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Critical Survey of Approaches to EWR Target Tracking: Endorsing Use of an EKF’S Structure Thomas H IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, VOL. 6, NO. 12, JUNE 2018 1 Critical Survey of Approaches to EWR Target Tracking: endorsing use of an EKF’s structure Thomas H. Kerr III, Ph.D., Life Senior, IEEE, Assoc. Fellow, AIAA, Member ION & Life NDIA Abstract—New methodologies for target tracking and for can be incurred). Among the first cogent modern treatments evaluating its efficacy have recently emerged, all potentially of Reentry Vehicle (RV) target modeling for radar target being a “magic bullet”. The questionable accuracy benefits, tracking were1 [290]-[292], [59]-[61] (and, afterwards, quickly missing rigor (in some cases), and definitely large CPU-time computer loading drawbacks of the new estimation approaches followed by several others [62], [293]-[295]). are discussed as compared to conventional Extended Kalman Filters (EKF’s) and the novel Batch Maximum Likelihood Least Squares algorithm, as the well-known previous candidates for use in land-based Early Warning Radar (EWR) target tracking. A reminder is that the existing 40 year old Cramer-Rao lower bound evaluation methodology is already rigorous and adequate for evaluating target tracking efficacy in Pd < 1 situations when confined to exo-atmospheric target tracking, as arises in EWR for NMD/GMD. We also discuss the more challenging and Fig. 1. Gating after each incremental EKF output enables MTT associations numerically sensitive angle-only filter methodologies, needed to handle target tracking when enemy escort jamming denies radar EKF’s are typically used for tracking the target state in a range measurements and impedes target tracking unless two or ballistic trajectory; but over the last 30+ years, some form more radars cooperatively triangulate synchronously to thereby of nonlinear batch least squares (BLS) algorithm has also enable joint tracking of enemy jammers within the tight target threat complex. (Sometimes merely one sensor suffices for AOT, been used for this purpose ([135], [14], [15]) on fast par- as discussed.) Finally, supporting technologies (some old, some allel processing machines by dynamically allocating and de- new) are discussed for enhancing the performance of these EKF’s allocating memory, as needed. However, EKF’s are still relied with only a modest increase in computational burden. Motivation upon for the measurement intensive routine data associations for these pursuits is the quest to gain more veracity in on- arising in first forming the initial hypotheses within multi- line filter covariance calculation to mitigate any tendency to be overly optimistic or pessimistic (which could otherwise adversely target tracking (MTT) before switching to BLS for later track affect multi-target track associations which typically utilize such enhancement of mature targets as part of the overall MTT pro- EKF covariances within its initial gating stage) occurring further cess prior to Fire Control dispatching a (non-nuclear) kinetic- downstream in the standard sequence of processing steps. kill vehicle 2 to eliminate the hostile RV threat entirely during Index Terms—EWR Target Tracking, Filter Models, Approx- its exo-atmospheric midcourse transit 3. Typical behavior of imate Nonlinear Filter, EKF, IEKF, Batch Least Squares, Un- target-associated Confidence Regions (CR) during tracking are scented Filter, IMM & MMM Filters, Particle Filter, Covariance conceptually depicted in Fig. 1, as they go from initially Fidelity, Covariance Intersection, Probability 1, Multi-target Tracking Alrernatives. being “a pancake” (at horizon break, upon first entering the radar fence (consisting of proprietary pre-programmed patterns of radar up-down pulse-pair chirps within multiple I. INTRODUCTION AND OVERVIEW pencil beams sweeping and scanning for initial detections and TRATEGIC target tracking typically employs a (public subsequent confirmation) to later being “a football” as even S domain) system dynamics target model that is nonlinear more confirming radar sensor return “hits” are accumulated (with inverse square gravity along with the earth’s second for this designated target. Target ID’s are assigned by the zonal harmonic [including J2] appearing in its associated radar controller/manager that subsequently “schedules” radar ODE description, similar to system and measurement models resources to systematically return to continue “viewing” these described in detail in [26], [107], [218], [284], [298] with initially identified moving targets to enable further improved parameter values as usually provided, but updated in [114]). following of these objects of interest that are suspected to be The EWR target model is also nonlinear in the algebraic sensor observation equation, where range-Doppler ambiguity 