43 research outputs found
Particle Filters for Multiple Target Tracking
No full textAbstractMultiple target tracking has immense application in areas such as surveillance, air traffic control, defense and computer vision. The aim of a target tracking algorithm is to estimate the target position precisely from the partial noisy observations available. The real challenges of multiple target tracking are to accomplish the same in the presence of measurement origin uncertainty and clutter. Optimal solutions are available by way of Kalman filters for the special case of linear dynamical systems with Gaussian noise. For a more general scenario, we resort to the suboptimal solutions like Particle filters which implement stochastic filtering through a sequential Monte Carlo approach. Measurement origin uncertainty is resolved by using a suitable data association technique prior to the filtering. This paper explores the possibilities of applying a variant of Ensemble Square Root Filters (EnSRF) in a multiple target tracking scenario and its tracking performance is compared with those of conventional Bootstrap and Auxiliary Bootstrap particle filters. The filtering scheme proposed here incorporates Sample based Joint Probabilistic Data Association (SJPDA) in the EnSRF framework for dealing with measurement origin uncertainty
Kudakrumia rangnekari Kumar & Lelej & Das & Raveendran & Loktionov 2019, sp. nov.
No full text<i>Kudakrumia rangnekari</i> Girish Kumar & Lelej, sp. nov. <p>(Figs. 1–10)</p> <p> <b>Type material.</b> Holotype ♂, mounted on card stock, <b>India</b>: Goa, South Goa district, Kotigao Wildlife Sanctuary (14°58’36’’N 74°12’22’’E, 108 m), 18.v.2018, Coll. P. Girish Kumar, ZSIK Regd. No. ZSI/ WGRC /IR/INV.12178. Paratype ♂, <b>India</b>: Kerala, Kasaragod district, Ranipuram Hill (12°24’56’’N 75°21’11’’E, 901 m), 21.i.2018, Coll. P.M. Rajan, ZSIK Regd. No. ZSI/ WGRC /IR/INV.12179.</p> <p> <b>Diagnosis</b>. Male. This new species is characterized by the following combination of characters: metasomal sternum 1 basally with distinct, long process (Fig. 1); metapleuron uniformly punctured, except median small smooth area (Fig. 5); propodeum punctate laterally (near metapleuron) (Fig. 5); propodeum strongly punctate without microsculptures (Fig. 5); parapenial lobe of basiparamere apically not modified, simple (Fig. 10). Female unknown.</p> <p> <b>Description</b>. Holotype male. Length: 3.28 mm. Body black but mandible except base, scape, pedicel and flagellum beneath brownish red; palpi, tegulae and legs testaceous except mesocoxa partially, metacoxa, apical half of mesofemur, metafemur almost entirely, meso- and metatibia except base, protarsomere 2–5, meso- and metatarsomere 1–5 black. Vestiture short and silvery, moderately dense and appressed on most of body, sparse erect setae also present between punctures. Wings hyaline, veins testaceous.</p> <p> <i>Head.</i> Sculpture dense, fine, at higher magnification polygonal in shape (Fig. 2); eye setae length about half frons setae length; apical clypeus margin not emarginated; mandible with three teeth; POL 0.605 × OOL; POL 1.619 × LOL; POL 2.44 diameter of posterior ocellus; scape (Fig. 3) 1.59 × as long as wide, inner lateral margin carinate, inner surface of flagellomeres 2–10 with few shorter, stouter setae.</p> <p> <i>Mesosoma</i>. Notauli almost touching anterior border of mesoscutum, parapsidal lines two-thirds of mesoscutum length, dorsum with slightly larger, more separated punctures, with microsculpture similar to that of head (Fig. 4); propodeum strongly punctate without microsculptures; metapleuron uniformly punctured, except median small area smooth. Forewing as in Fig. 6; basal part of medial vein of hindwing curved but not angulate (Fig. 7).</p> <p> <i>Metasoma</i>. First two metasomal terga with fine, subcontiguous punctures, with microsculpture almost similar to that of mesosomal dorsum, remaining terga with finer, slightly separated punctures (Fig. 8); sternum 1 basally with distinct long process (Fig. 1); second sternum with larger subcontiguous punctures, remaining sterna with small subcontiguous punctures (Fig. 9). Genitalia as in Fig. 10. Parapenial lobe of basiparamere apically not modified, simple.</p> <p>Female. Unknown.</p> <p> <b>Etymology</b>. The species is named after Mr. Parag Rangnekar, a well-known butterfly and dragonfly specialist from Goa who helped the first author to conduct a collection tour in Goa state during which the holotype was collected.</p> <p> <b>Distribution</b>. India: Goa, Kerala.</p> <p> <b>Remark</b>. The differences between the male of this new species and <i>Kudakrumia mirabilis</i> are given in the key below.</p>Published as part of <i>Kumar, Girish P., Lelej, Arkady S., Das, Dipanwita, Raveendran, Hanima K. P. & Loktionov, Valery M., 2019, Discovery of the genus Kudakrumia Krombein, 1979 (Hymenoptera: Mutillidae) in India and description of a new species, pp. 260-266 in Zootaxa 4612 (2)</i> on pages 261-264, DOI: 10.11646/zootaxa.4612.2.8, <a href="http://zenodo.org/record/3234350">http://zenodo.org/record/3234350</a>
Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification
No full textThis thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional
nonlinear filtering problems.
