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EMORF/S: EM-Based Outlier-Robust Filtering and Smoothing With Correlated Measurement Noise
Abstract
In this article, we consider the problem of outlier-robust state estimation where the measurement noise can be correlated. Outliers in data arise due to many reasons like sensor malfunctioning, environmental behaviors, communication glitches, etc. Moreover, noise correlation emerges in several real-world applications e.g. sensor networks, radar data, GPS-based systems, etc. We consider these effects in system modeling which is subsequently used for inference. We employ the Expectation- Maximization (EM) framework to derive both outlier-resilient filtering and smoothing methods, suitable for online and offline estimation respectively. The standard Gaussian filtering and the Gaussian Rauch–Tung–Striebel (RTS) smoothing results are leveraged to devise the estimators. In addition, Bayesian Cramer- Rao Bounds (BCRBs) for a filter and a smoother which can perfectly detect and reject outliers are presented. These serve as useful theoretical benchmarks to gauge the error performance of different estimators. Lastly, different numerical experiments, for an illustrative target tracking application, are carried out that indicate performance gains compared to similarly engineered state-of-the-art outlier-rejecting state estimators. The advantages are in terms of simpler implementation, enhanced estimation quality, and competitive computational performance.
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Advanced robotics and autonomous vehicles rely on filtering and sensor fusion techniques to a large extent. These mobile applications need to handle the computations onboard at high rates while the computing capacities are limited. Therefore, any improvement that lowers the CPU time of the filtering leads to more accurate control or longer battery operation. This article introduces a generic computational relaxation for the unscented transformation (UT) that is the key operation of the Unscented Kalman filter-based applications. The central idea behind the relaxation is to pull out the linear part of the filtering model and avoid the calculations for the kernel of the nonlinear part. The practical merit of the proposed relaxation is demonstrated through a simultaneous localization and mapping (SLAM) implementation that underpins the superior performance of the algorithm in the practically relevant cases, where the nonlinear dependencies influence only an affine subspace of the image space. The numerical examples show that the computational demand can be mitigated below 50% without decreasing the accuracy of the approximation. The method described in this article is implemented and published as an open-source C ++ library RelaxedUnscentedTransformation on GitHub.
In this article, we investigate the problem of dynamically estimating the instantaneous position, orientation, velocity, and angular velocity of an arbitrarily shaped object during its free flight based on image frames taken simultaneously by two high-speed cameras. Aerodynamic effects, including drag, lift, and Magnus forces, are modeled to describe the object’s flight. Observables are derived from combining dynamics with a camera projection model assuming two-view geometry, via the use of multiple quaternions. The state of the composed system can then be estimated via constrained Kalman filtering, to which a solution is presented for the case of multiple quadratic constraints. To keep track of appearing and disappearing visual features during flight, the estimation algorithm employs a graph matching-based technique to maintain a set of evolving hypotheses through evaluation, pruning, and addition. Experiments conducted over various objects have either provided validation against motions independently estimated using multiple accelerometers, or formed verification by matching flight images against projections based on the state estimates.
The wrapping operation causes discontinuities in phase angle measurements from synchrophasor devices. While various unwrapping algorithms traditionally used for synchrophasor data have proven effective under typical operating conditions, they are likely to fail when faced with atypical data because of equipment malfunctions. For example, the underestimation of the phase angle jump when the data originates from a device with an internal clock or other timing mechanism can introduce this kind of error. This letter proposes using an unscented Kalman filter (UKF) for unwrapping one dimensional synchrophasor data. This technique is especially suitable for analyzing low-quality data. The effectiveness of this method is demonstrated on real phase angle measurements from devices with documented timing issues in the Dominion Energy power system.
