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Showing papers on "Kalman filter published in 2008"


Journal ArticleDOI
TL;DR: In this article, a modified OCV-SoC relationship based on the conventional OCV/SoC was proposed to avoid the defects of the extended Kalman filter (EKF) by preventing the relationship from varying.

601 citations


Journal ArticleDOI
TL;DR: It is proved that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small.
Abstract: In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and on the estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain for scalar systems. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we show that although the joint optimization of the consensus matrix and the Kalman gain is in general a non-convex problem, it is possible to compute them under some relevant scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.

515 citations


Journal ArticleDOI
TL;DR: A distributed Kalman filter to estimate the state of a sparsely connected, large-scale, n -dimensional, dynamical system monitored by a network of N sensors is presented and the proposed algorithm achieves full distribution of the Kalman Filter.
Abstract: This paper presents a distributed Kalman filter to estimate the state of a sparsely connected, large-scale, n -dimensional, dynamical system monitored by a network of N sensors. Local Kalman filters are implemented on nl-dimensional subsystems, nl Lt n, obtained by spatially decomposing the large-scale system. The distributed Kalman filter is optimal under an Lth order Gauss-Markov approximation to the centralized filter. We quantify the information loss due to this Lth-order approximation by the divergence, which decreases as L increases. The order of the approximation L leads to a bound on the dimension of the subsystems, hence, providing a criterion for subsystem selection. The (approximated) centralized Riccati and Lyapunov equations are computed iteratively with only local communication and low-order computation by a distributed iterate collapse inversion (DICI) algorithm. 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. Nowhere in the network, storage, communication, or computation of n-dimensional vectors and matrices is required; only nl Lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors. In other words, knowledge of the state is itself distributed.

482 citations


Journal ArticleDOI
TL;DR: It is shown that the minimum error covariance estimator is time-varying, stochastic, and it does not converge to a steady state, and the architecture is independent of the communication protocol and can be implemented using a finite memory buffer if the delivered packets have a finite maximum delay.
Abstract: In this note, we study optimal estimation design for sampled linear systems where the sensors measurements are transmitted to the estimator site via a generic digital communication network. Sensor measurements are subject to random delay or might even be completely lost. We show that the minimum error covariance estimator is time-varying, stochastic, and it does not converge to a steady state. Moreover, the architecture of this estimator is independent of the communication protocol and can be implemented using a finite memory buffer if the delivered packets have a finite maximum delay. We also present two alternative estimator architectures that are more computationally efficient and provide upper and lower bounds for the performance of the time-varying estimator. The stability of these estimators does not depend on packet delay but only on the overall packet loss probability. Finally, algorithms to compute critical packet loss probability and estimators performance in terms of their error covariance are given and applied to some numerical examples.

478 citations


Proceedings ArticleDOI
F.O. Heimes1
12 Dec 2008
TL;DR: This paper presents an approach and solution to the IEEE 2008 Prognostics and Health Management conference challenge problem that utilizes an advanced recurrent neural network architecture to estimate the remaining useful life of the system.
Abstract: This paper presents an approach and solution to the IEEE 2008 Prognostics and Health Management conference challenge problem. The solution utilizes an advanced recurrent neural network architecture to estimate the remaining useful life of the system. The recurrent neural network is trained with back-propagation through time gradient calculations, an Extended Kalman Filter training method, and evolutionary algorithms to generate an accurate and compact algorithm. This solution placed second overall in the competition with a very small margin between the first and second place finishers.

470 citations


Journal ArticleDOI
TL;DR: In this article, a simple procedure to include state constraints in the UKF is proposed and tested and the overall impression is that the performance of UKF was better than the EKF in terms of robustness and speed of convergence.

