A polynomial-time approximation algorithm for joint probabilistic data association

On August 30, 2005, we successfully demonstrated a large-scale, real-time, surveillance and control application on a wireless sensor network. The task was to track multiple human targets walking through a 5041 square meter sensor field and dispatch simulated pursuers to capture them. We employed a multi-target tracking algorithm that was a combination of a multi-sensor fusion algorithm for fusing binary detections and a Markov chain Monte Carlo data association (MCMCDA) algorithm that can initiate and terminates tracks autonomously and is robust to a high level of false alarms and missing measurements, a common problem in sensor networks. The tracks were used by a multi-agent coordination and control algorithm to capture the evaders. We were able to demonstrate successful pursuit of two crossing targets and successful tracking of three targets moving through a 144 node sensor field. To the authors' best knowledge, this experiment is the largest demonstration to date of a real-time tracking and control system on a wireless sensor network that does not use classification information

This paper presents an algorithm for multiple-object tracking without using object detection. We concentrate on creating long-term trajectories for unknown moving objects by using a model-free tracking algorithm. Each individual object is tracked by modeling the temporal relationship between sequentially occurring local motion patterns. The algorithm is based on shape and motion descriptors of moving objects, obtained at two hierarchical levels from an event understanding system. By considering both local and global motion patterns, two sets of initial tracks, called linklets, are obtained. Then, a set of sparse tracks, referred to in the literature as tracklets, is produced by grouping linklets demonstrating similar motion patterns. This produces two sets of independent tracklets, referred to as the lowand high-level tracklets. We adopt Markov Chain Monte Carlo Data Association (MCMCDA) to estimate a varying number of trajectories given a set of tracklets as input. To this end, we formulate tracklet association as a Maximum A Posteriori (MAP) problem to create a chain of tracklets. The final output of the data association algorithm is a partition of the set of tracklets such that those belong to individual objects have been grouped. This yields individual tracks for each object in a video.

Multiple target tracking (MTT) has received much attention recently for various applications in the military as well as the Strategic Defense Initiative areas. Data association is one of the critical computation in MTT problems, because erroneous data associations often result in lost tracks. The joint probabilistic data association (JPDA) algorithm is a good approach to solve the data association problem. However, the computation complexity of this algorithm increases rapidly with the number of targets and radar returns. Neural networks have been considered to approximate the JPDA and ease the computation burden through the parallel processing. In this paper, we propose a neural network data association (NNDA) algorithm for the solution of the data association problems. Simulation results show the following three controversial issues: first, NNDA can track multiple targets with performance compatible with JPDA. Second, when the prediction filter can not provide an enough accurate prediction data ( This sometimes occurs when the prediction model can not match the tracking environment precisely enough), the neural computation provides better performace than JPDA. Third, the performance of NNDA is not affected by the number while that of JPDA degrades with the increase of target number. As a whole, this paper presents a neural network which not only possesses the intrinsic ability of parallel computation but also provides conditionally better tracking performance than JPDA.

