In this paper, we discuss multi-target tracking for a submarine model based on incomplete observations. The submarine model is a weakly interacting stochastic dynamic system with several submarines in the underlying region. Observations are obtained at discrete times from a number of sonobuoys equipped with hydrophones and consist of a nonlinear function of the current locations of submarines corrupted by additive noise. We use filtering methods
to find the best estimation for the locations of the submarines.
Our signal is a measure-valued process, resulting in filtering equations that can not be readily implemented. We develop Markov
chain approximation approach to solve the filtering equation for our model. Our Markov chains are constructed by dividing the multi-target state space into cells, evolving particles in these cells,
and employing a random time change approach. These approximations converge to the unnormalized conditional distribution of the signal process based on the back observations. Finally we present some simulation results by using the refining stochastic grid (REST) filter (developed from our Markov chain approximation method).
In this note, we consider the problem of detecting network portscans through the use of anomaly detection. First, we introduce some static tests for analyzing traffic rates. Then, we make use of two dynamic chi-square tests to detect anomalous packets. Further, we model network traffic as a marked point process and introduce a general portscan model. Simulation results for correct detects and false alarms are presented using this portscan model and the statistical tests.
Predicting the future state of a random dynamic signal based on corrupted, distorted, and partial observations is vital for proper real-time control of a system that includes time delay. Motivated by problems from Acoustic Positioning Research Inc., we consider the continual automated illumination of an object moving within a bounded domain, which requires object location prediction due to inherent mechanical and physical time lags associated with robotic lighting. Quality computational predictions demand high fidelity models for the coupled moving object signal and observation equipment pair. In our current problem, the signal represents the vector position, orientation, and velocity of a stage performer. Acoustic observations are formed by timing ultrasonic waves traveling from four perimeter speakers to a microphone attached to the performer. The goal is to schedule lighting movements that are coordinated with the performer by anticipating his/her future position based upon these observations using filtering theory.
Particle system based methods have experienced rapid development and have become an essential technique of contemporary filtering strategies. Hitherto, researchers have largely focused on continuous state particle filters, ranging from traditional weighted particle filters to adaptive refining particle filters, readily able to perform path-space estimation and prediction. Herein, we compare the performance of a state-of-the-art refining particle filter to that of a novel discrete-space particle filter on the acoustic positioning problem. By discrete space particle filter we mean a Markov chain that counts particles in discretized cells of the signal state space in order to form an approximated unnormalized distribution of the signal state. For both filters mentioned above, we will examine issues like the mean time to localize a signal, the fidelity of filter estimates at various signal to noise ratios, computational costs, and the effect of signal fading; furthermore, we will provide visual demonstrations of filter performance.
Particle-based nonlinear filters have proven to be effective and versatile methods for computing approximations to difficult filtering problems. We introduce a novel hybrid particle method, thought to possess an excellent compromise between the unadaptive nature of the weighted particle methods and the overly random resampling in classical interactive particle methods, and compare this new method to our previously introduced refining branching particle filter. Our experiments involve various fixed numbers of particles and compare computational efficiency of our new method to the incumbent. The hybrid method is demonstrated to outperform two previous particle filters on our simulated test problems. To highlight the flexibility of particle filters, we choose to test our methods on a rectangularly-constrained Markov signal that does not satisfy a typical stochastic equation but rather a Skorohod, local time formulation. Whereas normal diffusive behavior occurs in the interior of the rectangular domain, immediate reflections are enforced at the boundary. The test problems involve a fish signal with boundary reflections and is motivated by the fish farming industry.