466 citations


Journal ArticleDOI
TL;DR: Human to Kalman filter behavior was compared to determine how humans take into account the statistical properties of errors and the reliability with which those errors can be measured, and how biological systems remain responsive to changes in environmental statistics.
Abstract: Rapid reaching to a target is generally accurate but also contains random and systematic error. Random errors result from noise in visual measurement, motor planning, and reach execution. Systematic error results from systematic changes in the mapping between the visual estimate of target location and the motor command necessary to reach the target (e.g., new spectacles, muscular fatigue). Humans maintain accurate reaching by recalibrating the visuomotor system, but no widely accepted computational model of the process exists. Given certain boundary conditions, a statistically optimal solution is a Kalman filter. We compared human to Kalman filter behavior to determine how humans take into account the statistical properties of errors and the reliability with which those errors can be measured. For most conditions, human and Kalman filter behavior was similar: Increasing measurement uncertainty caused similar decreases in recalibration rate; directionally asymmetric uncertainty caused different rates in different directions; more variation in systematic error increased recalibration rate. However, behavior differed in one respect: Inserting random error by perturbing feedback position causes slower adaptation in Kalman filters but had no effect in humans. This difference may be due to how biological systems remain responsive to changes in environmental statistics. We discuss the implications of this work.

405 citations


Journal ArticleDOI
TL;DR: An extended Kalman filter is presented for precisely determining the unknown transformation between a camera and an IMU and it is proved that the nonlinear system describing the IMU-camera calibration process is observable.
Abstract: Vision-aided inertial navigation systems (V-INSs) can provide precise state estimates for the 3-D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved by combining inertial measurements from an inertial measurement unit (IMU) with visual observations from a camera under the assumption that the rigid transformation between the two sensors is known. Errors in the IMU-camera extrinsic calibration process cause biases that reduce the estimation accuracy and can even lead to divergence of any estimator processing the measurements from both sensors. In this paper, we present an extended Kalman filter for precisely determining the unknown transformation between a camera and an IMU. Contrary to previous approaches, we explicitly account for the time correlation of the IMU measurements and provide a figure of merit (covariance) for the estimated transformation. The proposed method does not require any special hardware (such as spin table or 3-D laser scanner) except a calibration target. Furthermore, we employ the observability rank criterion based on Lie derivatives and prove that the nonlinear system describing the IMU-camera calibration process is observable. Simulation and experimental results are presented that validate the proposed method and quantify its accuracy.

367 citations


Proceedings Article
26 Sep 2008
TL;DR: This paper surveys numerous curvilinear models and compares their performance using a tracking tasks which includes the fusion of GPS and odometry data with an Unscented Kalman Filter and a highly accurate reference trajectory has been recorded.
Abstract: The estimation of a vehiclepsilas dynamic state is one of the most fundamental data fusion tasks for intelligent traffic applications. For that, motion models are applied in order to increase the accuracy and robustness of the estimation. This paper surveys numerous (especially curvilinear) models and compares their performance using a tracking tasks which includes the fusion of GPS and odometry data with an Unscented Kalman Filter. For evaluation purposes, a highly accurate reference trajectory has been recorded using an RTK-supported DGPS receiver. With this ground truth data, the performance of the models is evaluated in different scenarios and driving situations.

363 citations


Journal ArticleDOI
TL;DR: The results obtained showed a remarkable improvement in the model forecasting skill, with a significant reduction of the required CPU time in the case of wind power prediction.

354 citations


Proceedings ArticleDOI
12 Dec 2008
TL;DR: This work considers the problem of reconstructing time sequences of spatially sparse signals from a limited number of linear "incoherent" measurements, in real-time, and uses Compressed Sensing to estimate the support set of the initial signal's transform vector.
Abstract: We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some transform domain referred to as the sparsity basis. For a single spatial signal, the solution is provided by Compressed Sensing (CS). The question that we address is, for a sequence of sparse signals, can we do better than CS, if (a) the sparsity pattern of the signal's transform coefficients' vector changes slowly over time, and (b) a simple prior model on the temporal dynamics of its current non-zero elements is available. The overall idea of our solution is to use CS to estimate the support set of the initial signal's transform vector. At future times, run a reduced order Kalman filter with the currently estimated support and estimate new additions to the support set by applying CS to the Kalman innovations or filtering error (whenever it is "large").