A single-sensor, single-target mixture reduction (MR) data association algorithm is extended for use in multisensor, multitarget tracking situations. MR is extended for tracking an arbitrary number of targets using an arbitrary number of sensors under the assumption that the sensor measurement errors are independent across sensors. Like the single-sensor, single-target MR algorithm, which gives better performance than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions give similar improvements in performance compared to the joint PDA (JPDA) and multisensor JPDA (MSJPDA) algorithms. Further, in the formulations for the multisensor and multitarget MR algorithms, the equations for the calculation of the data association probabilities have been put in the same form as for the JPDA, thus allowing previously developed fast JPDA computational techniques to be applicable. N the problem of tracking targets in random clutter, the optimal Bayesian solution leads to Gaussian mixture distributions that consist of an exponentially increasing number of components.1 In practice, the number of components in each mixture is kept in check by approximating it with fewer components. The nearest neighbor (NN) approximation reduces each target's mixture to its largest component.13 The joint probabilistic data association (JPDA) approximation merges the components of each target's mixture into a single Gaussian component.1'4 However, when there are several significant, well-spaced components in the original mixture, important information may be lost by using the NN or JPDA methods. A more flexible approximation method for single-sensor, single-target tracking, known as mixture reduction (MR), has been proposed by Salmond.5 This MR algorithm preserves the mean and covariance of the original mixture of components, successively merging components until the number of components is reduced to some userspecified limit. In this paper, we first review Salmond's MR algorithm for single-sensor tracking of a single target in clutter. We then derive extensions to Salmond's MR algorithm for use in tracking multiple targets and when there are measurements available from multiple sensors. Just as the single-sensor, single-target MR algorithm gives better performance5 than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions are shown to give similar improvements in performance as compared to the JPDA and multisensor JPDA (MSJPDA)6 algorithms. Extension of the MR algorithm for tracking of multiple targets is necessary for use in realistic tracking scenarios where there are usually many targets that need to be tracked. Moreover, many current tracking systems have been designed with multiple sensors, thus requiring the further extension to a multisensor algorithm. The paper is organized as follows. In Sec. II, the target dynamics and measurement equations are defined. We review the singlesensor, single-target MR algorithm5 in Sec. Ill, and we extend the algorithm to the multitarget and multisensor cases in Sec. IV and V, respectively. In Sec. VI, simulation results evaluating the performances of the MR extensions are presented. Finally, concluding remarks are given in Sec. VII.

The imaging of microvessels and the quantification of their blood flow is of particular interest in the characterization of tumor vasculature. The imaging resolution (50-200 μm) of high-frequency ultrasound (US) (20-50 MHz) is not sufficient to image microvessels (~10 μm) and Doppler sensitivity is not high enough to measure capillary blood flow (~1 mm/s). For imaging of blood flow in microvessels, our approach is to detect single microbubbles (MBs), track them over several frames, and to estimate their velocity. First, positions of MBs will be detected by separating B-mode frames in a moving foreground and a static background. For the crucial task of association of these positions to tracks, we implemented a modified Markov chain Monte Carlo data association (MCMCDA) algorithm, which can handle a high number of MBs. False alarms, the detection, initiation, and termination of MBs tracks are incorporated in the underlying model. To test the performance of algorithms, a US imaging simulation of a vessel tree with flowing MBs was set up (resolution 148 μm). The trajectories and flow velocity in the vessels with a lateral distance of 100 μm were reconstructed with super-resolution. In a phantom experiment, a suspension of MBs was pumped through a tube (diameter 0.4 mm) at speeds of 2.2, 4.2, 6.3, and 10.5 mm/s and was imaged with a Vevo2100 system (Visualsonics). Estimated mean speeds of the MBs were 2.1, 4.7, 7, and 10.5 mm/s. To demonstrate the applicability for in vivo measurements, a tumor xenograft-bearing mouse was imaged by this approach. The tumor vasculature was visualized with higher resolution than in a maximum intensity persistence image and the velocity values were in the expected range 0-1 mm/s.

The crucial problem in multiple target tracking is the hit-to-track data association. A hit is a received signal from a target or background clutter which provides positional information. If an incorrect hit is associated with a track, that track could diverge and prematurely terminate or cause other tracks to also diverge. Most methods for hit-to-track data association fall into two categories: Multiple Hypothesis Tracking (MHT) and Joint Probabilistic Data Association (JPDA). Versions of MHT use all or some reasonable hits to update a track and delay the decision on which hit was correct. JPDA uses a weighted sum of the reasonable hits to update a track. These weights are the probability that the hit originated from the target in track. The computational load for the joint probabilities increase exponentially as the number of targets increases and therefore, is not an attractive algorithm when expecting to track many targets. This paper reviews the JPDA filter and two simple approximations of the joint probabilities which increase linearly in computational load as the number of targets increase. Then a new class of near optimal JPDA algorithms is introduced which run in polynomial time. The power of the polynomial is an input to the algorithm. This algorithm bridges the gap in computational load and accuracy between the very fast simple approximations and the efficient optimal algorithms.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Recent literature has introduced several methods for processing an out-of-sequence measurement (OOSM) in tracking for both the 1-step-lag and ¿-step-lag case. However, in a realistic tracking application, a data association algorithm, such Joint Probabilistic Data Association (JPDA) must be used in order to associate measurements with tracks in a cluttered environment. This paper investigates the OOSM problem in tracking for both the 1-step-lag and ¿-step-lag cases using JPDA. The OOSM algorithms presented in the literature are extended to support JPDA and the results are analyzed. The resulting algorithms are then applied to an automotive frontal pre-crash system, where OOSM and JPDA are vital factors in improving the performance of such a system.

