modified STF by searching the fading factor based on the Least Squared Estimation. In hybrid estimation, the well known Interacting Multiple Model (IMM) Technique can model the change of the system modes. So one can design a new adaptive filter — SIMM. In this filter, our modified STF is a parameter adaptive part and IMM is a mode adaptive part. The benefit of the new filter is that the number of models can be reduced considerably. The simulations show that SIMM greatly improves accuracy of velocity and acceleration compared with the standard IMM to track the maneuvering target when 2 model conditional estimators are used in both filters. And the computation burden of SIMM increases only 6% compared with IMM.

One compound approach combining factor-analytic model with AMMI and GGE biplot to improve multi-environment trials analysis

To improve multi-environmental trial(MET)analysis,a compound method—which combines factor analytic(FA)model with additive main effect and multiplicative interaction(AMMI)and genotype main effect plus genotype-by-environment interaction(GGE)biplot—was conducted in this study.The diameter at breast height of 36 open-pollinated(OP)families of Pinus taeda at six sites in South China was used as a raw dataset.The best linear unbiased prediction(BLUP)data of all individual trees in each site was obtained by fitting the spatial effects with the FA method from raw data.The raw data and BLUP data were analyzed and compared by using the AMMI and GGE biplot.BLUP results showed that the six sites were heterogeneous and spatial variation could be effectively fitted by spatial analysis with the FA method.AMMI analysis identified that two datasets had highly significant effects on the site,family,and their interactions,while BLUP data had a smaller residual error,but higher variation explaining ability and more credible stability than raw data.GGE biplot results revealed that raw data and BLUP data had different results in mega-environment delineation,test-environment evaluation,and genotype evaluation.In addition,BLUP data results were more reasonable due to the stronger analytical ability of the first two principal components.Our study suggests that the compound method combing the FA method with the AMMI and GGE biplot could improve the analysis result of MET data in Pinus teada as it was more reliable than direct AMMI and GGE biplot analysis on raw data.

Consecutive tracking for ballistic missile based on bearings-only during boost phase

This paper proposes a modified centralized shifted Rayleigh filter（MCSRF） algorithm for tracking boost phase of ballistic missile（BM） trajectory with a highly nonlinear dynamical model based on bearings-only.This paper contributes three folds.Firstly,the mathematical model of an MCSRF for multiple passive sensors is derived.Then,minimum entropy based onedimensional optimization search to adaptively adjust the probability of the different filters for real time state estimation is deployed.Finally,the unscented transform（UT） is introduced to resolve the asymmetric state estimation problem.Simulation results show that the proposed algorithm can consecutively track the BM precisely during the boost phase.In comparison with the unscented Kalman filter（UKF） algorithm,the proposed algorithm effectively reduces the tracking position and velocity root mean square（RMS） errors,which will make more sense for early precision interception.

Application of Road Information in Ground Moving Target Tracking

A new algorithm is developed to achieve accurate state estimation in ground moving target tracking by means of using road information. It is an adaptive variable structure interacting multiple model estimator with dynamic models modification （DMM VS-IMM for short）. Firstly, road information is employed to modify the target dynamic models used by filter, including modification of state transition matrix and process noise. Secondly, road information is applied to update the model set of a VS-IMM estimator. Predicted state estimation and road information are used to locate the target in the road network on which the model set is updated and finally IMM filtering is implemented. As compared with traditional methods, the accuracy of state estimation is improved for target moving not only on a single road, but also through an intersection. Monte Carlo simulation demonstrates the efficiency and robustness of the proposed algorithm with moderate computational loads.