Book
08 Oct 2008
TL;DR: This paper focuses on Kalman State Estimation in Networked Systems with Asynchronous Communication Channels and Switched Sensors and some properties of the Joint Entropy of a Random Vector and Discrete Quantity References Index.
Abstract: Preface Introduction Topological Entropy, Observability, Robustness, Stabilizability, and Optimal Control Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels Detectability and Output Feedback Stabilizability of Nonlinear Systems via Limited Capacity Communication Channels Robust Set-Valued State Estimation via Limited Capacity Communication Channels An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noiseless Plants via Noisy Discrete Channels An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noisy Plants via Noisy Discrete Channels An Analog of Shannon Information Theory: Stable in Probability Control and State Estimation of Linear Noisy Plants via Noisy Discrete Channels Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks H-infinity State Estimation via Communication Channels Kalman State Estimation and Optimal Control Based on Asynchronously and Irregularly Delayed Measurements Optimal Computer Control via Asynchronous Communication Channels Linear-Quadratic Gaussian Optimal Control via Limited Capacity Communication Channels Kalman State Estimation in Networked Systems with Asynchronous Communication Channels and Switched Sensors Robust Kalman State Estimation with Switched Sensors Appendix A: Proof of Proposition 7.6.13 Appendix B: Some Properties of Square Ensembles of Matrices Appendix C: Discrete Kalman Filter and Linear-Quadratic Gaussian Optimal Control Problem Appendix D: Some Properties of the Joint Entropy of a Random Vector and Discrete Quantity References Index

Proceedings ArticleDOI
01 Dec 2008
TL;DR: This work obtains a more natural form of LQG duality by replacing the Kalman-Bucy filter with the information filter and generalizes this result to non-linear stochastic systems, discrete stochastics systems, and deterministic systems.
Abstract: Optimal control and estimation are dual in the LQG setting, as Kalman discovered, however this duality has proven difficult to extend beyond LQG. Here we obtain a more natural form of LQG duality by replacing the Kalman-Bucy filter with the information filter. We then generalize this result to non-linear stochastic systems, discrete stochastic systems, and deterministic systems. All forms of duality are established by relating exponentiated costs to probabilities. Unlike the LQG setting where control and estimation are in one-to-one correspondence, in the general case control turns out to be a larger problem class than estimation and only a sub-class of control problems have estimation duals. These are problems where the Bellman equation is intrinsically linear. Apart from their theoretical significance, our results make it possible to apply estimation algorithms to control problems and vice versa.

Proceedings ArticleDOI
01 Dec 2008
TL;DR: A new partial differential equation (PDE) based on the Lighthill-Whitham-Richards PDE, which serves as a flow model for velocity, is introduced and a Godunov discretization scheme is formulated to cast the PDE into a Velocity Cell Transmission Model (CTM-v), which is a nonlinear dynamical system with a time varying observation matrix.
Abstract: Traffic state estimation is a challenging problem for the transportation community due to the limited deployment of sensing infrastructure. However, recent trends in the mobile phone industry suggest that GPS equipped devices will become standard in the next few years. Leveraging these GPS equipped devices as traffic sensors will fundamentally change the type and the quality of traffic data collected on large scales in the near future. New traffic models and data assimilation algorithms must be developed to efficiently transform this data into usable traffic information. In this work, we introduce a new partial differential equation (PDE) based on the Lighthill-Whitham-Richards PDE, which serves as a flow model for velocity. We formulate a Godunov discretization scheme to cast the PDE into a Velocity Cell Transmission Model (CTM-v), which is a nonlinear dynamical system with a time varying observation matrix. The Ensemble Kalman Filtering (EnKF) technique is applied to the CTM- v to estimate the velocity field on the highway using data obtained from GPS devices, and the method is illustrated in microsimulation on a fully calibrated model of I880 in California. Experimental validation is performed through the unprecedented 100-vehicle Mobile Century experiment, which used a novel privacy-preserving traffic monitoring system to collect GPS cell phone data specifically for this research.

Journal ArticleDOI
TL;DR: A variational treatment of dynamic models that furnishes time-dependent conditional densities on the path or trajectory of a system's states and the time-independent densities of its parameters using exactly the same principles is presented.

Journal ArticleDOI
TL;DR: A new Rauch-Tung-Striebel type form of the fixed-interval unscented Kalman smoother is derived, which is not based on running two independent filters forward and backward in time, but on a separate backward smoothing pass which recursively computes corrections to the forward filtering result.
Abstract: This note considers the application of the unscented transform to optimal smoothing of nonlinear state-space models. In this note, a new Rauch-Tung-Striebel type form of the fixed-interval unscented Kalman smoother is derived. The new smoother differs from the previously proposed two-filter-formulation-based unscented Kalman smoother in the sense that it is not based on running two independent filters forward and backward in time. Instead, a separate backward smoothing pass is used, which recursively computes corrections to the forward filtering result. The smoother equations are derived as approximations to the formal Bayesian optimal smoothing equations. The performance of the new smoother is demonstrated with a simulation.