We study the properties of a sequence of dependent random variables generated with the following scheme. A sequence of independent identically distributed random variables /spl alpha/ arrives at the input of a k-register; the random variables take values 0 and 1 with probabilities not equal to 1/2. The sequence /spl eta/ of random variables generated by the k-register for k/spl ges/2 is a stationary random sequence with dependent components. The sequence /spl eta/ is taken as the input to a memoryless binary symmetrical channel with input-independent noise, i.e. /spl eta/ is added coordinatewise modulo 2 to a sequence /spl beta/ of independent identically distributed random variables that also take the values 0 and 1 with probabilities not equal to 1/2 and are independent with the sequence /spl alpha/. In this paper we derive upper and lower estimates for the entropy of the stationary non-Markov random source identified with the channel output. The upper estimate is based on the well-known subadditivity property of the entropy of a finite-dimensional distribution. The main result is the proof of nontrivial lower estimate of the entropy for two particular k-registers: k=2 and k=3. If the probabilities of 0 and 1 in the sequences /spl alpha/ and /spl beta/ are close to 1/2, this estimate shows that the entropy of the source increases when k grows from 1 to 3. Pre-transformation of /spl alpha/ by the k-register, k>1, yields the increase of the entropy of the additive source /spl alpha/+/spl beta/ over the case k=1. This property of increase of the entropy is significant for constructing a strong random source from several weak ones.

For a single-mode laser it is generally believed that far above threshold the detected noise level is determined by the pump noise if the quantum efficiency of conversion from pump excitation quantum to detected photons is close to unity. This allows the generation of sub-shot noise light by operating a semiconductor laser far above threshold with a quiet pump. We have found, however, that weak nonorthogonality of the cavity eigenmodes can add significant Petermann excess noise. This seriously impedes intensity noise squeezing even for an effectively single mode laser, i.e. a laser in which the intensity noise of the lasing mode a equal to the intensity noise of the total light output. The crucial point is that nonorthogonality leads to effects in the intensity noise in first order of the non-lasing mode amplitudes, in contrast to the usually considered second-order multi-mode effects. We have extended the quantum Langevin approach for the intensity noise of a laser by incorporating the effect of the nonorthogonal cavity modes in a quantum mechanically consistent way. For the intensity noise far above threshold we find S=1+/spl eta/[2(K-1)+/spl epsiv/-1], where S is the intensity noise relative to shot noise, K is the Petermann K-factor, /spl eta/ the ratio of outcoupling loss and internal loss, /spl epsiv/ quantifies the noise of the pump (/spl epsiv/=0 quiet pump, /spl epsiv/=1 Poissonian pump). This formula clearly shows a very interesting result: for K/spl ges/1.5 the intensity noise, S, is always above shot noise and intensity squeezing is no longer possible. Experimental evidence confirms the theory.

To improve the accuracy of multiple target tracking in the clutter environment, a new joint probabilistic data association (JPDA) algorithm based on variational Bayesian adaptive moment estimation is proposed. First, considering the existence of measurements, the posterior distribution of the target state in JPDA is composed of two parts of probability weighting, that is, the posterior distribution of the target state that the real measurement exists in the association gate and the posterior distribution of the target state that the real measurement does not exist in the association gate. By combining the conjugate properties of the prior and posterior distributions, the prior distributions of the target state in the two cases are classified to provide more accurate a priori information to filter, so as to improve the accuracy of data association. Second, considering the coupling effect between state estimation and data association process, combined with variational Bayesian inference, the problem of minimizing Kullback–Leibler divergence is transformed into the problem of maximizing the evidence lower bound, thereby effectively measuring the distance between the posterior distribution of target state estimation and the real posterior distribution, so as to improve the accuracy of data association again from the perspective of optimizing nonlinear filter. Finally, the adaptive momentum estimation strategy is introduced to iteratively solve the variable distribution that meets the maximization of the evidence lower bound, and the optimization of the posterior distribution of the target state is completed. Theoretical derivation and simulation experiments are conducted to verify the feasibility and effectiveness of the algorithm.

