<title>Utilizing negative information to track ground vehicles through move-stop-move cycles</title>

Abstract

Ground vehicles can be effectively tracked using a moving target indicator (MTI) radar. However, vehicles whose velocity along the line-of-sight to the radar falls below the minimum detectable velocity (MDV) are not detected. One way targets avoid detection, therefore, is to execute a series of move-stop-move motion cycles. While a target can be acquired after beginning to move again, it may not be recognized as a target previously in track. Particularly for the case of high-value targets, it is imperative that a vehicle be continuously tracked. We present an algorithm for determining the probability that a target has stopped and an estimate of its stopped state (which could be passed to a tasker to schedule a spot synthetic aperature radar (SAR) measurement). We treat a non-detection event as evidence that can be used to update the target state probability density function (PDF). Updating the target state PDF using a non-detection event pushes the probability mass into regions of the state space in which the vehicle is either stopped or traveling at a speed such that the range-rate fails the MDV. The target state PDF updated with the non-detection events is then used to derive an estimate of the stopped target's location. Updating the target state PDF using a non-detection event is, in general, non-trivial and approximations are required to evaluate the updated PDF. When implemented with a particle filter, however, the updating formula is simple to evaluate and still captures the subtleties of the problem.

On exploiting ‘negative’ sensor evidence for target tracking and sensor data fusion

“…ÔnegativeÕ evidence, seems to be accepted in the tracking and sensor data fusion community (see, e.g., Refs. [2,3]). Speaking of a ÔnegatedÕ sensor output in this context is perhaps a more appropriate way of expressing what is meant.…”

Long term vehicle motion prediction and tracking in large environments

“…As the signal coverage range is limited to only a few hundred meters, data collectors are recommended to be placed at regions with heavy traffic and high timing uncertainty, such as special context areas and intersections. This paper considers both positive and negative information as described in [17] and [18]. The positive information is given by the detection of a vehicle in sensor range indicating its presence.…”

An enhanced particle filtering method for GMTI radar tracking

“…According to the properties of GMTI radars, no measurements will be detected if the target radial velocity is within the Doppler blind region. In addition, even the target radial velocity v r t is outside the Doppler blind region, the target is not always detected but with a detection probability PD (see, e.g., [11]). The actual measurement zt takes the values in the set Z = {R 3 ∪ ∅}, where ∅ denotes a missing measurement, i.e.…”

“…Here the multiple-model-based approaches were chosen for a fair comparison as our proposed approach considers multiple state models. In particular, the NRDB-MM algorithm in [12] was used as the benchmark algorithm for comparison purposes, whereas the MMPF approach is a widely used algorithm in the literature (see, e.g., [11], [4] and [26]). The parameter for the NRDB-MM was set exactly the same as in [12].…”

“…To solve the problem that negative weights may possibly arise in the Gaussian mixture approximation, an extra approximation stage was introduced in [10] to replace the resulting negative Gaussian mixture with one having strictly positive mixture weights, and thus improving on algorithmic stability. The algorithm in [11] applied the particle filtering method and treated each non-detection case as evidence. The corresponding likelihood function of the non-detection evidence was formulated and incorporated into the particle filtering procedure to update the target state probability distribution when no measurements are recorded.…”