In this paper, we present an efficient data association algorithm for tracking ground targets that perform move-stop-move maneuvers using ground moving target indicator (GMTI) radar. A GMTI radar does not detect the
targets whose radial velocity falls below a certain minimum detectable velocity. Hence, to avoid detection enemy
targets deliberately stop for some time before moving again. When targets perform move-stop-move maneuvers,
a missed detection of a target by the radar leads to an ambiguity as to whether it is because the target has
stopped or due to the probability of detection being less than one. A solution to track move-stop-move target
tracking is based on the variable structure interacting multiple model (VS-IMM) estimator in an ideal scenario
(single target tracking with no false measurements) has been proposed. This solution did not consider the data
association problem. Another solution, called two-dummy solution, considered the data association explicitly and
proposed a solution based on the multiframe assignment algorithm. This solution is computationally expensive,
especially when the scenario is complex (e.g., high target density) or when one wants to perform high dimensional
assignment. In this paper, we propose an efficient multiframe assignment-based solution that considers the second
dummy measurement as a real measurement than a dummy. The proposed algorithm builds a less complex
assignment hypothesis tree, and, as a result, is more efficient in terms of computational resource requirement.
In this paper we describe computationally efficient assignment-based algorithms to solve the data association
problem in synchronous passive multisensor tracking systems. A traditional assignment-based solution to this
problem is to solve the measurement-to-measurement association using multidimensional (S-dimensional or SD
with S sensors) assignment formulation and the measurement-to-track association using two-dimensional
assignment formulation. Even though this solution has been proven to be effective, it is computationally very
expensive. One of the reasons is that in calculating the assignment cost of each possible candidate association one
requires to find the maximum likelihood (ML) estimate of the unknown target state. The algorithms proposed in
this paper use prior information of the targets that are being tracked to reduce the requirement for the costly ML
estimation. The first algorithm is similar to the traditional two step technique except that it uses the predicted
track information to avoid building the whole assignment tree in the measurement-to-measurement association.
In particular, based on the predicted track information first validation gates are constructed for every target.
Then, when forming the assignment tree, only the branches connecting measurements that satisfy the validation gate requirement are constructed. The second algorithm is a one-step algorithm in that it directly assigns the measurements to the tracks. We pose the data association problem as an (S + 1)-D assignment with the first dimension being the predicted state information of the tracks, and the rest of the S dimensions are the lists of measurements from the sensors. The costs of each possible (S + 1)-tuple are calculated based on the predicted track information, hence, the requirement for an ML estimate is eliminated. Further, we show that when the target maneuvers are not very high, and when the sensor measurements are uncorrelated the (S+1)-D assignment approximately decomposes into S individual 2-D assignments, resulting in huge computational savings.
Proc. SPIE. 6567, Signal Processing, Sensor Fusion, and Target Recognition XVI
KEYWORDS: Unmanned aerial vehicles, MATLAB, Sensors, Receivers, Monte Carlo methods, Intelligence systems, Chemical elements, Computer engineering, Optimization (mathematics), Global Positioning System
In this paper, two new solutions to the localization of an emitter using time difference of arrival (TDOA)
measurements are proposed. The maximum likelihood estimation for this problem will result in a nonlinear and
nonconvex optimization problem, which is very difficult to solve. The solutions presented in this paper consider
an alternate formulation, which is based on the sensor-emitter geometry. This formulation results in quadratic
(however, nonconvex) optimization problem.
The first solution relaxes the original optimization problem into a semidefinite program (SDP). Using the
solution to this relaxed SDP, emitter is localized using a randomization technique. The second solution forms
the Lagrangian dual of the original problem, and it is shown that the dual problem is an SDP. From the solution
to the dual problem a solution to the original problem is found. It has to be noted that the solution obtained
using the optimal dual variable, is optimal to the original problem only if strong duality holds. This has not
been proven in this paper analytically. Extensive simulations performed suggests that the strong duality may
hold for this problem.
Invited Panel Discussion Topics: Research Challenges in Sensor Management; Fundamental Statistics for Resource Management; Issues in Formulating Utility Functions for Sensor
Management; Resource Management for Distributed Attention in Sensor Networks; Research Challenges in Network and Service Management for Distributed Net-Centric Fusion; Resource Management in Sensor Networks; Performance Metrics for Combed Tracking and Sensor Management.