Modified switched IMM estimator based on autoregressive extended Viterbi method for maneuvering target tracking

In this paper, a new approach of maneuvering target tracking algorithm based on the autoregressive extended Viterbi(AREV) model is proposed. In contrast to weakness of traditional constant velocity(CV) and constant acceleration(CA) models to noise effect reduction, the autoregressive(AR) part of the new model which changes the structure of state space equations is proposed. Also using a dynamic form of the state transition matrix leads to improving the rate of convergence and decreasing the noise effects. Since AR will impose the load of overmodeling to the computations, the extended Viterbi(EV) method is incorporated to AR in two cases of EV1 and EV2. According to most probable paths in the interacting multiple model(IMM) during nonmaneuvering and maneuvering parts of estimation, EV1 and EV2 respectively can decrease load of overmodeling computations and improve the AR performance. This new method is coupled with proposed detection schemes for maneuver occurrence and termination as well as for switching initializations. Appropriate design parameter values are derived for the detection schemes of maneuver occurrences and terminations. Finally, simulations demonstrate that the performance of the proposed model is better than the other older linear and also nonlinear algorithms in constant velocity motions and also in various types of maneuvers.

Tracking a maneuvering target in clutter with out-of-sequence measurements for airborne radar

There are many proposed optimal or suboptimal al- gorithms to update out-of-sequence measurement（s） （OoSM（s）） for linear-Gaussian systems, but few algorithms are dedicated to track a maneuvering target in clutter by using OoSMs. In order to address the nonlinear OoSMs obtained by the airborne radar located on a moving platform from a maneuvering target in clut- ter, an interacting multiple model probabilistic data association （IMMPDA） algorithm with the OoSM is developed. To be practical, the algorithm is based on the Earth-centered Earth-fixed （ECEF） coordinate system where it considers the effect of the platform＇s attitude and the curvature of the Earth. The proposed method is validated through the Monte Carlo test compared with the perfor- mance of the standard IMMPDA algorithm ignoring the OoSM, and the conclusions show that using the OoSM can improve the track- ing performance, and the shorter the lag step is, the greater degree the performance is improved, but when the lag step is large, the performance is not improved any more by using the OoSM, which can provide some references for engineering application.

Improved IMM algorithm based on support vector regression for UAV tracking

With the development of technology, the relevant performance of unmanned aerial vehicles(UAVs) has been greatly improved, and various highly maneuverable UAVs have been developed, which puts forward higher requirements on target tracking technology. Strong maneuvering refers to relatively instantaneous and dramatic changes in target acceleration or movement patterns, as well as continuous changes in speed,angle, and acceleration. However, the traditional UAV tracking algorithm model has poor adaptability and large amount of calculation. This paper applies support vector regression(SVR)to the interacting multiple model(IMM) algorithm. The simulation results show that the improved algorithm has higher tracking accuracy for highly maneuverable targets than the original algorithm, and can adjust parameters adaptively, making it more adaptable.

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.

Maneuvering target state estimation based on separate model-ing of target trajectory shape and dynamic characteristics

The state estimation of a maneuvering target,of which the trajectory shape is independent on dynamic characteristics,is studied.The conventional motion models in Cartesian coordinates imply that the trajectory of a target is completely determined by its dynamic characteristics.However,this is not true in the applications of road-target,sea-route-target or flight route-target tracking,where target trajectory shape is uncoupled with target velocity properties.In this paper,a new estimation algorithm based on separate modeling of target trajectory shape and dynamic characteristics is proposed.The trajectory of a target over a sliding window is described by a linear function of the arc length.To determine the unknown target trajectory,an augmented system is derived by denoting the unknown coefficients of the function as states in mileage coordinates.At every estimation cycle except the first one,the interaction(mixing)stage of the proposed algorithm starts from the latest estimated base state and a recalculated parameter vector,which is determined by the least squares(LS).Numerical experiments are conducted to assess the performance of the proposed algorithm.Simulation results show that the proposed algorithm can achieve better performance than the conventional coupled model-based algorithms in the presence of target maneuvers.

Novel sensor selection strategy for LPI based on an improved IMMPF tracking method

Sensor platforms with active sensing equipment such as radar may betray their existence, by emitting energy that will be intercepted by enemy surveillance sensors. The radar with less emission has more excellent performance of the low probability of intercept（LPI）. In order to reduce the emission times of the radar, a novel sensor selection strategy based on an improved interacting multiple model particle filter（IMMPF） tracking method is presented. Firstly the IMMPF tracking method is improved by increasing the weight of the particle which is close to the system state and updating the model probability of every particle. Then a sensor selection approach for LPI takes use of both the target＇s maneuverability and the state＇s uncertainty to decide the radar＇s radiation time. The radar will work only when the target＇s maneuverability and the state＇s uncertainty exceed the control capability of the passive sensors. Tracking accuracy and LPI performance are demonstrated in the Monte Carlo simulations.