The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of
locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon-
Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.
The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the
likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling.
The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes.
In Chapter 4, we explore the possibility of unscented transformation on Gaussian random
variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully
treating relatively larger dimensional filtering problems.
We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence.
The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank
incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for
highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications.
The thesis is finally wound up in Chapter 7 by summarizing these developments and
briefly outlining the future research direction
Particle Filter based Massive MIMO Channel Estimation
No full textMassive multiple-input multiple-output (MIMO) communication systems have
drawn significant interest recently in next-generation wireless communications.
The use of a large number of antennas in massive MIMO makes the estimation of
channel state information very challenging. Accurate channel state information
is essential in capitalizing the advantages of the massive MIMO technology.
This paper proposes the application of the Ensemble Square Root Filter (EnSRF)
and a variant of EnSRF, namely a Particle wise Update version of the Ensemble
Square Root Filter (PUEnSRF) to estimate the time-selective frequency-flat
fading channel coefficients in the massive MIMO scenario. Simulation results
clearly indicate the remarkably superior accuracy and filter convergence of
PUEnSRF estimates as compared to the conventional particle filters
Iterated gain-based stochastic filters for dynamic system identification
No full textWe propose a novel form of nonlinear stochastic filtering based on an iterative evaluation of a Kalman-like gain matrix computed within a Monte Carlo scheme as suggested by the form of the parent equation of nonlinear filtering (Kushner-Stratonovich equation) and retains the simplicity of implementation of an ensemble Kalman filter (EnKF). The numerical results, presently obtained via EnKF-like simulations with or without a reduced-rank unscented transformation, clearly indicate remarkably superior filter convergence and accuracy vis-a-vis most available filtering schemes and eminent applicability of the methods to higher dimensional dynamic system identification problems of engineering interest. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved
A Nearly Exact Reformulation of the Girsanov Linearization for Stochastically Driven Nonlinear Oscillators
No full textThe Girsanov linearization method (GLM), proposed earlier in Saha, N., and Roy, D., 2007, ``The Girsanov Linearisation Method for Stochastically Driven Nonlinear Oscillators,'' J. Appl. Mech., 74, pp. 885-897, is reformulated to arrive at a nearly exact, semianalytical, weak and explicit scheme for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the reformulated linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories while weakly applying the Girsanov correction (the Radon-Nikodym derivative) for the linearization errors. The semianalyticity is due to an explicit linearization of the nonlinear drift terms and it plays a crucial role in keeping the Radon-Nikodym derivative ``nearly bounded'' above by the inverse of the linearization time step (which means that only a subset of linearized trajectories with low, yet finite, probability exceeds this bound). Drift linearization is conveniently accomplished via the first few (lower order) terms in the associated stochastic (Ito) Taylor expansion to exclude (multiple) stochastic integrals from the numerical treatment. Similarly, the Radon-Nikodym derivative, which is a strictly positive, exponential (super-) martingale, is converted to a canonical form and evaluated over each time step without directly computing the stochastic integrals appearing in its argument. Through their numeric implementations for a few low-dimensional nonlinear oscillators, the proposed variants of the scheme, presently referred to as the Girsanov corrected linearization method (GCLM), are shown to exhibit remarkably higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own
Iterated stochastic filters with additive updates for dynamic system identification: Annealing-type iterations and the filter bank
No full textA nonlinear stochastic filtering scheme based on a Gaussian sum representation of the filtering density and an annealing-type iterative update, which is additive and uses an artificial diffusion parameter, is proposed. The additive nature of the update relieves the problem of weight collapse often encountered with filters employing weighted particle based empirical approximation to the filtering density. The proposed Monte Carlo filter bank conforms in structure to the parent nonlinear filtering (Kushner-Stratonovich) equation and possesses excellent mixing properties enabling adequate exploration of the phase space of the state vector. The performance of the filter bank, presently assessed against a few carefully chosen numerical examples, provide ample evidence of its remarkable performance in terms of filter convergence and estimation accuracy vis-a-vis most other competing filters especially in higher dimensional dynamic system identification problems including cases that may demand estimating relatively minor variations in the parameter values from their reference states. (C) 2014 Elsevier Ltd. All rights reserved
Mobile Station Tracking in Multipath Wireless Networks Using Ensemble Square Root Filter
No full textA scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification
No full textImpoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-a-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. (C) 2013 Elsevier Ltd. All rights reserved
