Unformatted text preview: DETECTION ALGORITHMS AND TRACK BEFORE DETECT ARCHITECTURE BASED ON NONLINEAR FILTERING FOR INFRARED SEARCH AND TRACK SYSTEMS TECHNICAL REPORT CAMS 98.9.1 Skirmantas Kligys, Boris Rozovsky, and Alexander Tartakovsky CENTER FOR APPLIED MATHEMATICAL SCIENCES University of Southern California Los Angeles, CA 90089 1113 SEPTEMBER 1998 Approved for public release; distribution unlimited DETECTION
CENTER 0 DETECTION ALGORITHMS AND TBD ARCHITECTURE FOR IRST
Contents 1 1. Introduction 2 2. Problem Formulation and Background 3 2.1. TbD Methods: Merits and Drawbacks 4 3. Signal and Observation Modeling 6 4. Clutter Suppression 7 4.1. Nonparametric Method 8 4.2. Semiparametric Filtering 8 5. Optimal Nonlinear Filtering for TbD 9 5.1. Modeling for TbD 9 5.2. Optimal Spatio-Temporal Nonlinear Filtering: The Basic Algorithm 10 5.3. Multi-Dimensional Spatio-Temporal Matched Filter as a Special Case of Nonlinear Filter 12 6. Track Appearance Disappearance Detection 14 6.1. Preliminaries 14 6.2. Problem Formulation and Model Description 16 6.3. Detection Algorithm 1: Fixed Sliding Window 17 6.4. Detection Algorithm 2: Fully Sequential Procedure 19 6.5. Algorithm 3: Joint Detection of Track Appearance and Disappearance 21 6.6. Adaptive Detection Algorithms 23 6.7. Choice of Thresholds and Performance Evaluation 24 6.8. TbD Model with Spatio-Temporal Matched Filter 29 6.9. TbD Model with Optimal Nonlinear Filter 31 7. Testing of the Developed Algorithms for IRST Data. Results of Experiments and Simulation 32 7.1. Clutter Removal: Real IRST Data 32 7.2. Example 1: TbD of a Target Based on IRST Data 33 7.3. Example 2: TbD of a Surface Skimming Missile 41 7.4. Appearance Disappearance Detection of a Skimming Missile 47 8. Conclusion. Future Research 50 9. Acknowledgement 50 References 51 2 CENTER FOR APPLIED MATHEMATICAL SCIENCES, USC 1. Introduction Cruise missiles over land and sea cluttered background are serious threats to Infrared Search and Track Systems IRST's. In general, these threats are stealth in both the infrared and radio frequency bands. That is, their thermal infrared signature and their radar cross section can be quite small. Future predicted threats, i.e. the next generation of cruise missiles, will be even more di cult to detect at a su cient range to counter. Further, low elevation trajectory objects, such as sea skimming missiles, have radar signals with large amounts of temporally and spatially correlated interference called multipath. This multipath problem remains an enormous obstacle to existing trackers. Hence, new technology is needed which will allow for the timely detection, tracking, and identi cation of such threats. IRST systems are one component of a multisensor suite which can meet the technical challenge of the timely detection track identi cation of low signal-to-noise+clutter ratio SN+CR targets. The multisensor suite should include an IRST, Radar, and a coherent laser Lidar. We envision a cueing hierarchy where the IRST can cue the Radar or the Radar cues the IRST. Once a candidate track is established the Lidar can be used to identify the target by its micro doppler signature. In this report we describe the developed computationally e cient algorithms and adaptive architecture with optimized overall performance statistical and computational for real-time reliable detection and tracking of low-observable targets in IRST systems. Despite the fact that we focus on an IRST against cruise missiles over land and sea cluttered backgrounds, the results are equally applicable to other sensors e.g., Radar, Lidar. In the research we concentrated on the three interrelated problems: 1 e cient clutter suppression; 2 development of the adaptive track-before-detect TbD architecture based on optimal nonlinear ltering ONF; 3 development of e cient algorithms for detection of a priori unknown number of targets that may appear and disappear at unknown points in time. The report is organized as follows. In Section 2 we formulate the problem, describe a structure of the system to be developed, outline popular track-before-detect methods that are in current use and suggest an alternative method, which is based on the optimal nonlinear ltering. In Section 3 we describe basic models and assumptions on signals and clutter that are used in developing of signal processing algorithms clutter suppression, track-before-detect and detection algorithms. In Section 4, two clutter removal algorithms are presented based on nonparametric and semiparametric spatio-temporal ltering. Section 5 is especially important. Here we describe an optimal nonlinear ltering technique that is used for track-before-detect of very low observable targets. Also, we show that the proposed method is a complete generalization of the multidimensional spatio-temporal matched ltering particularly, 3D matched lter. Furthermore it is shown that the spatio-temporal matched lter coincides with the developed optimal nonlinear lter when a target moves according to deterministic trajectory. In Section 6 we develop three track appearance disappearance algorithms all of which take into account requirements speci c for surveillance systems. The results of simulation and processing real IR data obtained from DETECTION ALGORITHMS AND TBD ARCHITECTURE FOR IRST 3 SPAWAR Space & Naval Warfare Systems Center, San Diego, CA are presented in Section 7. Finally in Section 8 we provide a conclusion and the plan of our future research. 2. Problem Formulation and Background The generalized block-diagram of the system under investigation is shown in Figure 1. We develop both the signal processing architecture clutter removal algorithms and TbD algorithms and track detection algorithms.