Consensus-based distributed Kalman filters for estimation with targets have attracted considerable attention. Most of the existing Kalman filters use the average consensus approach, which tends to have a low convergence speed. They also rarely consider the impacts of limited sensing range and target mobility on the information flow topology. In this article, we address these issues by designing a novel distributed Kalman consensus filter (DKCF) with an information-weighted consensus structure for random mobile target estimation in continuous time. A new moving target information-flow topology for the measurement of targets is developed based on the sensors' sensing ranges, targets' random mobility, and local information-weighted neighbors. Novel necessary and sufficient conditions about the convergence of the proposed DKCF are developed. Under these conditions, the estimates of all sensors converge to the consensus values. Simulation and comparative studies show the effectiveness and the superiority of this new DKCF.
This paper proposes a decentralized algorithm for real-time estimation of the dynamic states of a power system. The scheme employs phasor measurement units (PMUs) for the measurement of local signals at each generation unit, and subsequent state estimation using unscented Kalman filtering (UKF). The novelty of the scheme is that the state estimation at one generation unit is independent from the estimation at other units, and therefore the transmission of remote signals to a central estimator is not required. This in turn reduces the complexity of each distributed estimator, and makes the estimation process highly efficient, accurate and easily implementable. The applicability of the proposed algorithm has been thoroughly demonstrated on a representative model.
Cramér–Rao lower bounds for the discrete-time nonlinear state estimation problem are treated. The Cramér–Rao bound for the mean-square error matrix of a state estimate is particularly important for quality evaluation of nonlinear state estimators as it represents a limit of cognizability of the state. Recursive relations for filtering, predictive, and smoothing Cramér–Rao bounds are derived to establish a unifying framework for several previously published derivation procedures and results. Lower bounds for systems with unknown parameters are newly provided. Computation of filtering, predictive, and smoothing Cramér–Rao bounds, their mutual comparison and utilization for quality evaluation of some nonlinear filters are shown in numerical examples.
Optimum-distributed signal detection system design is studied for
cases with statistically dependent observations from sensor to sensor.
The common parallel architecture is assumed. Here, each sensor sends a
decision to a fusion center that determines a final binary decision
using a nonrandomized fusion rule. General L sensor cases are
considered. A discretized iterative algorithm is suggested that can
provide approximate solutions to the necessary conditions for optimum
distributed sensor decision rules under a fixed fusion rule. The
algorithm is shown to converge in a finite number of iterations, and the
solutions obtained are shown to approach the solutions to the original
problem, without discretization, as the variable step size shrinks to
zero. In the formulation, both binary and multiple-bit sensor decisions
cases are considered. Illustrative numerical examples are presented for
two-, three-, and four-sensor cases, in which a common random Gaussian
signal is to be detected in Gaussian noise
Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.
In some target tracking applications, angle measurements are absent due to sensor characteristics, which makes Cartesian states unobservable for a single stationary sensor. When multi-sensor target tracking techniques with only range or Doppler measurements are applied to produce Cartesian state estimates, their performance and efficiency can be benefited from accurate range and Doppler estimates obtained from single sensors. This paper investigates the range and Doppler estimation problem based on motion modeling in range-squared coordinate considering range-squared as a generic coordinate. A pseudostate vector consisting of range squared and its derivatives is defined to completely summarize the dynamic of the Cartesian nearly constant velocity (NCV) motion and it is found time evolution of the pseudostate is linear based on the methodology of state space representation. To estimate the pseudostate from range-Doppler or range-only measurements, a recursive filter is developed using the decorrelated unbiased converted measurement (DUCM) method. Finally, the pseudostate estimates in the range-squared coordinate are converted into the range coordinate using the scaled unscented transformation (SUT) method to produce range and Doppler estimates. Although the conversion is nonlinear, it is performed outside the filtering recursions without propagating nonlinearity approximation errors in the filtering recursions. Numerical experiments with various conditions of measurements demonstrate the superior performance benefits from the proposed accurate linear state equation and estimation method.