Journal ArticleDOI
01 Mar 2008-Tellus A
TL;DR: In this paper, the authors proposed a deterministic EnKF (DEnKF) which is a linear approximation of the EnKf with perturbed observations, which is based on the recognition that in the case of small corrections to the forecast, without perturbation observations, the traditional enKF without perturbing observations reduces the forecast error covariance by an amount that is nearly twice as large as that is needed to match Kalman filter.
Abstract: The use of perturbed observations in the traditional ensemble Kalman filter (EnKF) results in a suboptimal filter behaviour, particularly for small ensembles. In this work, we propose a simple modification to the traditional EnKF that results in matching the analysed error covariance given by Kalman filter in cases when the correction is small; without perturbed observations. The proposed filter is based on the recognition that in the case of small corrections to the forecast the traditional EnKF without perturbed observations reduces the forecast error covariance by an amount that is nearly twice as large as that is needed to match Kalman filter. The analysis scheme works as follows: update the ensemble mean and the ensemble anomalies separately; update the mean using the standard analysis equation; update the anomalies with the same equation but half the Kalman gain. The proposed filter is shown to be a linear approximation to the ensemble square root filter (ESRF). Because of its deterministic character and its similarity to the traditional EnKF we call it the ‘deterministic EnKF’, or the DEnKF. A number of numerical experiments to compare the performance of the DEnKF with both the EnKF and an ESRF using three small models are conducted. We show that the DEnKF performs almost as well as the ESRF and is a significant improvement over the EnKF. Therefore, the DEnKF combines the numerical effectiveness, simplicity and versatility of the EnKF with the performance of the ESRFs. Importantly, the DEnKF readily permits the use of the traditional Schur product-based localization schemes.

Journal ArticleDOI
TL;DR: A robust new algorithm based on the scaled unscented transformation called unscenting FastSLAM (UFastSLAM) is provided, which overcomes the important drawbacks of the previous frameworks by directly using nonlinear relations.
Abstract: The Rao-Blackwellized particle filter (RBPF) and FastSLAM have two important limitations, which are the derivation of the Jacobian matrices and the linear approximations of nonlinear functions. These can make the filter inconsistent. Another challenge is to reduce the number of particles while maintaining the estimation accuracy. This paper provides a robust new algorithm based on the scaled unscented transformation called unscented FastSLAM (UFastSLAM). It overcomes the important drawbacks of the previous frameworks by directly using nonlinear relations. This approach improves the filter consistency and state estimation accuracy, and requires smaller number of particles than the FastSLAM approach. Simulation results in large-scale environments and experimental results with a benchmark dataset are presented, demonstrating the superiority of the UFastSLAM algorithm.

Proceedings ArticleDOI
19 May 2008
TL;DR: This paper describes a motion planning algorithm for a quadrotor helicopter flying autonomously without GPS, and uses the Belief Roadmap (BRM) algorithm, an information-space extension of the Probabilistic Roadmap algorithm, to plan vehicle trajectories that incorporate sensing.
Abstract: This paper describes a motion planning algorithm for a quadrotor helicopter flying autonomously without GPS. Without accurate global positioning, the vehicle's ability to localize itself varies across the environment, since different environmental features provide different degrees of localization. If the vehicle plans a path without regard to how well it can localize itself along that path, it runs the risk of becoming lost. We use the Belief Roadmap (BRM) algorithm [1], an information-space extension of the Probabilistic Roadmap algorithm, to plan vehicle trajectories that incorporate sensing. We show that the original BRM can be extended to use the Unscented Kalman Filter (UKF), and describe a sampling algorithm that minimizes the number of samples required to find a good path. Finally, we demonstrate the BRM path- planning algorithm on the helicopter, navigating in an indoor environment with a laser range-finder.

