Suboptimal joint probabilistic data association

A significant 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 terminate. Prior methods for this data association problem include various optimal and suboptimal two-dimensional assignment algorithms which make hit-to-track associations. Another method is to assign a weight for the reasonable hits and use a weighted centroid of those hits to update the track. The method of weighting the hits is known as joint probabilistic data association (JPDA). The authors review the JPDA approach and a simple ad hoc approximation and then introduce a new suboptimal JPDA algorithm. Examples which compare an optimal two-dimensional assignment algorithm with the ad hoc and the new suboptimal JPDA formulation are given     

Effectiveness of track monitoring with multiple 2D passive sensors

An analytical technique is presented which can be used to evaluate the effectiveness of the track monitoring scheme presented by J.A. Roecker (see ibid., vol.27, no.6, p.872-6, Nov. 1991) in detecting false track-to-track (ghost track) assignments without the use of simulations. It is shown that when two tracks are traveling in parallel and in the direction of the inclination angle, it is impossible to determine which tracks to associate. However, track monitoring is effective under all other circumstances. A tracking algorithm designer can use this technique to determine the length of time before track-to-track initiation for good ghost track rejection. This technique also determines the probability of accepting ghost tracks during mature track monitoring.<>     

On combining multidimensional target location ellipsoids

N.M. Blachman (1989) presented a method for combining the two-dimensional target location ellipses using the equation of an ellipse. A method is presented for combining N-dimensional location ellipsoids by using the location covariance matrix. The general result is formulated in simple matrix form. The results presented contain Blachman's results as a special case. Examples for both two and three dimensions are presented     

Target tracking in maneuver-centered coordinates

Aircraft targets normally maneuver on circular paths, which has led to tracking filters based on circular turns. A coordinate system to track circular maneuvers with a simple Kalman filter is introduced. This system is a polar coordinate system located at the center of the maneuver. It leads to a tracking filter with range, angle, and angular velocity in the state vector. Simulation results are presented, showing that the algorithm displays improved performance over methods based on constant x-y acceleration when tracking circular turns     

Track monitoring when tracking with multiple 2D passive sensors

A fast method of track monitoring is presented which determines what tracks are good and what tracks have had data association problems and should be eliminated. The philosophy of tracking in a dense target environment with limited central processing unit (CPU) time is to acquire the targets, track them with as simple a filter as will meet requirements, and monitor the tracks to determine if they are still tracking a target or are tracking incorrect returns and should be terminated. After termination the true targets are reacquired. However, it is difficult to determine from simple track monitoring the correct interpretation of a poor track. Poor tracks can be a result of a sensor failure, target maneuver, or incorrect data association. The author describes track monitoring and provides a solution to this dilemma when tracking with multiple two-dimensional passive sensors. The method is much faster than other monitoring methods.<>     

A class of near optimal JPDA algorithms

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 increases exponentially as the number of targets increases and therefore, is not an attractive algorithm when expecting to track many targets. Reviewed here is 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     

Multiple scan joint probabilistic data association

This paper presents a multiple scan or n-scan-back joint probabilistic data association (JPDA) algorithm which addresses the problem of measurement-to-track data association in a multiple target and clutter environment. The standard single scan JPDA algorithm updates a track with weighted sum of the measurements which could have reasonably originated from the target in track. The only information the standard JPDA algorithm uses is the measurements on the present scan and the state vectors and covariance matrices of the present targets. The n-scan-back algorithm presented here uses multiple scans of measurements along with the present target information to produce better weights for data association. The standard JPDA algorithm can utilize a formidable amount of processing power and the n-scan-back version only worsens the problem. Therefore, along with the algorithm presentation, implementations which make this algorithm practical are discussed and referenced. An example is also shown for a few n-scan-back window lengths     

Comparison of two-sensor tracking methods based on state vectorfusion and measurement fusion

There are two approaches to the two-sensor track-fusion problem. Y Bar-Shalom and L. Campo (ibid., vol.AES-22, 803-5, Nov. 1986) presented the state vector fusion method, which combines state vectors from the two sensors to form a new estimate while taking into account the correlated process noise. The measurement fusion method or data compression of D. Willner et al. (1976) combines the measurements from the two sensors first and then uses this fused measurement to estimate the state vector. The two methods are compared and an example shows the amount of improvement in the uncertainty of the resulting estimate of the state vector with the measurement fusion method