EE Seminar: Optimal Geometries and Trajectory Planning for DDOP

24 במאי 2017, 15:30 
חדר 011, בניין כיתות-חשמל 

 

Speaker: David Refael

M.Sc. student under the supervision of Prof. Anthony J. Weiss

 

Wednesday, May 24th 2017 at 15:30

Room 011, Kitot Bldg., Faculty of Engineering

Optimal Geometries and Trajectory Planning for DDOP

Abstract

Consider moving sensors, continuously collecting DDOP measurements of a stationary emitter. In this work, we seek the optimal trajectory for localization of a stationary target. Various optimality criteria exist in the literature. The so-called D-optimality- criterion refers to the determinant of the Fisher Information Matrix which is inversely proportional to the area of the uncertainty ellipse determined by the Cramér-Rao Lower Bound (CRLB). The E-criterion refers to the largest Eigen value of the CRLB matrix which corresponds to the largest axis of the uncertainty ellipse. The A-criterion refers to the trace of the CRLB matrix which corresponds to the sum of both axes of the uncertainty ellipse. All three have their merits. We discuss all, but focus on the E- criterion. The question at hand is what should be the optimal trajectory to best locate a stationary target. Two scenarios are of interest:

1. Sensors with constant mutual distance.

2. Sensors with no mutual constraints.

It is shown that sensor placing for best localization is not unique. We then check if moving in a circle around the target is a local optimal geometric solution for 2 DDOP sensors. We will find the FIM of 2 DDOP sensors moving in an arbitrary path and in a circular path. We will compare the determinant (D criterion) of a circular path with a circular path in which one of the locations was moved to an arbitrary place (single-point-out) to find the local optimality criterion for a circular path to be an optimal path. We will compare our results with those in the literature. Next, we will find the optimal angular spread of more than 2 sensors with respect to the reference sensor using the A criterion.

In order to have some basis for comparison, we presented the problem as a steering-vector problem, only deriving an explicit set of equations for the general D-criterion equation. Although interesting recursive dependencies arise, no simple geometric shape can be deduced from these equations. Future work and coding can benefit from those relations.

We proposed a greedy algorithm, based on the E-criterion, which finds the optimal path as a function of the initial conditions. Its results are verified. DDOP sensors have various optimal trajectories depending on the constraints. Some of the options are not intuitive. We analyzed the effect of various challenges on the greedy algorithm, such as different sensor formations, angular maneuver constraints and threats. Optimal geometry of the sensors is discussed and the performance of the algorithm is numerically validated for 3 sensors.

Finally, we introduce the concept of genetic algorithms. Although applied mostly to classical NP problems, we introduce coding of chromosomes, mating, mutations and elitism concepts in the field of multi sensor localization in order to find the optimal trajectory and validate its performance for 2 sensors. 

אוניברסיטת תל אביב עושה כל מאמץ לכבד זכויות יוצרים. אם בבעלותך זכויות יוצרים בתכנים שנמצאים פה ו/או השימוש
שנעשה בתכנים אלה לדעתך מפר זכויות, נא לפנות בהקדם לכתובת שכאן >>