Journal ArticleDOI
TL;DR: The authors developed a Kalman filter model to track dynamic mutual fund factor loadings and then used the estimates to analyze whether managers with market-timing ability can be identified ex ante.
Abstract: This article develops a Kalman filter model to track dynamic mutual fund factor loadings. It then uses the estimates to analyze whether managers with market-timing ability can be identified ex ante. The primary findings are as follows: (i) Ordinary least squares (OLS) timing models produce false positives (nonzero alphas) at too high a rate with either daily or monthly data. In contrast, the Kalman filter model produces them at approximately the correct rate with monthly data; (ii) In monthly data, though the OLS models fail to detect any timing among fund managers, the Kalman filter does; (iii) The alpha and beta forecasts from the Kalman model are more accurate than those from the OLS timing models; (iv) The Kalman filter model tracks most fund alphas and betas better than OLS models that employ macroeconomic variables in addition to fund returns.

Journal ArticleDOI
TL;DR: Efficient denoising and lossy compression schemes for electrocardiogram (ECG) signals based on a modified extended Kalman filter (EKF) structure are presented, suitable for a hybrid system that integrates these algorithmic approaches for clean ECG data storage or transmission scenarios with high output SNRs, high CRs, and low distortions.
Abstract: This paper presents efficient denoising and lossy compression schemes for electrocardiogram (ECG) signals based on a modified extended Kalman filter (EKF) structure. We have used a previously introduced two-dimensional EKF structure and modified its governing equations to be extended to a 17-dimensional case. The new EKF structure is used not only for denoising, but also for compression, since it provides estimation for each of the new 15 model parameters. Using these specific parameters, the signal is reconstructed with regard to the dynamical equations of the model. The performances of the proposed method are evaluated using standard denoising and compression efficiency measures. For denosing, the SNR improvement criterion is used, while for compression, we have considered the compression ratio (CR), the percentage area difference (PAD), and the weighted diagnostic distortion (WDD) measure. Several Massachusetts Institute of Technology-Beth Israel Deaconess Medical Center (MIT-BIH) ECG databases are used for performance evaluation. Simulation results illustrate that both applications can contribute to and enhance the clinical ECG data denoising and compression performance. For denoising, an average SNR improvement of 10.16 dB was achieved, which is 1.8 dB more than the next benchmark methods such as MAB WT or EKF2. For compression, the algorithm was extended to include more than five Gaussian kernels. Results show a typical average CR of 11.37:1 with WDD < 1.73 %. Consequently, the proposed framework is suitable for a hybrid system that integrates these algorithmic approaches for clean ECG data storage or transmission scenarios with high output SNRs, high CRs, and low distortions.

Journal ArticleDOI
TL;DR: For decentralized tracking applications, distributed Kalman filtering and smoothing algorithms are derived for any-time MMSE optimal consensus-based state estimation using WSNs.
Abstract: Distributed algorithms are developed for optimal estimation of stationary random signals and smoothing of (even nonstationary) dynamical processes based on generally correlated observations collected by ad hoc wireless sensor networks (WSNs). Maximum a posteriori (MAP) and linear minimum mean-square error (LMMSE) schemes, well appreciated for centralized estimation, are shown possible to reformulate for distributed operation through the iterative (alternating-direction) method of multipliers. Sensors communicate with single-hop neighbors their individual estimates as well as multipliers measuring how far local estimates are from consensus. When iterations reach consensus, the resultant distributed (D) MAP and LMMSE estimators converge to their centralized counterparts when inter-sensor communication links are ideal. The D-MAP estimators do not require the desired estimator to be expressible in closed form, the D-LMMSE ones are provably robust to communication or quantization noise and both are particularly simple to implement when the data model is linear-Gaussian. For decentralized tracking applications, distributed Kalman filtering and smoothing algorithms are derived for any-time MMSE optimal consensus-based state estimation using WSNs. Analysis and corroborating numerical examples demonstrate the merits of the novel distributed estimators.

Proceedings ArticleDOI
19 May 2008
TL;DR: It is analytically proved that when the Jacobians of the state and measurement models are evaluated at the latest state estimates during every time step, the linearized error-state system model of the EKF- based SLAM has observable subspace of dimension higher than that of the actual, nonlinear, SLAM system.
Abstract: In this work, we study the inconsistency of EKF- based SLAM from the perspective of observability. We analytically prove that when the Jacobians of the state and measurement models are evaluated at the latest state estimates during every time step, the linearized error-state system model of the EKF- based SLAM has observable subspace of dimension higher than that of the actual, nonlinear, SLAM system. As a result, the covariance estimates of the EKF undergo reduction in directions of the state space where no information is available, which is a primary cause of inconsistency. To address this issue, a new "first estimates Jacobian" (FEJ) EKF is proposed, which is shown to perform better in terms of consistency. In the FEJ- EKF, the filter Jacobians are calculated using the first-ever available estimates for each state variable, which insures that the observable subspace of the error-state system model is of the same dimension as that of the underlying nonlinear SLAM system. The theoretical analysis is validated through extensive simulations.