Typically, the posterior Cramer-Rao lower bound (PCRLB) is the performance bound of choice in tracking
applications. This is primarily due to the availability of a computationally efficient recursive formulation of the
bound. It has been shown, however, that this bound is weak in certain applications. Weiss-Weinstein lower bound (WWLB) is another second-order error bound that is free from the regularity conditions and it is applicable in a wide range of problems. In addition, it has free variables that can be tuned to get tighter bounds. In this paper, we develop the WWLB for maneuvering target tracking. In particular, we utilize the ability of the WWLB to handle continuous and discrete random variables: target motion model is represented by a separate discrete variable and the bound is calculated over the continuous state and discrete motion model variables. The bound is tightened by optimizing with respect to the free variables.
In this paper, we present a framework for tracking multiple mobile targets in an urban environment based on data from multiple sources of information, and for evaluating the threat these targets pose to assets of interest (AOI). The motivating scenario is one where we have to track many targets, each with different (unknown) destinations and/or intents. The tracking algorithm is aided by information about the urban environment (e.g., road maps, buildings, hideouts), and strategic and intelligence data. The tracking algorithm needs to be dynamic in that it has to handle a time-varying number of targets and the ever-changing urban environment depending on the locations of the moving objects and AOI. Our solution uses the variable structure interacting multiple model (VS-IMM) estimator, which has been shown to be effective in tracking targets based on road map information. Intelligence information is represented as target class information and incorporated through a combined likelihood calculation within the VS-IMM estimator. In addition, we develop a model to calculate the probability that a particular target can attack a given AOI. This model for the calculation of the probability of attack is based on the target kinematic and class information. Simulation results are presented to demonstrate the operation of the proposed framework on a representative scenario.
Previous researches related to geolocation based on the time difference of arrival (TDOA) technique focused mainly on solving the nonlinear equations that relate the TDOA measurements to the unknown source location. They, however, considered a rather simplistic scenario: a single emitter with no possibility of either missed detections, or false measurements. In real world scenarios, one must resolve the important issue of measurement-origin uncertainty, before applying these techniques. This paper proposes an algorithm for the geolocation and tracking of multiple emitters in practical scenarios. The focus is on solving the all important data association problem, i.e., deciding from which target, if any, a measurement originated. A previous solution for data association based on the assignment formulation for passive measurement tracking systems relied on solving two assignment problems: an S-dimensional (or, SD, where S ≥ 3) assignment for association across sensors, and a 2D assignment for measurement-to-track association. Here, an (S + 1)D assignment algorithm, which performs the data association in one step, is introduced. As can be seen later, the (S+1)D assignment formulation reduces the computational cost significantly. Incorporation of correlated measurements (which is the case with TDOA measurements) into the SD framework that typically assumes uncorrelated measurements, is also discussed. The nonlinear TDOA equations are posed as an optimization problem, and solved using SolvOpt: a nonlinear optimization solver. The interacting multiple model (IMM) estimator is used in conjunction with the unscented Kalman filter (UKF) to track the geolocated emitters.
In geolocating by time difference of arrival (TDOA), an array of sensors at known locations receive the signal from an emitter whose location is to be estimated. Signals received at two sensors are used to obtain the TDOA measurement. A number of algorithms are available to solve the set of nonlinear TDOA equations whose solution is the emitter location. An implicit assumption in these algorithms is that all the measurements obtained are from a single emitter. In practice, however, one has to deal with measurement origin uncertainty, which is a result of either multiple emitters being present in the region of interest, or clutter returns. In this paper, a method to determine the location of multiple emitters in a cluttered environment is presented. Several unmanned aerial vehicles (UAVs) are assumed as receivers of the electromagnetic emission from the emitter. Emissions received by different UAVs are used to obtain the TDOAs. Using a constrained optimization procedure, measurement-to-emitter associations are determined. Then, the resulting nonlinear equations are solved to find the emitter locations. An Interacting Multiple Model (IMM) estimator is used to track the located sources and to obtain their motion parameters.