This paper considers the fusion of multiple estimates of a spatially extended object, where the object extent is modeled as an ellipse that is parameterized by the orientation and semi-axes lengths. For this purpose, we propose a novel systematic approach that employs a distance measure for ellipses, i.e., the Gaussian Wasserstein distance, as a cost function. We derive an explicit expression for the Minimium Mean Gaussian Wasserstein distance (MMGW) estimate. Based on the concept of a MMGW estimator, we develop efficient methods for the fusion of extended target estimates. The proposed fusion methods are evaluated in a simulated experiment and the benefits of the novel methods are discussed.
A widely-used approach to track elliptical objects is based on random matrices @cite_20 . In @cite_23 , a method is proposed to combine two target estimates by summing their (symmetric positive definite) shape matrices weighted by a factor depending on the number of measurements while also considering the distance between the two targets' centers. There also exist approaches to combine measurements from multiple sensors for one target update @cite_24 , similar to the random matrix update by @cite_1 , but using the sum of the measurement spreads from all sensors.
@cite_24 @cite_1 @cite_23 @cite_20
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The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i.e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. In both cases, tracking and data association under the “one target-one detection” assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a symmetric positive definite random matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the mentioned Bayesian approach suffers from in certain applications. An efficient approach for deriving accurate pose and heading values through multi-sensor fusion of data from several inexpensive sensors (such as multiple GPS (Global Positioning Systems), EC (electronic compass), rate gyro) is presented. The proposed multisensor fusion approach is composed of several sub-methods namely initial heading calculation, classification and weighing (CnW), extended Kalman filter (EKF) and then covariance intersection (CI) algorithms. The consecutive implementation of the sub-methods gives an accurate heading value with lesser RMSE (root mean square error) compared to the original GPS COG (course over ground) and EC. Several experimental tests were done to confirm the good performance of the proposed process. We present a novel approach for multi-object tracking which considers object detection and spacetime trajectory estimation as a coupled optimization problem. Our approach is formulated in a minimum description length hypothesis selection framework, which allows our system to recover from mismatches and temporarily lost tracks. Building upon a state-of-the-art object detector, it performs multiview multicategory object recognition to detect cars and pedestrians in the input images. The 2D object detections are checked for their consistency with (automatically estimated) scene geometry and are converted to 3D observations which are accumulated in a world coordinate frame. A subsequent trajectory estimation module analyzes the resulting 3D observations to find physically plausible spacetime trajectories. Tracking is achieved by performing model selection after every frame. At each time instant, our approach searches for the globally optimal set of spacetime trajectories which provides the best explanation for the current image and for all evidence collected so far while satisfying the constraints that no two objects may occupy the same physical space nor explain the same image pixels at any point in time. Successful trajectory hypotheses are then fed back to guide object detection in future frames. The optimization procedure is kept efficient through incremental computation and conservative hypothesis pruning. We evaluate our approach on several challenging video sequences and demonstrate its performance on both a surveillance-type scenario and a scenario where the input videos are taken from inside a moving vehicle passing through crowded city areas. We demonstrate a simple greedy algorithm that can reliably recover a vector v ∈ R from incomplete and inaccurate measurements x = Φv + e. Here Φ is a N × d measurement matrix with N ≪ d, and e is an error vector. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to close the gap between two major approaches to sparse recovery. It combines the speed and ease of implementation of the greedy methods with the strong guarantees of the convex programming methods. For any measurement matrix Φ that satisfies a Uniform Uncertainty Principle, ROMP recovers a signal v with O(n) nonzeros from its inaccurate measurements x in at most n iterations, where each iteration amounts to solving a Least Squares Problem. The noise level of the recovery is proportional to √ logn‖e‖2. In particular, if the error term e vanishes the reconstruction is exact. This stability result extends naturally to the very accurate recovery of approximately sparse signals.