Algorithms are presented for managing sensor information to reduce the effects of bias when tracking interacting targets. When targets are close enough together that their measurement validation gates overlap, the measurement from one target can be confused with another. Data association algorithms such as the joint probabilistic data association (JPDA) algorithm can effectively continue to track targets under these conditions, but the target estimates may become biased. A modification of the covariance control approach for sensor management can reduce this effect. Sensors are chosen based on their ability to reduce the extent of measurement gate overlap as judged by a set of heuristic parameters derived in this work. Monte Carlo simulation results show that these are effective methods of reducing target estimate bias in the JPDA algorithm when targets are close together. An analysis of the computational demands of these algorithms shows that while they are computationally demanding, they are not prohibitively so.

An important step in multitarget tracking (MTT) is the assignment of measurement/target pairing probabilities, i.e., the probability that a certain measurement is associated with a particular target. This is one of the more computationally intensive steps of the Joint Probabilistic Data Association (JPDA) and other MTT algorithms. Determining such assignment probabilities in the conventional JPDA algorithm involves the generation and analysis of all possible binary feasibility matrices, where each feasibility matrix represents the feasible event that each measurement is due to only one target (or clutter) and that each target causes at most one measurement. We discuss a new and most efficient technique for obtaining the measurement/target pairing probabilities directly (without first producing the feasibility matrices) and its implementation on a new analog optical computer.

TM surface waves on an interface between semiconductors, ferrites or artificial dielectrics are considered. The normalised phase coefficient, /spl beta//k/sub 0/, is calculated for a range of values for the two media, first with (/spl epsiv//sub r1/ = 1, /spl mu//sub r1/ = 1) and then with (/spl epsiv//sub r1/ = 1, /spl mu//sub r1/ = -1) assuming -5 < /spl mu//sub r2///spl mu//sub r1/ < 5, -5 < /spl epsiv//sub r2///spl epsiv//sub r1/ < 0. This range of parameters includes some double negative cases for the second medium. Dispersion diagrams are presented for the case where region I is an artificial magnetic dielectric and region 2 is a semiconductor plasma. The results have implications for the design of miniature passive components.

The unshunted (un) SQUID is a two-junction device whose Josephson junctions are damped at high frequencies only. Single-valued rather than hysteretic behaviour on the negative resistance region is obtained by using a voltage bias rather than a current bias. We have studied numerically the noise properties of the un SQUID with a double-loop (dl) washer configuration, in which the SQUID inductance is capacitively split into two loops. Our simulations with /spl beta//sub c/=0.7 and /spl beta//sub l/=0.5-3 suggest that noise level in the un dl SQUID depends more weakly on the device parameters than in the un SQUID. The best energy resolution obtained in the smooth area of the IV curves is /spl epsiv//spl ap/5k/sub B/T/spl radic/(LC) but in narrow pockets in the non-smooth region /spl epsiv//spl ap/3k/sub B/T/spl radic/(LC) is approached.

Recently it has become clear, that a key issue in quantum computation is understanding how interaction with the environment, or decoherence, affects the computational power of quantum computers. We adopt the standard physical method of describing systems which are interwound with their environment by density matrices, and within this framework define a model of decoherence in quantum computation. Our results show that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. We first present a simulation of decohered sequential quantum computers, on a classical probabilistic Turing machine, and prove that the expected slowdown of this simulation is polynomial in time and space of the quantum computation, for any non zero decoherence rate. Similar results hold for quantum computers that are allowed to operate on logarithmic number of qubits at a time. For decohered quantum circuits (with local gates), the situation is more subtle and depends on the decoherence rate, /spl eta/. We find that our simulation is efficient for circuits with decoherence rate /spl eta/ higher than some constant /spl eta//sub 1/ but exponential for a general (random) circuit subjected to decoherence rate lower than some constant /spl eta//sub 2/. The transition from exponential cost to polynomial cost happens in a short range of decoherence rates. We use computer experiments to exhibit the phase transitions in various quantum circuits.