Signal Processing Block
Clutter Suppression (Nonparametric or Semiparametric Spatio-Temporal Filtering) IR Frames, Preprocessing Track-Before-Detect (Optimal Nonlinear Spatio-Temporal Filtering) Track Appearance/ Disappearance Detection Detections (Blips) Figure 1. Generalized block-diagram of the developed system
New algorithms concerning the stages of data processing speci ed above are developed under the following realistic conditions. Cluttered background is much more intensive than both equivalent intrinsic instrumental noise of the sensor and signal intensity of the targets to be detected. This causes a necessity of practically complete suppression of a clutter. Exterior conditions of observation are characterized by an extremely high variability and prior uncertainty and may not be predicted with su cient accuracy. Prior information that is needed to develop ideal Bayes data processing algorithms is not available. Particularly, statistical models of signals and moreover exterior background as well as the models of changing target situation are extremely unreliable. Such models can be useful only as tools for performance evaluation in certain scenarios but not for development of data processing algorithms. Practical data processing algorithms should be developed on the base of sequential application of robust, adaptive and minimax methods that are invariant to the prior uncertainty. In practice the estimated parameters of targets for example, trajectory parameters should be guaranteed for any degree of prior uncertainty. Speci cally, each estimate should be supplemented with an appropriate domain of minimum size that contains the real unknown value of estimated parameter with 100 or at least 1 , " assurance. 2.1. TbD Methods: Merits and Drawbacks. The most challenging problem for an IRST system is the detection of a maneuvering target against a strong clutter background. To illustrate the importance of this task, we remark that under certain conditions a few seconds decrease in the time it takes to detect a sea surface skimming cruise missile can yield a signi cant increase in the probability of raid annihilation. The problem of detection is extremely di cult in low SN+CR when localization of the target based upon a single non-stationary image is impossible. In this case one has to align successive frames according to typical patterns of target dynamics and any results of preliminary" tracking. This approach to detection of a low SN+CR target is usually referred to as track-before-detect" TbD. Its success depends crucially on the quality of the preliminary" tracker. Thus, the development of the e cient coherent signal processing based on the TbD methodology becomes crucial point in the low-observable target detection problem. In contrast to other TbD methods, we solve this problem by applying optimal nonlinear ltering approach. We now overview several popular methods for tracking before detection that are in current use. 2.1.1. Spatio-Temporal Matched Filters and Velocity Filter Banks. Given a sequence of frames, consider the problem of detecting a small unresolved target against a clutter background. The probabilities of errors can be decreased by applying a 3,D spatio-temporal matched lter prior to detection thresholding operation. If the spatial distribution of the target and its velocity remain unchanged i.e., if targets move with known constant speed along a line on the plane and the noise and the clutter are Gaussian processes, the 3,D lter is the optimal method of detection, see 39 . It is easily shown that the same result is true for more dimensions, i.e. a m + 1,D matched lter is an optimal method of processing under aforementioned conditions m is the spatial dimensionality. Also, under these conditions the target" component of the multi-dimensional matched lter separates into spatial and temporal components. The temporal component is usually called a velocity lter. Typically the target velocity is unknown and hence the single velocity lter cannot be used. This problem is usually overcome by hypothesizing velocities and implementing a velocity lter bank see, e.g., 44, 49, 51 . One of the main drawbacks of spatio-temporal matched lters and other modi cations such as banks of assumed velocity lters is that they are not able to work with maneuvering targets. Performance of the algorithms is substantially degraded in the presence of velocity mismatch or in event of target maneuver. 2.1.2. Dynamic Programming Methods. The Dynamic Programming methods for TbD showed a big advantage over the conventional MHT method and over the 3,D matched lter with velocity mismatch 1, 2, 7, 21, 58 . Particularly the results of Fernandez et al. 21 show that application of the Viterbi TbD algorithm over 10 frames of IR data yields about a 7 dB improvement in detection sensitivity over conventional thresholding peak-detection procedures. 