A nonlinear IMM algorithm for maneuvering target tracking

In target tracking, the measurement noise is usually assumed to be Gaussian. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. We develop a new algorithm that can effectively track a maneuvering target in the glint environment The algorithm incorporates the nonlinear Masreliez filter into the interactive multiple model (IMM) method. Simulations demonstrate the superiority of the new algorithm     

Maneuvering target tracking with colored noise

It is known that colored noise may degrade the performance of a tracking algorithm. A common remedy is to model colored noise as an autoregressive (AR) process and apply the measurement difference method. One problem with the approach is that the AR parameters are usually unknown. In this work, we propose a new method to adaptively estimate the AR parameters. It is shown that this method is simple and practically feasible. We incorporate oar method into the interacting multiple model (IMM) tracking algorithm and show that the performance is almost as good as that in the known parameters case     

Robust guidance for electro-optical missiles

A robust guidance law is presented which renders zero miss distance (ZMD) against deterministically or randomly maneuvering targets for all missile parametric uncertainties. Since the resulting guidance controller is a phase-lead network, it is mainly suitable for systems characterized by moderate glint levels such as electro-optical missiles. The structured uncertainties in missile dynamics are modeled by interval transfer functions. It is first shown that for the nominal case, when the total missile transfer function is positive real, ZMD can be obtained. When uncertainties are considered, the problem becomes design of a guidance controller which renders a family of transfer functions positive real. A new algorithm for the design of such controllers is proposed. An example illustrating a typical design procedure for a nonlinear real-life missile model is given, showing the simplicity and effectiveness of the proposed robust guidance. The main conclusion of this work is that the newly developed guidance law performs well against highly maneuvering targets and may be a suitable alternative to optimal guidance laws in low-glint systems.     

Detection and diagnosis of sensor and actuator failures using IMMestimator

An approach to detection and diagnosis of multiple failures in a dynamic system is proposed. It is based on the interacting multiple-model (IMM) estimation algorithm, which is one of the most cost-effective adaptive estimation techniques for systems involving structural as well as parametric changes. The proposed approach provides an integrated framework for fault detection, diagnosis, and state estimation. It is able to detect and isolate multiple faults substantially more quickly and more reliably than many existing approaches. Its superiority is illustrated in two aircraft examples for single and double faults of both sensors and actuators, in the forms of “total”, “partial”, and simultaneous failures. Both deterministic and random fault scenarios are designed and used for testing and comparing the performance fairly. Some new performance indices are presented. The robustness of the proposed approach to the design of model transition probabilities, fault modeling errors, and the uncertainties of noise statistics are also evaluated     

Radar Target Pointing Error Reduction Using Extended Kalman Filtering

A new method of reducing target glint errors in radar systems is presented. The target is modeled as n reflectors whose magnitudes and phases are known. The reflector positions are described by a dynamical model driven by white Gaussian noise. The resulting vibrations of the target reflectors produce glintlike pointing errors in the radar system. An extended Kalman filter is developed to estimate the positions of the target reflectors; this information is used to substantially reduce the pointing error due to glint. Data illustrating this glint reduction is given. The model is extended by the inclusion of clutter effects modeled in the same fashion as the glint phenomenon. The results presented indicate the limits of usefulness of this technique as a function of both receiver noise and relative clutter amplitude.     

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     

A Real-Time Statistical Radar Target Model

Radar glint arises from the spatial phase perturbations of the radar signal echoed from a complex target. The glint phenomenon is closely related to the target radar cross section (RCS). This relationship plays a significant part in modern missile seeker signal processing. We present a statistical glint/RCS target model for realtime simulation of target signatures. Particular emphasis is placed upon the modeling and simulation of the appropriate glint/RCS statistical dependency. The fundamental approximation of locating uniformly distributed scatterers around the instantaneous radar centroid employed in the Delano-Gubonin [1, 2, 3] model is removed. A key result which follows from this representation is that the mean glint estimator is unbiased. This enables the estimation of model parameters from the first-order glint and RCS statistics which can easily be computed from measured data. A method of estimating model parameters is presented, and the results are applied to data from a typical combat aircraft target. It is shown that the Delano-Gubonin results are a special case of the results presented here. The 14.6 percent probability of glint falling beyond the target extent as derived by Delano [1] is not true in general. It is further shown that glint and RCS are uncorrelated but are statistically dependent. A Monte-Carlo simulation is performed to verify the assumptions made and to demonstrate the feasibility of the working models.     

Target racking with glint noise

In tracking targets, there can be an uncertainty associated with the measurements in addition to their inaccuracy, which is usually modeled by aDditive Gaussian noise. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. An algorithm is developed which can significantly improve the tracking performance when glint noise is present     

A recursive multiple model approach to noise identification

Correct knowledge of noise statistics is essential for an estimator or controller to have reliable performance. In practice, however, the noise statistics are unknown or not known perfectly and thus need to be identified. Previous work on noise identification is limited to stationary noise and noise with slowly varying statistics only. An approach is presented here that is valid for nonstationary noise with rapidly or slowly varying statistics as well as stationary noise. This approach is based on the estimation with multiple hybrid system models. As one of the most cost-effective estimation schemes for hybrid system, the interacting multiple model (IMM) algorithm is used in this approach. The IMM algorithm has two desirable properties: it is recursive and has fixed computational requirements per cycle. The proposed approach is evaluated via a number of representative examples by both Monte Carlo simulations and a nonsimulation technique of performance prediction developed by the authors recently. The application of the proposed approach to failure detection is also illustrated     

