A New Reduction Scheme for Gaussian Sum Filters

In many signal processing applications it is required to estimate the unobservable state of a dynamic system from its noisy measurements. For linear dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum Filters (GSF) provide the MMSE state estimate by tracking the GM posterior. However, since the number of the clusters of the GM posterior grows exponentially over time, suitable reduction schemes need to be used to maintain the size of the bank in GSF. In this work we propose a low computational complexity reduction scheme which uses an initial state estimation to find the active noise clusters and removes all the others. Since the performance of our proposed method relies on the accuracy of the initial state estimation, we also propose five methods for finding this estimation. We provide simulation results showing that with suitable choice of the initial state estimation (based on the shape of the noise models), our proposed reduction scheme provides better state estimations both in terms of accuracy and precision when compared with other reduction methods

Distributing the Kalman Filter for Large-Scale Systems

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/ . Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la

Challenges with bearings only tracking for missile guidance systems and how to cope with them.

This paper addresses the problem of closed loop missile guidance using bearings and target angular extent information. Comparison is performed between particle filtering methods and derivative free methods. The extent information characterizes target size and we show how this can help compensate for observability problems. We demonstrate that exploiting angular extent information improves filter estimation accuracy. The performance of the filters has been studied over a testing scenario with a static target, with respect to accuracy, sensitivity to perturbations in initial conditions and in different seeker modes (active, passive and semi-active)

Information Acquisition with Sensing Robots: Algorithms and Error Bounds

Utilizing the capabilities of configurable sensing systems requires addressing difficult information gathering problems. Near-optimal approaches exist for sensing systems without internal states. However, when it comes to optimizing the trajectories of mobile sensors the solutions are often greedy and rarely provide performance guarantees. Notably, under linear Gaussian assumptions, the problem becomes deterministic and can be solved off-line. Approaches based on submodularity have been applied by ignoring the sensor dynamics and greedily selecting informative locations in the environment. This paper presents a non-greedy algorithm with suboptimality guarantees, which does not rely on submodularity and takes the sensor dynamics into account. Our method performs provably better than the widely used greedy one. Coupled with linearization and model predictive control, it can be used to generate adaptive policies for mobile sensors with non-linear sensing models. Applications in gas concentration mapping and target tracking are presented.Comment: 9 pages (two-column); 2 figures; Manuscript submitted to the 2014 IEEE International Conference on Robotics and Automatio

MR-BART: Multi-Rate Available Bandwidth Estimation in Real-Time

In this paper, we propose Multi-Rate Bandwidth Available in Real Time (MR-BART) to estimate the end-to-end Available Bandwidth (AB) of a network path. The proposed scheme is an extension of the Bandwidth Available in Real Time (BART) which employs multi-rate (MR) probe packet sequences with Kalman filtering. Comparing to BART, we show that the proposed method is more robust and converges faster than that of BART and achieves a more AB accurate estimation. Furthermore, we analyze the estimation error in MR-BART and obtain analytical formula and empirical expression for the AB estimation error based on the system parameters.Comment: 12 Pages (Two columns), 14 Figures, 4 Tables