**Publications**(114)

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^{2}m) where n,m are the current numbers of tracks resp. measurements. This paper generalizes the GLMB filter to fully integrated multitarget tracking and sensor management, in which dynamically moving sensors can appear and disappear and in which the states of these sensors are estimated via measurements collected by internal actuator sensors.

*Cardinalized*)

*Probability Hypothesis Density*(PHD), application of the proposed KLA fusion rule leads to a consensus (C)PHD filter which can be successfully exploited for distributed multitarget tracking over a peer-to-peer sensor network.

_{k+1}and the target-birth rate B

_{k+1|}

_{k}. I exhibit counterexamples to these claims. Because of the CM model, the MIF (1) does not subsume the conventional PHD filter as a special case; (2) cannot estimate B

_{k+1|k}when there are no clutter generators; and (3) cannot estimate λ

_{k+1}when the target birth-rate and target death-rate are "conjugate." By way of contrast, PHD filters with UM models do include the PHD filter as a special case, and can estimate the clutter intensity function κ

_{k+1}(z). I also show that the MIF is essentially identical to the UM-model PHD filter when the target birth-rate and death-rate are both small.

*cardinalized*PHD CPHD),

*filter*, which propagates not only the PHD but also the entire probability distribution on target number. Since the CPHD filter has computational complexity O(

*m*

^{3}) in the number

*m*of measurements, additional approximation is desirable. In this paper we discuss a second-order approximation called the "binomial filter."

^{M}- 1 numbers are required to specify a Dempster-Shafer basic mass assignment (b.m.a.) on a space with M elements; whereas only M - 1 numbers are required to specify a probability distribution on the same space. Consequently, any conversion of b.m.a.'s to probability distributions will result in a huge loss of information. In addition, conversion from one uncertainty representation formalism to another should be consistent with the data fusion methodologies intrinsic to these formalisms. For b.m.a.'s to be consistently converted to fuzzy membership functions, for example, Dempster's combination should be transformed into fuzzy conjunction in some sense. In this paper we show that a path out of such quandaries is to realize that in many applications all information must ultimately be reduced to state estimates and covariances. Adopting a Bayesian approach, we identify Bayes-invariant conversions between various uncertainty representation formalisms.

*cardinalized PHD (CPHD), filter*, which propagates not only the PHD but also the entire probability distribution on target number.

_{1},...,x

_{n}} exhibits discontinuous jumps in target number: X = 0, X = {x

_{1}}, X = {x

_{1}, x

_{2}}, etc. However, it is possible to extend X to a continuous multitarget state X = {x

_{1},..., x

_{n}} via the concept of a point target-cluster x = (a,x) where x is interpreted as multiple targets co-located at target-state x, the expected number of which is a. We generalize the EKF to multitarget problems. We illustrate the approach by deriving predictor and corrector equations for a single-sensor, single-target EKF that integrates the functions of detection and tracking in the presence of missed detections and false alarms.

*Targets of Interest*(ToIs) having high tactical importance. In principle one could simply wait until accumulated information strongly suggests that particular targets are probable ToIs and then bias the allocation of sensor resources to those targets. However, such

*ad hoc*techniques have inherent limitations. To avoid these limitations

*target preference must be incorporated into the fundamental statistical description of multisensor-multitarget problems*. In this paper we show that

*finite-set statistics*(FISST) has built-in mathematical tools for doing this, thereby allowing target preference to be incorporated into sensor management objective functions.

*Cluster tracking*is the problem of detecting and tracking clustered formations of large numbers of targets, without necessarily being obligated to track each and every individual target. We address this problem by generalizing to the dynamic case a static Bayesian finite-mixture data-clustering approach due to P. Cheeseman. After summarizing Cheeseman's approach, we show that it implicitly draws on

*random set theory*. Making this connection explicit allows us to incorporate it into a multitarget recursive Bayes filter, thereby leading to a rigorous Bayesian foundation for finite-mixture cluster tracking. A computational approach is proposed, based on an approximate, multitarget first-order moment filter (“cluster PHD” filter).

_{T}(x

_{1},...,x

_{T}Z) that there are T targets (T an unknown number) with unknown locations specified by the multitarget state X equals (x

_{1},...,x

_{T})

^{T}conditioned on a set of observations Z. This paper presents a numerical approximation for implementing JMP in detection, tracking and sensor management applications. A problem with direct implementation of JMP is that, if each x

_{t}, t equals 1,...,T, is discretized on a grid of N elements, N

^{T}variables are required to represent JMP on the T-target sector. This produces a large computational requirement even for small values of N and T. However, when the sensor easily separates targets, the resulting JMP factorizes and can be approximated by a product representation requiring only O(T

^{2}N) variables. Implementation of JMP for multitarget tracking requires a Bayes' rule step for measurement update and a Markov transition step for time update. If the measuring sensor is only influenced by the cell it observes, the JMP product representation is preserved under measurement update. However, the product form is not quite preserved by the Markov time update, but can be restored using a minimum discrimination approach. All steps for the approximation can be performed with O(N) effort. This notion is developed and demonstrated in numerical examples with at most two targets in a 1-dimensional surveillance region. In this case, numerical results for detection and tracking for the product approximation and the full JMP are very similar.

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