1Paralleling similar precedents, circa 1967, by earlier initial trailblazers: is compensated for within the plane of the antenna face [11], James R. Huddle (Litton), Stanley Schmidt & George Schmidt (Draper Lab.), and Arthur Gelb (TASC) in first recognizing the Kalman Filter’s utility for [295], using a transformation algorithm [133] (that should Inertial Navigation Systems (INS). be updated [134], [356] to reduce the maximum error that 2Possibly with a terrestrial-based command guidance or more likely with some form of on-board self-contained proportional navigation guidance. Manuscript received February 14, 2016. This research funded by TeK 3Successful Terminal Phase intercept during atmospheric reentry requires Associates’ IR&D Contract No. 15-102. more than merely 6 filter states to account for the effect of lift and drag on T. H. Kerr III is CEO/Principal Investigator at TeK Associates, the targets and sometimes considerations of micro-motions, all of which are 21 Cummings Park, Suite 230, Woburn, Massachusetts 01801; E-mail: beyond the scope of this paper. This paper considers only aspects historically thomas h [email protected]. related to UEWR, which has a goal of mid-course exo-atmospheric intercept. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, VOL. 6, NO. 12, JUNE 2018 2 potential threats (after having already passed a comparison test Velocity Cartesian Coordinates (RVCC), and R-U-V [11]- weeding them out from known background satellites and space [13], and to novel Batch Maximum Likelihood Least Squares debris listed in an up-to-date Space Object Catalog of 13,000+ (BLS) algorithms [14], [15], [189, App. 2], as three well- entries 4). known historical candidates for use in radar target tracking within land-based EWR. (Recall that Ref. [113] has already demonstrated that partitioned filters can be unsatisfactory in some situations and are therefore undesirable even for crossing targets.) In Sec. V, the existing 40+ year old Cramer-Rao lower bound evaluation methodology [16]-[24] is shown to be rigor- Fig. 2. Assumed Gaussian CR goes from being a pancake (at horizon break) ous and flexible enough to adequately evaluate target tracking to a football afterwards efficacy in Pd < 1 situations for specified detection threshold settings when confined to exo-atmospheric midcourse inter- ception of a target and its prior tracking, as arises in EWR, where truth model process noise is theoretically zero. The filter model can have nonzero process noise tuning 5 and still abide by this Q = 0 constraint dictated by the truth model’s Fig. 3. Functional overview of the MTT Data Association Aspect of Track structure. However, Farina et al’s formulation [9] (based on Maintenance [53] [25]) is useful for evaluating Indo-atmospheric tracking, which is a more challenging situation, where system truth model Among the new approaches to target tracking and for process noise is definitely nonzero (reflecting atmospheric evaluating its efficacy are unscented filters [1]-[4]; Covariance buffeting associated with reentry drag, or maneuvering, or with Intersection (CI) filters [5], [6] (discussed in depth in Sec. II); a projectile undergoing late stage thrusting). Particle Filters (PF) [388], [8], [177]; and Farina et al’s new formulation of Cramer-Rao Lower Bound evaluation for non- As discussed in Sec. VI, motivation for these pursuits is unity probability of detection (for Pd < 1) [9], all offering the the quest to gain more veracity in on-line filter covariance lure of potentially being a “magic bullet”. One of the clearest calculation to mitigate their tendency to be overly optimistic discussions of both historical and recent estimation algorithms (or, much more rarely, pessimistic) since any hand-over or (including EKF, UKF, MMM, INN, and Particle Filters [PF’s]), multi-target (MTT) associations rely on their veracity (Figs. 2, their underlying assumptions/mechanization equations and that 6) and errors in the values of these covariances (being the also provides extremely useful insight into important aspects only ones actually available in one-shot real world trials) and distinctions in their implementations is offered in [177, are sensitive. In Sec. VII, we recommend pursuit of good Chapts. 1-3]. We offer additional new practical observations tracking accuracy with probability one success (as pioneered herein in further considering how these algorithms relate to by the late Frank Kozin in the 1960’s and 1970’s) over current the EWR application. The questionable accuracy benefits, the Monte-Carlo-based mean square averaging techniques, which missing rigor (in some cases), and definitely large computer captures only aggregate behavior. In Sec. VIII, we mention loading drawbacks of the new estimation approaches all need the relevance of solutions for the Lambert Problem to EWR to be considered
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