Journal ArticleDOI
TL;DR: This paper presents a simultaneous localization and mapping algorithm suitable for large-scale visual navigation based on the viewpoint augmented navigation (VAN) framework using an extended information filter.
Abstract: This paper presents a simultaneous localization and mapping algorithm suitable for large-scale visual navigation. The estimation process is based on the viewpoint augmented navigation (VAN) framework using an extended information filter. Cholesky factorization modifications are used to maintain a factor of the VAN information matrix, enabling efficient recovery of state estimates and covariances. The algorithm is demonstrated using data acquired by an autonomous underwater vehicle performing a visual survey of sponge beds. Loop-closure observations produced by a stereo vision system are used to correct the estimated vehicle trajectory produced by dead reckoning sensors.

Journal ArticleDOI
TL;DR: A hybrid converter model that is valid for the whole operating regime, and an a posteriori analysis proves, by deriving a piecewise-quadratic Lyapunov function, that the closed-loop system is exponentially stable.
Abstract: DC-DC converters pose challenging hybrid control problems, since the semiconductor switches induce different modes of operation and several constraints (on the duty cycle and the inductor current) are present. In this paper, we propose a novel approach to the modeling and controller design problem for fixed-frequency DC-DC converters, using a synchronous step-down DC-DC converter as an illustrative example. We introduce a hybrid converter model that is valid for the whole operating regime. Based on this model, we formulate and solve a constrained optimal control problem. To make the scheme implementable, we derive offline the explicit state-feedback control law, which can be easily stored and implemented in a lookup table. A Kalman filter is added to account for unmeasured load variations and to achieve zero steady-state output voltage error. An a posteriori analysis proves, by deriving a piecewise-quadratic Lyapunov function, that the closed-loop system is exponentially stable. Simulation results demonstrate the potential advantages of the proposed control methodology.

Journal ArticleDOI
TL;DR: The authors focus on a fast feature-based approach to estimate human motion features for real-time applications to provide a realistic look-alike of the real motion of the person.
Abstract: Radar can be an extremely useful sensing technique to observe persons. It perceives persons behind walls or at great distances and in situations where persons have no or poor visibility. Human motion modulates the radar signal which can be observed in the spectrogram of the received signal. Extraction of these movements enables the animation of a person in virtual reality. The authors focus on a fast feature-based approach to estimate human motion features for real-time applications. The human walking model of Boulic is used, which describe the human motion with three parameters. Personification information is obtained by estimating the individual leg and torso parameters. These motion parameters can be estimated from the temporal maximum, minimum and centre velocity of the human motion distribution. Three methods are presented to extract these velocities. Additionally, we extract an independent human motion repetition frequency estimate based on velocity slices in the spectrogram. Kalman filters smooth the parameters and estimate the global Boulic parameters. These estimated parameters are input to the human model of Boulic which forms the basis for animation. The methods are applied to real radar measurements. The animated person generated with the extracted parameters provides a realistic look-alike of the real motion of the person.

Proceedings ArticleDOI
14 Oct 2008
TL;DR: This paper shows how Gaussian process models can be integrated into other Bayes filters, namely particle filters and extended Kalman filters, and provides a complexity analysis of these filters and evaluates the alternative techniques using data collected with an autonomous micro-blimp.
Abstract: Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. The most common instantiations of Bayes filters are Kalman filters (extended and unscented) and particle filters. Key components of each Bayes filter are probabilistic prediction and observation models. Recently, Gaussian processes have been introduced as a non-parametric technique for learning such models from training data. In the context of unscented Kalman filters, these models have been shown to provide estimates that can be superior to those achieved with standard, parametric models. In this paper we show how Gaussian process models can be integrated into other Bayes filters, namely particle filters and extended Kalman filters. We provide a complexity analysis of these filters and evaluate the alternative techniques using data collected with an autonomous micro-blimp.

