Multiple-model estimation with variable structure. IV. Design andevaluation of model-group switching algorithm

For pt. III see ibid., vol. 35, pp. 225-41 (1999). A variable-structure multiple-model (VSMM) estimator, called model-group switching (MGS) algorithm, has been presented in Part III, which is the first VSMM estimator that is generally applicable to a large class of problem with hybrid (continuous and discrete) uncertainties. In this algorithm, the model-set is made adaptive by switching among a number of predetermined groups of models. It has the potential to be substantially more cost-effective than fixed-structure MM (FSMM) estimators, including the Interacting Multiple-Model (IMM) estimator. A number of issues of major importance in the application of this algorithm are investigated here, including the model-group adaptation logic and model-group design. The results of this study are implemented via a detailed design for a problem of tracking a maneuvering target using a time-varying set of models, each characterized by a representative value of the expected acceleration of the target. Simulation results are given to demonstrate the performance (based on more reasonable and complete measures than commonly used rms errors alone) and computational complexity of the MGS algorithm, relative to the fixed-structure IMM (FSIMM) estimator using all models, under carefully designed and fair random and deterministic scenarios     

Minimal submodel-set algorithm for maneuvering target tracking

The variable structure multiple model (VSMM) approach to the maneuvering target tracking problem is considered. A new VSMM design, the minimal submodel-set switching (MSMSS) algorithm for tracking a maneuvering target is presented. The MSMSS algorithm adaptively determines the minimal set of models from the total model set and uses this to perform multiple models (MM) estimation. In addition, an iterative MSMSS algorithm with improved maneuver detection and termination properties is developed. Simulations results demonstrate that, compared with a standard interacting MM (IMM), the proposed algorithms require significantly lower computation while maintaining similar tracking performance. Alternatively, for a computational load similar to IMM, the new algorithms display significantly improved performance.     

Feedback structure based entropy approach for multiple-model estimation

The variable-structure multiple-model（VSMM）approach,one of the multiple-model（MM）methods,is a popular and effective approach in handling problems with mode uncertainties.The model sequence set adaptation（MSA）is the key to design a better VSMM.However,MSA methods in the literature have big room to improve both theoretically and practically.To this end,we propose a feedback structure based entropy approach that could fnd the model sequence sets with the smallest size under certain conditions.The fltered data are fed back in real time and can be used by the minimum entropy（ME）based VSMM algorithms,i.e.,MEVSMM.Firstly,the full Markov chains are used to achieve optimal solutions.Secondly,the myopic method together with particle flter（PF）and the challenge match algorithm are also used to achieve sub-optimal solutions,a trade-off between practicability and optimality.The numerical results show that the proposed algorithm provides not only refned model sets but also a good robustness margin and very high accuracy.     

Geometrical entropy approach for variable structure multiple-model estimation

The variable structure multiple-model(VSMM) estimation approach, one of the multiple-model(MM) estimation approaches, is popular in handling state estimation problems with mode uncertainties.In the VSMM algorithms, the model sequence set adaptation(MSA) plays a key role.The MSA methods are challenged in both theory and practice for the target modes and the real observation error distributions are usually uncertain in practice.In this paper, a geometrical entropy(GE) measure is proposed so that the MSA is achieved on the minimum geometrical entropy(MGE) principle.Consequently, the minimum geometrical entropy multiple-model(MGEMM) framework is proposed, and two suboptimal algorithms, the particle filter k-means minimum geometrical entropy multiple-model algorithm(PF-KMGEMM) as well as the particle filter adaptive minimum geometrical entropy multiple-model algorithm(PF-AMGEMM), are established for practical applications.The proposed algorithms are tested in three groups of maneuvering target tracking scenarios with mode and observation error distribution uncertainties.Numerical simulations have demonstrated that compared to several existing algorithms, the MGE-based algorithms can achieve more robust and accurate estimation results when the real observation error is inconsistent with a priori.     