4 CENTER FOR APPLIED MATHEMATICAL SCIENCES, USC DETECTION ALGORITHMS AND TBD ARCHITECTURE FOR IRST 5 This approach avoided problems with velocity mismatch and could handle targets with slow maneuvers. However, good performance of dynamic programming algorithms is observed for moderate SN+CR over 3 dB after preprocessing and clutter suppression with rapid degradation as SN+CR reduces further 58 . In addition, the computational complexity of these sophisticated methods is fairly high. 2.1.3. Extended Kalman Filter. To date, the extended Kalman lter EKF along with minor variations have been the dominant algorithm technology in real-time tracking. It is the basis for current practical single- or multi-target trackers for point equivalent targets. A major reason for its success has been the fact that the EKF has o ered a reasonable compromise between real-time operation and accurate performance in many nonlinear problems. On the other hand, the EKF is a suboptimal and completely heuristic algorithm whose e ciency varies from case to case. For instance, the EKF is unstable in situations that involve acute maneuvering, missing measurement, low SNR, multipath, and many other situations where the posterior distribution may not be approximated well enough by a Gaussian distribution. It is very di cult, if even possible, to develop rigorous evaluation metrics for assessing the quality of data processing based on the EKF technology. Improvements to the EKF e.g. iterated EKF work satisfactory in a number of important applications where the EKF fails, but still, it is di cult to overcome the fundamental limitations of the EKF algorithm that stem from its dependence on the assumption that the posterior distribution may be well approximated by a Gaussian distribution. The typical posterior density built upon the realistic IR image is shown in Figure 17, Section 7. One sees that it has multi-peak form and hence is very far from being Gaussian. Our experiments show that EKF is typically fails for this kind of data. 2.1.4. An Alternative TbD Method Optimal Nonlinear Filtering. In spite of the aforementioned shortcomings, the above outlined methods remain the basis for the great majority of existing signal processing systems. In particular, until recently no other information technology was able to e ectively compete with the EKF in target tracking. However the situation has changed with recent advances in the mathematical theory and algorithmic support for optimal nonlinear ltering ONF. These advances coupled with improvements to modern digital hardware technology make optimal nonlinear ltering an attractive alternative to the multi-dimensional matched lter, dynamic programming based algorithms and EKF in many practical and important applications. These include signal processing for infrared and acoustic sensors, imaging radar and sonar including SAR and SAS, and other passive and active sensors 17, 46, 50 . Advanced optimal nonlinear lters can now provide: real-time operation; optimal, theoretically sound solutions of the full nonlinear problem; distributional versatility no constraints on the form of prior or posterior probability distributions; 6 CENTER FOR APPLIED MATHEMATICAL SCIENCES, USC superior accuracy and robustness; facility to e ectively incorporate realistic physical models; explicit quantitative performance metrics exact error estimates, con dence areas, etc.. Our analysis of advanced algorithms based on ONF technologies shows great promise in: trackbefore-detect of unresolved targets in low SN+CR up to ,6dB after preprocessing; fusion of imaging and kinematic data for target identi cation; tracking of agile extended targets in cluttered environment as well as with certain other applications. We argue that just as the EKF superseded the , , trackers, so the optimal nonlinear lter is set to replace the EKF as the dominant tracking technology within 10-15 years. In Section 5 we describe the ONF techniques that will be used in de ning and developing the appropriate technology for application in an end-to-end IRST signal processing architecture. The architecture will be su ciently exible to allow for an adaptive optimization of the signal discrimination processors utilizing existing engineering parameters. This adaptive optimization will use the output of an EO IR sensor diagnostic tool to utilize current meteorological and environmental information as well as current intelligence on likely threat scenarios. 3. Signal and Observation Modeling It is assumed that a sensor has m,component resolution capability for radar typically m = 6, for IR EO m = 4. By r = r1; : : : ; rm will be denoted a phase coordinate vector for IRST typically angles and angle velocities of an object in a certain coordinate system. The sensor carries out a periodic surveillance of de nite area in m,dimensional domain D m R m , where R m is the m,dimensional Euclidean space. After standard preprocessing the result of one observation step is a frame of measurements, 3.1
