A Sequential Detection and Tracking of Very Low SNR Objects

A sequential detection and tracking (SDT) approach is proposed for detection and tracking of very low signal-to-noise (SNR) objects. The proposed approach is compared with two existing particle filter track-before-track (TBD) methods. It is shown that the former outperforms the latter. A conventional detection and tracking (CDT) approach, based on one-data-frame thresholding, is considered as a benchmark for comparison. Simulations demonstrate the performance.

Detection and Tracking of Low Observable Objects in a Sequence of Image Frames Using Particle Filter

A track-before-detect (TBD) particle filter-based method for detection and tracking of low observable objects based on a sequence of image frames in the presence of noise and clutter is studied. At each time instance after receiving a frame of image, first, some preprocessing approaches are applied to the image. Then, it is sent to the detection and tracking algorithm which is based on a particle filter. Performance of the approach is evaluated for detection and tracking of an object in different scenarios including noise and clutter.

Guidance Trajectory Mathematical Modeling

A trajectory of a destination-directed moving object (e.g. an aircraft from an origin airport to a destination airport) has three main components: an origin, a destination, and motion in between. We call such a trajectory that end up at the destination \textit{destination-directed trajectory (DDT)}. A class of conditionally Markov (CM) sequences (called CM$_\text{L}$) has the following main components: a joint density of two endpoints and a Markov-like evolution law. A CM$_\text{L}$ dynamic model can describe the evolution of a DDT but not of a guided object chasing a moving guide. The trajectory of a guided object is called a \textit{guided trajectory (GT)}. Inspired by a CM$_\text{L}$ model, this paper proposes a model for a GT with a moving guide. The proposed model reduces to a CM$_\text{L}$ model if the guide is not moving. We also study filtering and trajectory prediction based on the proposed model. Simulation results are presented.

Gaussian Conditionally Markov Sequences: Dynamic Models and Representations of Reciprocal and Other Classes

Conditionally Markov (CM) sequences are powerful mathematical tools for modeling problems. One class of CM sequences is the reciprocal sequence. In application, we need not only CM dynamic models, but also know how to design model parameters. Models of two important classes of nonsingular Gaussian (NG) CM sequences, called $CM_L$ and $CM_F$ models, and a model of the NG reciprocal sequence, called reciprocal $CM_L$ model, were presented in our previous works and their applications were discussed. In this paper, these models are studied in more detail, in particular their parameter design. It is shown that every reciprocal $CM_L$ model can be induced by a Markov model. Then, parameters of each reciprocal $CM_L$ model can be obtained from those of the Markov model. Also, it is shown that a NG $CM_L$ ($CM_F$) sequence can be represented by a sum of a NG Markov sequence and an uncorrelated NG vector. This (necessary and sufficient) representation provides a basis for designing parameters of a $CM_L$ ($CM_F$) model. From the CM viewpoint, a representation is also obtained for NG reciprocal sequences. This representation is simple and reveals an important property of reciprocal sequences. As a result, the significance of studying reciprocal sequences from the CM viewpoint is demonstrated. A full spectrum of dynamic models from a $CM_L$ model to a reciprocal $CM_L$ model is also presented. Some examples are presented for illustration.