We describe the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X), a probeclass mission concept that will provide an unprecedented view of the X-ray sky, performing timing and spectroscopy over both a broad energy band (0.2–30 keV) and a wide range of timescales from microseconds to years. STROBE-X comprises two narrow-field instruments and a wide field monitor. The soft or low-energy band (0.2–12 keV) is covered by an array of lightweight optics (3-m focal length) that concentrate incident photons onto small solid-state detectors with CCD-level (85–175 eV) energy resolution, 100 ns time resolution, and low background rates. This technology has been fully developed for NICER and will be scaled up to take advantage of the longer focal length of STROBE-X. The higher-energy band (2–30 keV) is covered by large-area, collimated silicon drift detectors that were developed for the European LOFT mission concept. Each instrument will provide an order of magnitude improvement in effective area over its predecessor (NICER in the soft band and RXTE in the hard band). Finally, STROBE-X offers a sensitive wide-field monitor (WFM), both to act as a trigger for pointed observations of X-ray transients and also to provide high duty-cycle, high time-resolution, and high spectral-resolution monitoring of the variable X-ray sky. The WFM will boast approximately 20 times the sensitivity of the RXTE All-Sky Monitor, enabling multi-wavelength and multi-messenger investigations with a large instantaneous field of view. This mission concept will be presented to the 2020 Decadal Survey for consideration.
This paper addresses the problem of detecting and tracking an unknown number of submarines in a body of water using a known number of moving sonobuoys. Indeed, we suppose there are N submarines collectively maneuvering as a weakly interacting stochastic dynamical system, where N is a random number, and we need to detect and track these submarines using M moving sonobuoys. These sonobuoys can only detect the superposition of all submarines through corrupted and delayed sonobuoy samples of the noise emitted from the collection of submarines. The signals from the sonobuoys are transmitted to a central base to analyze, where it is required to estimated how many submarines there are as well as their locations, headings, and velocities. The delays induced by the propagation of the submarine noise through the water mean that novel historical filtering methods need to be developed. We summarize these developments within and give initial results on a simplified example.
A hybrid weighted interacting particle filter, the selectively resampling particle filter (SERP), is used to detect and track multiple ships maneuvering in a region of water. The ship trajectories exhibit nonlinear dynamics and interact in a nonlinear manner such that the ships do not collide. There is no prior knowledge on the number of ships in the region. The observations model a sensor tracking the ships from above the region, as in a low observable SAR or infrared problem. The SERP filter simulates particles to provide the approximated conditional distribution of the signal in the signal domain at a particular time, given the sequence of observations. After each observation, the hybrid filter uses selective resampling to move some particles with low weights to locations that have a higher likelihood of being correct, without resampling all particles or creating bias. Such a method is both easy to implement and highly computationally efficient. Quantitative results recording the capacity of the filter to determine the number of ships in the region and the location of each ship are presented. Thy hybrid filter is compared against an earlier particle filtering method.
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.
Particle-based nonlinear filters provide a mathematically optimal (in the limit) and sound method for solving a number of difficult filtering problems. However, there are a number of practical difficulties that can occur when applying particle-based filtering techniques to real world problems. These problems include highly directed signal dynamics highly definitive observations clipped observation data. Current approaches to solving these problems generally require increasing the number of particles, but to obtain a given level of performance the number of particles required may be extremely large. We propose a number of techniques to ameliorate these difficulties. We adopt the ideas of simulated annealing and add noise which is damped in time to the particle states when they are evolved or duplicated, and also add noise which is damped in time to the interpretation of the observations by the filter, to deal with signal dynamics and observation problems. We modify the method by which particles are duplicated to deal with different information flows into the system depending on the location of the particle and the information flow into the particle. We discuss the success we have had with these solutions on some of the problems of interest to Lockheed Martin and the MITACS-PINTS research center.
Particle approximations are used to track a maneuvering signal given only a noisy, corrupted sequence of observations, as are encountered in target tracking and surveillance. The signal exhibits nonlinearities that preclude the optimal use of a Kalman filter. It obeys a stochastic differential equation (SDE) in a seven-dimensional state space, one dimension of which is a discrete maneuver type. The maneuver type switches as a Markov chain and each maneuver identifies a unique SDE for the propagation of the remaining six state parameters. Observations are constructed at discrete time intervals by projecting a polygon corresponding to the target state onto two dimensions and incorporating the noise. A new branching particle filter is introduced and compared with two existing particle filters. The filters simulate a large number of independent particles, each of which moves with the stochastic law of the target. Particles are weighted, redistributed, or branched, depending on the method of filtering, based on their accordance with the current observation from the sequence. Each filter provides an approximated probability distribution of the target state given all back observations. All three particle filters converge to the exact conditional distribution as the number of particles goes to infinity, but differ in how well they perform with a finite number of particles. Using the exactly known ground truth, the root-mean-squared (RMS) errors in target position of the estimated distributions from the three filters are compared. The relative tracking power of the filters is quantified for this target at varying sizes, particle counts, and levels of observation noise.