Efficient fault tolerant estimation using the IMM methodology

Space systems are characterized by a low-intensity process noise resulting from uncertain forces and moments. In many cases, their scalar measurement channels can be assumed to be independent, with one-dimensional internal dynamics. The nominal operation of these systems can be severely damaged by faults in the sensors. A natural method that can be used to yield fault tolerant estimates of such systems is the interacting multiple model (IMM) filtering algorithm, which is known to provide very accurate results. However, having been derived for a general class of systems with switching parameters, the IMM filter does not utilize the independence of the measurement errors in different channels, nor does it exploit the fact that the process noise is of low intensity. Thus, the implementation of the IMM in this case is computationally expensive. A new estimation technique is proposed herein, that explicitly utilizes the aforementioned properties. In the resulting estimation scheme separate measurement channels are handled separately, thus reducing the computational complexity. It is shown that, whereas the IMM complexity is exponential in the number of fault-prone measurements, the complexity of the proposed technique is polynomial. A simulation study involving spacecraft attitude estimation is carried out. This study shows that the proposed technique closely approximates the full-blown IMM algorithm, while requiring only a modest fraction of the computational cost.     

Efficient L-D factorization algorithms for PDA, IMM, and IMMPDAfilters

Efficient algorithms exist for the square-root probabilistic data association filter (PDAF). The same approach is extended to develop square-root versions of the interacting multiple model (IMM) Kalman filter and the IMMPDAF algorithms. The computational efficiency of the method stems from the fact that the terms needed in the overall covariance updates of PDAF, IMM, and IMMPDAF can be obtained as part of the square-root covariance update of an ordinary Kalman filter. In addition, a new square-root covariance prediction algorithm that is substantially faster than the usual modified weighted Gram-Schmidt (MWG-S) algorithm, whenever the process noise covariance matrix is time invariant, is proposed     

Tracking a maneuvering target using input estimation versus theinteracting multiple model algorithm

Two maneuvering-target tracking techniques are compared. The first, called input estimation, models the maneuver as constant unknown input, estimates its magnitude and onset time, and then corrects the state estimate accordingly. The second models the maneuver as a switching of the target state model, where the various state models can be of different dimension and driven by process noises of different intensities, and estimates the state according to the interacting multiple model (IMM) algorithm. While the first requires around twenty parallel filters, it is shown that the latter, implemented in the form of the IMM, performs equally well or better with two or three filters     

Diversity methods in phase monopulse tracking-a new approach

A novel approach relating target glint (difference between the phase-front gradient of the scattered field and the true target direction vector) to the analytic properties of the overall field is used to suggest a method by which the error in conventional (single frequency) phase monopulse trackers can be reduced. The approximate relationship between glint and amplitude is briefly developed, and an improved glint reduction scheme appropriate for single frequency data is described. The effectiveness in reducing direction angle error is demonstrated with simulated data. It is shown how techniques devised for multiple frequency data sets can be applied to multiple aspect data sets.<>     

Maneuvering target tracking using IMM method at high measurementfrequency

The problem of tracking a maneuvering target with a high measurement frequency is considered. The measurement noise is significantly correlated when the measurement frequency is high. A simple decorrelation process is proposed to enhance the interacting multiple model (IMM) algorithm to track a maneuvering target with correlated measurement noise. It is found that the decorrelation process may improve system performance significantly, especially in velocity and acceleration estimations     

ALGORITHMS FOR TRACKING MANEUVERING TARGET WITH PHASED ARRAY RADAR

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Feedback median filter for robust preprocessing of glint noise

Glint noise may arise in a target tracking system. The non-Gaussian behavior of glint noise can severely degrade the tracking performance. Measurement preprocessing at the front-end of the tracker is an effective method to reduce glint noise. The preprocessor proposed by Hewer, Martin, and Zeh (1987), which used the computationally intensive M-estimator, may not be suitable for practical implementation. An alternative method employing the median filter is studied here. The median filter is well known for its simplicity and robustness. However, the efficiency of the median filter can be seriously degraded if input samples are not identically distributed. This is what we may encounter in the tracking problem. A feedback median filter is then proposed to overcome this impediment without substantially increasing complexity. Simulations show that the new preprocessor can greatly improve tracking performance in the glint noise environment.     

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.     

Maximum likelihood identification of glint noise

If the non-Gaussian distribution function of radar glint noise is known, the Masreliez filter can be applied to improve target tracking performance. We investigate the glint identification problem using the maximum likelihood (ML) method. Two models for the glint distribution are used, a mixture of two Gaussian distributions and a mixture of a Gaussian and a Laplacian distribution. An efficient initial estimate method based on the QQ-plot is also proposed. Simulations show that the ML estimates converge to truths     

Robust Preprocessing for Kalman Filtering of Glint Noise

The non-Gaussian character of glint noise is demonstrated by exploratory data analysis. This non-Gaussian behavior is characterized by outliers in the form of glint spikes. Since glint noise is processed by an angle-tracking Kalman filter, and since the latter is quite nonrobust, strategies are proposed to minimize the effect of these glint spikes. One of the strategies, which involves robust preprocessing of the data, is pursued in detail. Finally, some results of a planar missile simulation are presented that clearly demonstrate the merits of the robust preprocessing strategy.     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.