Multiple-model estimation with variable structure. V. Likely-modelset algorithm

For pt. IV see ibid., vol. 35, no. 1, p. 242-254 (1999). A multiple-model (MM) estimator with a variable structure, called likely-model set (LMS) algorithm, is presented, which is generally applicable to most hybrid estimation problems and is easily implementable. It uses a set of models that are not unlikely to match the system mode in effect at any given time. Different versions of the algorithm are discussed. The model set is made adaptive in the simplest version by deleting all unlikely models and activating all models to which a principal model may jump so as to anticipate the possible system mode transitions. The generality, simplicity, and ease in the design and implementation of the LMS estimator are illustrated via an example of tracking a maneuvering target and an example of fault detection and identification. Comparison of its cost-effectiveness with other fixed- and variable-structure MM estimators is given     

Variable structure multiple model fixed-interval smoothing

This paper focuses on fixed-interval smoothing for stochastic hybrid systems. When the truth-mode mismatch is encountered, existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable. We develop a fixed-interval smoothing method based on forward- and backward-filtering in the Variable Structure Multiple Model (VSMM) framework in this paper. We propose to use the Simplified Equivalent model Interacting Multiple Model (SEIMM) in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters, and design a re-filtering procedure in the model-switching stage to enhance the estimation performance. To improve the computational efficiency, we make the basic model-set adaptive by the Likely-Model Set (LMS) algorithm. It turns out that the smoothing performance is further improved by the LMS due to less competition among models. Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.     

A novel variable structure multi-model approach based on error-ambiguity decomposition

Model Set Adaptation (MSA) plays a key role in the Variable Structure Multi-Model tracking approach (VSMM). In this paper, the Error-Ambiguity Decomposition (EAD) principle is adopted to derive the EAD-MSA criterion that is optimal in the sense of minimizing the square error between the estimate and the truth. Consequently, the EAD Variable Structure first-order General Pseudo Bayesian (EAD-VSGPB1) algorithm and the EAD Variable Structure Interacting Multiple Model (EAD-VSIMM) algorithm are constructed. The proposed algorithms are tested in two groups of maneuvering target tracking scenarios under different modes and observation error conditions. The simulation results demonstrate the effectiveness of the EAD-VSMM approach and show that, compared to some existing multi-model algorithms, the proposed EAD-VSMM algorithms achieve more robust and accurate tracking results.     

EM-ML algorithm for track initialization using possibly noninformative data

Initializing and maintaining a track for a low observable (LO) (low SNR, low target detection probability and high false alarm rate) target can be very challenging because of the low information content of measurements. In addition, in some scenarios, target-originated measurements might not be present in many consecutive scans because of mispointing, target maneuvers, or erroneous preprocessing. That is, one might have a set of noninformative scans that could result in poor track initialization and maintenance. In this paper an algorithm based on the expectation-maximization (EM) algorithm combined with maximum likelihood (ML) estimation is presented for tracking slowly maneuvering targets in heavy clutter and possibly noninformative scans. The adaptive sliding-window EM-ML approach, which operates in batch mode, tries to reject or weight down noninformative scans using the Q-function in the M-step of the EM algorithm. It is shown that target features in the form of, for example, amplitude information (AI), can also be used to improve the estimates. In addition, performance bounds based on the supplemented EM (SEM) technique are also presented. The effectiveness of new algorithm is first demonstrated on a 78-frame long wave infrared (LWIR) data sequence consisting of an Fl Mirage fighter jet in heavy clutter. Previously, this scenario has been used as a benchmark for evaluating the performance of other track initialization algorithms. The new EM-ML estimator confirms the track by frame 20 while the ML-PDA (maximum likelihood estimator combined with probabilistic data association) algorithm, the IMM-MHT (interacting multiple model estimator combined with multiple hypothesis tracking) and the EVIM-PDA estimator previously required 28, 38, and 39 frames, respectively. The benefits of the new algorithm in terms of accuracy, early detection, and computational load are illustrated using simulated scenarios as well.     