Z n = S n + bn + n n = 1; 2; : : : ; or Z n = kZi nk = kSi n + bi n + i nk ; i = 1; : : : ; N; where S n = kSink is a signal from target, bn = kbink is an exterior background clutter, and = kink is a noise of the sensor. Here we assume that after preprocessing sampling of data is done in discrete points di, i = 1; : : : ; N , uniformly in the area D m i is a pixel. The noise is assumed to be zero mean and uncorrelated in both time n and space i, E in = 0, 2 E i n = E is a symbol of expectation. The clutter is de ned as 3.2 bin = bri + n; n where br; n is a function describing the background spatial distribution of the clutter after preprocessing in the point r, and n = 1n; : : : ; m n is an unknown current bias of sensor coordinate system with respect to the reference one due to the jitter. DETECTION ALGORITHMS AND TBD ARCHITECTURE FOR IRST 7 The signal component is modeled as 3.3 Sin = kn X j =1 Aj nhri + n , rj n where hr is a normalized sensor function; kn is an unknown total number of targets at the moment n; Aj n and rj n are unknown signal intensity and coordinates of the j th target, respectively. It is assumed that the clutter br; n has a relatively big spatial variance the change of br; n between two nearest values of ri is comparable with the maximum value of br; n. Besides, br; n varies locally as fast as the signal function does in spatial coordinates. Even in cases where these assumptions do not exactly hold, the algorithms that rely on them will be robust, which is the most important requirement. The second assumption shows that if only spatial information is used, then the background may be interpreted as a target. Thus spatial ltering alone is not su cient for clutter suppression and temporal ltering is needed. We always assume that b is an arbitrary unknown function of r and slowly changing function in n: there exists such T that jbr; n + T , br; nj . The latter assumption, which often holds, shows that variations of the clutter in time are caused mainly by uncontrolled vibrations n of the sensor. These vibrations are unknown and unpredictable except for a natural restriction, j nj , imposed on the absolute value of bias of coordinate system. No assumptions on statistical behavior of clutter is made. It is our belief that such popular models as homogeneous random eld, especially Gaussian, are valuable only for purely academic research and lead to highly non-robust ltering algorithms. Perhaps the most important feature of our approach to algorithm design is that we refuse to use any arti cial and unreliable statistical models of br; n, n, kn, and Aj n. The algorithms developed on the basis of such models fail even for small deviation of a model from reality. The essence of the new suggested approach is the development of algorithms that are invariant and or adaptive with respect to prior uncertainty. The speci c feature of the problem is its extremely high dimensionality. The value of N can be of the order of 106 , 108 and the total number of targets can be several hundreds. Thus, along with the mathematical issue of data processing, serious attention should be paid to the computational complexity, parallelization and HPC realization. 4. Clutter Suppression Two classes of algorithms for background ltering are proposed. In either case there are two basic problems to be solved: a to transform the sequence of input frames into the new frame such that the clutter would be reduced and the signal would be preserved clutter removal; b for every n the location of the coordinate system of the sensor i.e. the bias n should be estimated with maximum possible accuracy jitter compensation. Below we propose two algorithms that allow the rst problem to be solved e ectively. Jitter compensation algorithms will be developed in the near future. 4.1. Nonparametric Method. The rst class is relied on the nonparametric regression approach to estimation of the function br; n. Our goal is to build a nonparametric clutter estimate such that the residuals between the original data and its smoothed version estimate would be reasonably approximated by signal plus noise models. That is, the estimate ^r; n of the br; n b ~r; n = Z r; n , ^r; n the signal should be built in such a way that in the ltered frame Z b would be preserved, wh...
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