State estimation of dynamical systems is crucial for providing new decision-making and system automation information in different applications. However, the assumptions on the standard computational models for sensor measurements can be violated in practice due to different types of data abnormalities such as outliers and biases. In this work, we focus on the occurrence of measurement biases and propose a robust filter for their detection and mitigation during state estimation of nonlinear dynamical systems. We model the presence of bias in each dimension within the generative structure of the state-space models. Subsequently, employing the theory of Variational Bayes and general Gaussian filtering, we devise a recursive filter which we call the Bias Detecting and Mitigating (BDM) filter. As the error detection mechanism is embedded within the filter structure its dependence on any external detector is obviated. Simulations verify the performance gains of the proposed BDM filter compared to similar Kalman filtering-based approaches in terms of robustness to temporary and persistent bias presence.
This article proposes a robust Bayesian inference approach for linear state-space models with nonstationary and heavy-tailed noise for robust state estimation. The predicted distribution is modeled as the hierarchical Student- t distribution, while the likelihood function is modified to the Student- t mixture distribution. By learning the corresponding parameters online, informative components of the Student- t mixture distribution are adapted to approximate the statistics of potential uncertainties. Then, the obstacle caused by the coupling of the updated parameters is eliminated by the variational Bayesian (VB) technique and fixed-point iterations. Discussions are provided to show the reasons for the achieved advantages analytically. Using the Newtonian tracking example and a three degree-of-freedom (DOF) hover system, we show that the proposed inference approach exhibits better performance compared with the existing method in the presence of modeling uncertainties and measurement outliers.
Considering a common case where measurements are obtained from independent sensors, we present a novel outlier-robust filter for nonlinear dynamical systems in this work. The proposed method is devised by modifying the measurement model and subsequently using the theory of Variational Bayes and general Gaussian filtering. We treat the measurement outliers independently for independent observations leading to selective rejection of the corrupted data during inference. By carrying out simulations for variable number of sensors we verify that an implementation of the proposed filter is computationally more efficient as compared to the proposed modifications of similar baseline methods still yielding similar estimation quality. In addition, experimentation results for various real-time indoor localization scenarios using Ultra-wide Band (UWB) sensors demonstrate the practical utility of the proposed method.
Steerable needles are a promising technology to provide safe deployment of tools through complex anatomy in minimally invasive surgery, including tumor-related diagnoses and therapies. For the 3-D localization of these instruments in soft tissue, fiber Bragg gratings (FBGs) based reconstruction methods have gained in popularity because of the inherent advantages of optical fibers in a clinical setting, such as flexibility, immunity to electromagnetic interference, nontoxicity, and the absence of line-of-sight issues. However, methods proposed thus far focus on shape reconstruction of the steerable needle itself, where accuracy is susceptible to errors in interpolation and curve fitting methods used to estimate the curvature vectors along the needle. In this study, we propose reconstructing the shape of the path created by the steerable needle tip based on the follow-the-leader nature of many of its variants. By assuming that the path made by the tip is equivalent to the shape of the needle, this novel approach paves the way for shape reconstruction through a single set of FBGs at the needle tip, which provides curvature information about every section of the path during navigation. We propose a Kalman-filter-based sensor fusion method to update the curvature information about the sections as they are continually estimated during the insertion process. The proposed method is validated through simulation,
in vitro
and
ex vivo
experiments employing a programmable bevel-tip steerable needle (PBN). The results show clinically acceptable accuracy, with 2.87-mm mean PBN tip position error, and a standard deviation of 1.63 mm for a 120-mm 3-D insertion.
We consider the robust filtering problem for a state-space model with outliers in correlated measurements. We propose a new robust filtering framework to further improve the robustness of conventional robust filters. Specifically, the measurement fitting error is processed separately during the reweighting procedure, which differs from existing solutions where a jointly processed scheme is involved. Simulation results reveal that, under the same setup, the proposed method outperforms the existing robust filter when the outlier-contaminated measurements are correlated, while it has the same performance as the existing one in the presence of uncorrelated measurements since these two types of robust filters are equivalent under such a circumstance.
This paper is concerned with the Tobit Kalman fusion
estimation problem for a class of multi-sensor systems subject to
parametric uncertainties and measurement censoring. The parametric
uncertainty is characterized by the multiplicative noise
appearing in both state and observation equations, and the measurement
censoring is governed by the Tobit observation model.