Precision large scale air traffic surveillance using IMM/assignmentestimators

We present the development and implementation of a multisensor-multitarget tracking algorithm for large scale air traffic surveillance based on interacting multiple model (IMM) state estimation combined with a 2-dimensional assignment for data association. The algorithm can be used to track a large number of targets from measurements obtained with a large number of radars. The use of the algorithm is illustrated on measurements obtained from 5 FAA radars, which are asynchronous, heterogeneous, and geographically distributed over a large area. Both secondary radar data (beacon returns from cooperative targets) as well as primary radar data (skin returns from noncooperative targets) are used. The target IDs from the beacon returns are not used in the data association. The surveillance region includes about 800 targets that exhibit different types of motion. The performance of an IMM estimator with linear motion models is compared with that of the Kalman filter (KF). A number of performance measures that can be used on real data without knowledge of the ground truth are presented for this purpose. It is shown that the IMM estimator performs better than the KF. The advantage of fusing multisensor data is quantified. It is also shown that the computational requirements in the multisensor case are lower than in single sensor case, Finally, an IMM estimator with a nonlinear motion model (coordinated turn) is shown to further improve the performance during the maneuvering periods over the IMM with linear models     

基于变结构多模型的SINS/DVL组合导航算法

对于无人水下航行器来说,SINS/DVL组合导航是其主要导航方式,由于DVL自身作用距离的限制,虽然它可以在水跟踪模式下工作,但洋流速度作为其测量误差会导致SINS/DVL组合导航性能下降甚至失败.针对上述问题,基于有向图切换方法,设置洋流速度模型群,利用所设置的模型群切换策略对子模型群进行激活和终止,通过变结构多模型...     

Optimum FFT-based frequency acquisition with application toCOSPAS-SARSAT

In the case of a single sinusoid or multiple well-separated sinusoids, a coarse estimator consisting of a windowed Fourier transform followed by a fine estimator which is an interpolator is a good approximation to an optimal frequency acquisition and measurement algorithm. The design tradeoffs are described. It is shown that for the fine-frequency estimator a good method is to fit a Gaussian function to the fast-Fourier-transform (FFT) peak and its two neighbors. This method achieves a frequency standard deviation and a bias in the order of only a few percent of a bin. In the case of short-time stationarity, for a moderate number of averages and for an adaptive threshold detector, only between 0.5 and 1 dB is lost when averaging is traded off for FFT length, in contrast to the asymptotic result of 1.5 dB. The COSPAS-SARSAT satellite system for emergency detection and localization is used to illustrate the concepts. The algorithm is analyzed theoretically, and good agreement is found with test results     

MAP estimation of target manoeuvre sequence with theexpectation-maximization algorithm

Two algorithms are derived for the problem of tracking a manoeuvring target based on a sequence of noisy measurements of the state. Manoeuvres are modeled as unknown input (acceleration) terms entering linearly into the state equation and chosen from a discrete set. The expectation maximization (EM) algorithm is first applied, resulting in a multi-pass estimator of the MAP sequence of inputs. The expectation step for each pass involves computation of state estimates in a bank of Kalman smoothers tuned to the possible manoeuvre sequences. The maximization computation is efficiently implemented using the Viterbi algorithm. A second, recursive estimator is then derived using a modified EM-type cost function. To obtain a dynamic programming recursion, the target state is assumed to satisfy a Markov property with respect to the manoeuvre sequence. This results in a recursive but suboptimal estimator implementable on a Viterbi trellis. The transition costs of the latter algorithm, which depend on filtered estimates of the state, are compared with the costs arising in a Viterbi-based manoeuvre estimator due to Averbuch, et al. (1991). It is shown that the two criteria differ only in the weighting matrix of the quadratic part of the cost function. Simulations are provided to demonstrate the performance of both the batch and recursive estimators compared with Averbuch's method and the interacting multiple model filter     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

Mars Global Surveyor Measurements of the Martian Solar Wind Interaction

The solar wind at Mars interacts with the extended atmosphere and small-scale crustal magnetic fields. This interaction shares elements with a variety of solar system bodies, and has direct bearing on studies of the long-term evolution of the Martian atmosphere, the structure of the upper atmosphere, and fundamental plasma processes. The magnetometer (MAG) and electron reflectometer (ER) on Mars Global Surveyor (MGS) continue to make many contributions toward understanding the plasma environment, thanks in large part to a spacecraft orbit that had low periapsis, had good coverage of the interaction region, and has been long-lived in its mapping orbit. The crustal magnetic fields discovered using MGS data perturb plasma boundaries on timescales associated with Mars' rotation and enable a complex magnetic field topology near the planet. Every portion of the plasma environment has been sampled by MGS, confirming previous measurements and making new discoveries in each region. The entire system is highly variable, and responds to changes in solar EUV flux, upstream pressure, IMF direction, and the orientation of Mars with respect to the Sun and solar wind flow. New insights from MGS should come from future analysis of new and existing data, as well as multi-spacecraft observations.     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

