Proposal strategies for joint state-space tracking with particle filters

A proposal function determines the random particle support of a particle filter. When this support is distributed close to the true target density, filter's estimation performance increases for a given number of particles. In this paper, a proposal strategy for joint state-space tracking using particle filters is given. The state-spaces are assumed Markovian and not-exact; however, each state-space is assumed to sufficiently describe the underlying phenomenon. The joint tracking is achieved by carefully placing the random support of the joint filter to where the final posterior is likely to lie. Computer simulations demonstrate improved performance and robustness of the joint state-space through the proposed strategy

Quantum critical behavior in the heavy Fermion single crystal Ce(Ni0.935_{0.935}Pd0.065_{0.065})2_2Ge2_2

We have performed magnetic susceptibility, specific heat, resistivity, and inelastic neutron scattering measurements on a single crystal of the heavy Fermion compound Ce(Ni$_{0.935}$Pd$_{0.065}$)$_2$Ge$_2$, which is believed to be close to a quantum critical point (QCP) at T = 0. At lowest temperature(1.8-3.5 K), the magnetic susceptibility behaves as $\chi(T)-\chi (0)$ $\propto$ $T^{-1/6}$ with $\chi (0) = 0.032 \times 10^{-6}$ m$^3$/mole (0.0025 emu/mole). For $T<$ 1 K, the specific heat can be fit to the formula $\Delta C/T = \gamma_0 - T^{1/2}$ with $\gamma_0$ of order 700 mJ/mole-K$^2$. The resistivity behaves as $\rho = \rho_0 + AT^{3/2}$ for temperatures below 2 K. This low temperature behavior for $\gamma (T)$ and $\rho (T)$ is in accord with the SCR theory of Moriya and Takimoto\cite{Moriya}. The inelastic neutron scattering spectra show a broad peak near 1.5 meV that appears to be independent of $Q$; we interpret this as Kondo scattering with $T_K =$ 17 K. In addition, the scattering is enhanced near $Q$=(1/2, 1/2, 0) with maximum scattering at $\Delta E$ = 0.45 meV; we interpret this as scattering from antiferromagnetic fluctuations near the antiferromagnetic QCP.Comment: to be published in J. Phys: Conference Serie

Sensor array calibration via tracking with the extended Kalman filter

Starting with a randomly distributed sensor array with unknown sensor orientations, array calibration is needed before target localization and tracking can be performed using classical triangulation methods. In this paper, we assume that the sensors are only capable of accurate direction of arrival (DOA) estimation. The calibration problem cannot be completely solved given the DOA estimates alone, since the problem is not only rotationally symmetric but also includes a range ambiguity. Our approach to calibration is based on tracking a single target moving at a constant velocity. In this case, the sensor array can be calibrated from target tracks generated by an extended Kalman filter (EKF) at each sensor. A simple algorithm based on geometrical matching of similar triangles will align the separate tracks and determine the sensor positions and orientations relative to a reference sensor. Computer simulations show that the algorithm performs well even with noisy DOA estimates at the sensors

Tracking of multiple wideband targets using passive sensor arrays and particle filters

In this paper, we present a way to track multiple maneuvering targets with varying time-frequency signatures. A particle filter is used to track targets that have constant speeds with changing heading directions. The target motion dynamics help the particle filter achieve an angular resolution otherwise not possible by the conventional beamforming techniques. Moreover, the particle filter has a built-in target association that eliminates the need for heuristic techniques commonly used in the multiple target tracking problems. Reference priors are used to derive the probability distribution function of the acoustic array outputs given the state of the multiple target states (MTS's). Local linearization is used to approximate the importance function used in the particle filter by a Gaussian pdf. Finally, computer simulations are used to demonstrate the performance of the algorithm with synthetic data

Fast initialization of particle filters using a modified Metropolis-Hastings algorithm: Mode-hungry approach

As a recursive algorithm, the particle filter requires initial samples to track a state vector. These initial samples must be generated from the received data and usually obey a complicated distribution. The Metropolis-Hastings (M-H) algorithm is used for sampling from intractable multivariate target distributions and is well suited for the initialization problem. Asymptotically, the M-H scheme creates samples drawn from the exact distribution. For the particle filter to track the state, the initial samples need to cover only the region around its current state. This region is marked by the presence of modes. Since the particle filter only needs samples around the mode, we modify the M-H algorithm to generate samples distributed around the modes of the target posterior. By simulations, we show that this "mode hungry" algorithm converges an order of magnitude faster than the original M-H scheme for both unimodal and multi-modal distributions

Acoustic node calibration using helicopter sounds and Monte Carlo markov chain methods

A Monte-Carlo method is used to calibrate a randomly placed sensor node using helicopter sounds. The calibration is based on using the GPS information from the helicopter and the estimated DOA's at the node. The related Cramer-Rao lower bound is derived and the effects of the GPS errors on the position estimates are derived. Issues related to the processing of the field data, e.g., time synchronization and data nonstationarity are discussed. The effects of the GPS errors are shown to be negligible under certain conditions. Finally, the results of the calibration on field data are given

2-D sensor position perturbation analysis: Equivalence to AWGN on array outputs

In this paper, the performance of a subspace beamformer, namely the multiple signal classification algorithm (MUSIC), is scrutinized in the presence of sensor position errors. Based on a perturbation model, a relationship between the array autocorrelation matrix and the source autocorrelation matrix is established. It is shown that under certain assumptions on the source signals, the Gaussian sensor perturbation errors can be modelled as additive white Gaussian noise (AWGN) for an array where sensor positions are known perfectly. This correspondence can be used to equate position errors to an equivalent signal-to-noise ratio (SNR) for AWGN in performance evaluation. Finally, Cramer-Rao bound for the position perturbations that can be computed using the Cramer-Rao bound relations for the additive Gaussian noise case at high SNR's