Journal ArticleDOI
TL;DR: It is established that under certain assumptions, the proposed Bayes' recursion reduces to the cardinalized probability hypothesis density (CPHD) recursion for a single target.
Abstract: This paper presents a novel and mathematically rigorous Bayes' recursion for tracking a target that generates multiple measurements with state dependent sensor field of view and clutter. Our Bayesian formulation is mathematically well-founded due to our use of a consistent likelihood function derived from random finite set theory. It is established that under certain assumptions, the proposed Bayes' recursion reduces to the cardinalized probability hypothesis density (CPHD) recursion for a single target. A particle implementation of the proposed recursion is given. Under linear Gaussian and constant sensor field of view assumptions, an exact closed-form solution to the proposed recursion is derived, and efficient implementations are given. Extensions of the closed-form recursion to accommodate mild nonlinearities are also given using linearization and unscented transforms.

Journal ArticleDOI
TL;DR: Analysis and simulations show that KF-like tracking based on m bits of iteratively quantized innovations communicated among sensors exhibits MSE performance identical to a KF based on analog-amplitude observations applied to an observation model with noise variance increased by a factor of [1-(1-2/pi)m]-1.
Abstract: Estimation and tracking of generally nonstationary Markov processes is of paramount importance for applications such as localization and navigation. In this context, ad hoc wireless sensor networks (WSNs) offer decentralized Kalman filtering (KF) based algorithms with documented merits over centralized alternatives. Adhering to the limited power and bandwidth resources WSNs must operate with, this paper introduces two novel decentralized KF estimators based on quantized measurement innovations. In the first quantization approach, the region of an observation is partitioned into N contiguous, nonoverlapping intervals where each partition is binary encoded using a block of m bits. Analysis and Monte Carlo simulations reveal that with minimal communication overhead, the mean-square error (MSE) of a novel decentralized KF tracker based on 2-3 bits comes stunningly close to that of the clairvoyant KF. In the second quantization approach, if intersensor communications can afford m bits at time n, then the ith bit is iteratively formed using the sign of the difference between the nth observation and its estimate based on past observations (up to time n-1) along with previous bits (up to i-1) of the current observation. Analysis and simulations show that KF-like tracking based on m bits of iteratively quantized innovations communicated among sensors exhibits MSE performance identical to a KF based on analog-amplitude observations applied to an observation model with noise variance increased by a factor of [1-(1-2/pi)m]-1.

Journal ArticleDOI
TL;DR: This work proposes a distributed object tracking system which employs a cluster-based Kalman filter in a network of wireless cameras and is able to achieve tracking accuracy comparable to the centralized tracking method, while requiring a significantly smaller number of message transmissions in the network.
Abstract: Local data aggregation is an effective means to save sensor node energy and prolong the lifespan of wireless sensor networks. However, when a sensor network is used to track moving objects, the task of local data aggregation in the network presents a new set of challenges, such as the necessity to estimate, usually in real time, the constantly changing state of the target based on information acquired by the nodes at different time instants. To address these issues, we propose a distributed object tracking system which employs a cluster-based Kalman filter in a network of wireless cameras. When a target is detected, cameras that can observe the same target interact with one another to form a cluster and elect a cluster head. Local measurements of the target acquired by members of the cluster are sent to the cluster head, which then estimates the target position via Kalman filtering and periodically transmits this information to a base station. The underlying clustering protocol allows the current state and uncertainty of the target position to be easily handed off among clusters as the object is being tracked. This allows Kalman filter-based object tracking to be carried out in a distributed manner. An extended Kalman filter is necessary since measurements acquired by the cameras are related to the actual position of the target by nonlinear transformations. In addition, in order to take into consideration the time uncertainty in the measurements acquired by the different cameras, it is necessary to introduce nonlinearity in the system dynamics. Our object tracking protocol requires the transmission of significantly fewer messages than a centralized tracker that naively transmits all of the local measurements to the base station. It is also more accurate than a decentralized tracker that employs linear interpolation for local data aggregation. Besides, the protocol is able to perform real-time estimation because our implementation takes into consideration the sparsity of the matrices involved in the problem. The experimental results show that our distributed object tracking protocol is able to achieve tracking accuracy comparable to the centralized tracking method, while requiring a significantly smaller number of message transmissions in the network.