自适应遗传神经网络算法在推力估计器设计中的应用

为了在全包线内能够准确方便估计出航空发动机推力,提出了一种自适应遗传神经网络算法:将遗传算法和神经网络技术相结合充分发挥遗传算法和神经网络各自的全局收敛性和局部搜索快速性的优点,其中通过自适应概率遗传操作及局部寻优算子直接优化出神经网络拓扑结构及权值(包括阈值),克服了神经网络隐层节点需凭经验尝试的缺点和神经网络对初始权值(包括阈值)敏感的缺点,再应用神经网络对上述优化的权值(包括阈值)进行"精调",最后设计出全包线推力估计器.经验证,此推力估计器具有较高估计精度和良好泛化能力.      

On-line Vehicle Motion Estimation from Visual Terrain Information Part II: Ground Velocity and Position Estimation

An algorithm, combining velocity/height estimates, obtained from an airborne body fixed image shift estimator with auxiliary on-board measurements and sparsely stored terrain profile information constitutes an entirely passive autonomous navigation system suitable for moderate-g flight missions. Two versions are addressed. The "naive estimator," in which altitude estimates are multiplied by velocity/height estimaters, yields ground velocity. Position, obtained by integration, diverges with time. The "extended Kalman filter" (EKF) version, in which velocity and position are defined as state space components, locks on the stored terrain profile and does not diverge with time. It degenerates into the "naive estimator" if the terrain is completely flat. Numerical examples indicate excellent performance potential of the EKF estimator.     

Sequential ensemble optimization based on general surrogate model prediction variance and its application on engine acceleration schedule design

The Efficient Global Optimization (EGO) algorithm has been widely used in the numerical design optimization of engineering systems. However, the need for an uncertainty estimator limits the selection of a surrogate model. In this paper, a Sequential Ensemble Optimization (SEO) algorithm based on the ensemble model is proposed. In the proposed algorithm, there is no limitation on the selection of an individual surrogate model. Specifically, the SEO is built based on the EGO by extending the EGO algorithm so that it can be used in combination with the ensemble model. Also, a new uncertainty estimator for any surrogate model named the General Uncertainty Estimator (GUE) is proposed. The performance of the proposed SEO algorithm is verified by the simulations using ten well-known mathematical functions with varying dimensions. The results show that the proposed SEO algorithm performs better than the traditional EGO algorithm in terms of both the final optimization results and the convergence rate. Further, the proposed algorithm is applied to the global optimization control for turbo-fan engine acceleration schedule design.     

基于自适应步长选择的周期格型线搜索估计

稀疏、含噪观测条件下周期点过程的周期估计是一个经典的信号处理问题。针对该问题,提出了一种格型线搜索(LLS)算法,该算法通过数值方式搜索似然函数的最大值,但其性能取决于人为预先选取的搜索步长。推导了一个步长计算公式,并利用该公式改进了LLS算法。改进的LLS算法能够自适应选择搜索步长,其达到的克拉美-罗界(CRLB)的信噪比(SNR)门限与最大似然估计(MLE)算法一致,但计算复杂度比后者低一个多的数量级。性能分析与仿真实验表明,所提算法比已有算法能更好地实现估计精度与复杂度的折中。     

Interacting acceleration compensation algorithm for trackingmaneuvering targets

The two-stage Kalman estimator has been studied for state estimation in the presence of random bias and applied to the tracking of maneuvering targets by treating the target acceleration as a bias vector. Since the target acceleration is considered a bias, the first stage contains a constant velocity motion model and estimates the target position and velocity, while the second stage estimates the target acceleration when a maneuver is detected, the acceleration estimate is used to correct the estimates of the first stage. The interacting acceleration compensation (IAC) algorithm is proposed to overcome the requirement of explicit maneuver detection of the two-stage estimator. The IAC algorithm is viewed as a two-stage estimator having two acceleration models: the zero acceleration of the constant velocity model and a constant acceleration model. The interacting multiple model (IMM) algorithm is used to compute the acceleration estimates that compensate the estimate of the constant velocity filter. Simulation results indicate the tracking performance of the IAC algorithm approaches that of a comparative IMM algorithm while requiring approximately 50% of the computations