Synthesis and Structure of a Zinc(II) Complex:[Zn(Pybta)·Cl_2]_n

The title compound, [Zn（Pybta）Cl2]n （Pybta = 1-（2-pyridylmethyl）benzontriazole）, has a zigzag chain structure. It crystallizes in the monoclinic system, space group P21/c with a = 9.0103（11）, b = 17.0276（18）, c = 9.2288（11）A,β = 101.309（6）°, Mr= 346.51, V= 1388.4（3）A^3, Z= 4, De= 1.658 g/cm^3, F（000） = 696,/a = 2.143 mm^-1, the final R = 0.0492 and wR = 0.1236 for 2545 observed reflections with I 〉 2σ（I）. The Zn atom is four-coordinated by two N and two Cl atoms, forming a slightly distorted tetrahedral geometry. Each zigzag chain links its adjacent symmetryrelated equivalents via multiple π-π interactions, which are not frequently observed in the previously reported architectures.

Maneuvering target tracking algorithm based on CDKF in observation bootstrapping strategy

The selection and optimization of model filters affect the precision of motion pattern identification and state estimation in maneuvering target tracking directly.Aiming at improving performance of model filters,a novel maneuvering target tracking algorithm based on central difference Kalman filter in observation bootstrapping strategy is proposed.The framework of interactive multiple model(IMM) is used to realize identification of motion pattern,and a central difference Kalman filter(CDKF) is selected as the model filter of IMM.Considering the advantage of multi-sensor fusion method in improving the stability and reliability of observation information,the hardware cost of the observation system for multiple sensors is adopted,meanwhile,according to the data assimilation technique in Ensemble Kalman filter(En KF),a bootstrapping observation set is constructed by integrating the latest observation and the prior information of observation noise.On that basis,these bootstrapping observations are reasonably used to optimize the filtering performance of CDKF by means of weight fusion way.The object of new algorithm is to improve the tracking precision of observed target by the multi-sensor fusion method without increasing the number of physical sensors.The theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm.

Interactive group decision making procedure based on uncertain multiplicative linguistic preference relations

Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts＇ weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.Finally,the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.

Genotype×year interaction of pod and seed mass and stability of Pongamia pinnata families in a semi-arid region

Sixteen pongamia families were evaluated in a field experiment for eight consecutive years in dryland conditions to identify stable,high-yielding families.The trial was conducted in a randomized complete block design with three replications.Each family,consisting of nine trees per replication,was planted at a spacing of3 m x 3 m.Yield stability was analyzed using(1)Eberhart and Russel’s regression coefficient(β_i)and deviation from regression(S_d^2),(2)Wrike’s ecovalence(W_i);(3)Shukla stability variance(σ_i^2);and(4)Piepho and Lotito’s stability index(L_i).Families were also analyzed for adaptability and stability using AMMI and GGE biplots graphical methods.The study revealed significant variances due to family and family x year interaction for pod and seed yield.Families performed differently and ranked differently across years.The performance of families was influenced by both genetic factor and environmental conditions in different years.Among families tested,TNMP20,Acc14,TNMP14 and Acc30 were high yielders for pods,and Acc14,Acc30,TNMP6,RAK19 and TNMP14 were high for seed yield.According to the Eberhart and Russell model,Acc30,TNMP14 and TNMP3 were stable across years.In the graphical view of family x year interaction based on AMMI methods,TNMP3,TNMP4 and TNMP14 had greater stability with moderate seed yield,and Acc14 and Acc30 had moderate stability with high seed yield.On the other hand,GGE biplots revealed Acc14,Acc30 and TNMP14 as high yielders with moderate stability.AMMI and GGE biplots were able to capture nonlinear parts of the family x year interaction that were not be captured by the Eberhart and Russel model while also identifying stable families.Based on different methodologies,Acc14,Acc30 and TNMP14 were identified as high yielding and stable families for promoting pongamia cultivation as a biofuel crop for semi-arid regions.

Bearings-only fusion tracking for maneuvering target with wavelettransform in three dimensional space

A new fusion tracking algorithm is presented to track maneuvering target in three-dimensional (3D) space with bearings-only measurements. With the introduction of passive location and interacting multiple model (IMM) algorithm based on multirate model, the high-rate sequence measurements of two sensors are utilized. Simulation results show that the performance of tracking has been improved. The new algorithm removes the barrier of processing high-rate bearings-only measurements.

A New Smoothing Approach with Diverse Fixed-lags Based on Target Motion Model

Recently, lots of smoothing techniques have been presented for maneuvering target tracking. Interacting multiple model-probabilistic data association （IMM-PDA） fixed-lag smoothing algorithm provides an efficient solution to track a maneuvering target in a cluttered environment. Whereas, the smoothing lag of each model in a model set is a fixed constant in traditional algorithms. A new approach is developed in this paper. Although this method is still based on IMM-PDA approach to a state augmented system, it adopts different smoothing lag according to diverse degrees of complexity of each model. As a result, the application is more flexible and the computational load is reduced greatly. Some simulations were conducted to track a highly maneuvering target in a cluttered environment using two sensors. The results illustrate the superiority of the proposed algorithm over comparative schemes, both in accuracy of track estimation and the computational load.

Adaptive Sampling for Near Space Hypersonic Gliding Target Tracking

For modern phased array radar systems,the adaptive control of the target revisiting time is important for efficient radar resource allocation,especially in maneuvering target tracking applications.This paper presents a novel interactive multiple model(IMM)algorithm optimized for tracking maneuvering near space hypersonic gliding vehicles(NSHGV)with a fast adaptive sam-pling control logic.The algorithm utilizes the model probabilities to dynamically adjust the revisit time corresponding to NSHGV maneuvers,thus achieving a balance between tracking accuracy and resource consumption.Simulation results on typical NSHGV targets show that the proposed algo-rithm improves tracking accuracy and resource allocation efficiency compared to other conventional multiple model algorithms.

Multi-Environment Evaluation and Genotype ×Environment Interaction Analysis of Sorghum [<i>Sorghum bicolor</i>(L.) Moench] Genotypes in Highland Areas of Ethiopia

Sorghum [Sorghum bicolor (L.) Moench] is a high-yielding, nutrient-use efficient, and drought tolerant crop that can be cultivated on over 80 per cent of the world’s agricultural land. However, a number of biotic and abiotic factors are limiting grain yield increase. Diseases (leaf and grain) are considered as one of the major biotic factors hindering sorghum productivity in the highland and intermediate altitude sorghum growing areas of Ethiopia. In addition, the yield performance of crop varieties is highly influenced by genotype × environment (G × E) interaction which is the major focus of researchers while generating improved varieties. In Ethiopia, high yielding and stable varieties that withstand biotic stress in the highland areas are limited. In line with this, the yield performance of 21 sorghum genotypes and one standard check were evaluated across 14 environments with the objectives of estimating magnitude G × E interaction for grain yield and to identify high yielder and stable genotypes across environments. The experiment was laid out using Randomized Complete Block Design with three replications in all environments. The combined analysis of variance across environments revealed highly significant differences among environments, genotypes and G × E interactions of grain yield suggesting further analysis of the G × E interaction. The results of the combined AMMI analysis of variance indicated that the total variation in grain yield was attributed to environments effects 71.21%, genotypes effects 4.52% and G × E interactions effects 24.27% indicating the major sources of variation. Genotypes 2006AN7010 and 2006AN7011 were high yielder and they were stable across environments and one variety has been released for commercial production and can be used as parental lines for genetic improvement in the sorghum improvement program. In general, this research study revealed the importance of evaluating sorghum genotypes for their yield and stability across diverse highland areas of Ethiopia before releasing for commercial production.