The fusion estimation is implemented via two stages: at the first
stage, each sensor sends its observations to the local estimator and,
at the second stage, the local estimates are then transmitted to
the fusion center so as to generate the fused estimate. The local
estimator realizes a Tobit Kalman filtering algorithm which is
devised in accordance with a modified regression model, whilst
the fusion center carries out the fusion estimation by resorting to
the federated fusion rule. Furthermore, the monotonicity of the
fused error covariance with respect to the censoring threshold
is discussed and, subsequently, the boundedness property is also
examined where both lower and upper bounds are acquired for
the fused error covariance. The validity of the fusion estimator is
finally shown via two numerical examples.
State estimation is a fundamental task in many engineering fields, and therefore robust nonlinear filtering techniques able to cope with misspecified, uncertain and/or corrupted models must be designed for real-life applicability. In this contribution we explore nonlinear Gaussian filtering problems where measurements may be corrupted by outliers,and propose a new robust variational-based filtering methodology able to detect and mitigate their impact. This method generalizes previous contributions to the case of multiple outlier indicators for both independent and dependent observation models. An illustrative example is provided to support the discussion and show the performance improvement.
This paper proposes an online scheme for state estimation of a generic class of non-linear dynamical systems, in the presence of abnormal measurement data from sensors. We thoroughly illustrate why the performance of standard recursive Bayesian inference degrades in the presence of any measurement distortion. After demonstrating how different abnormalities can be accommodated explicitly inside a generic state-space model, we propose a robust mechanism to perform recursive Bayesian inference on the presented model to not only detect but also mitigate the effect of corrupted measurements in the final state estimates. Using simulations and experimentation, we demonstrate the success of the proposed framework in reducing the impact of different types of distortions in measurements. The ability to tackle different kinds of measurement abnormalities during online inference sets the proposed method apart from the existing techniques.
In this letter, we consider the problem of dynamic state estimation (DSE) in scenarios where sensor measurements are corrupted with outliers. For such situations, we propose a filter that utilizes maximum
a posteriori
estimation in the extended Kalman filtering framework to identify and discard the outlier-ridden measurements from a faulty sensor at any given time instant. However, during this process, all those measurements that are not affected by outliers are still utilized for state estimation. Using an illustrative example of dynamic target tracking, we demonstrate the effectiveness of the proposed estimator.
This paper presents a new method for handling outliers in nonlinear filtering problems by extending the unscented Kalman filter (UKF). In this method, two Gaussian observation error models with distinct covariance matrices are used: one for observations with regular errors, and another with a larger variance specified by a scale parameter for outliers. In addition to the system state, this method estimates an indicator variable that switches between the two models and the scale parameter for outliers. With the inclusion of the indicator variable and scale parameter, the estimated error covariance matrix can handle both regular observations and outliers appropriately at each time step. Furthermore, by estimating the scale parameter, the proposed method can be applied to a dataset without requiring additional tuning to account for outlier characteristics. Through numerical experiments, we find that our method can estimate the system state better than existing methods for both datasets with and without outliers.
Mass is an important parameter in vehicle dynamics because it affects not only safety but also comfort. The mass influences the three movements corresponding to vehicle dynamics. Therefore, having an accurate value of mass is essential for having a suitable model which will lead to proper controller and observer operation. Additionally, unlike other vehicle parameters, the mass can vary during a trip due to loading and unloading items and passengers onto the vehicle, greatly influencing its dynamics. This is critical in heavy vehicles where the mass can vary by around 400%. Therefore, the mass must be updated on-line. The novelty of this paper is the construction of a state-parameter observer which allows the mass under static and dynamic driving conditions to be estimated using measurements from sensors that can be mounted easily on vehicles. In this study, a vertical complete model is considered based on the dual Kalman filter for mass and road irregularities estimation using the data obtained from suspension deflection sensors and a vertical accelerometer. Both simulation and experimental results are carried out to prove the effectiveness of the proposed algorithm.
Cambridge Core - Communications and Signal Processing - Computational Bayesian Statistics - by M. Antónia Amaral Turkman
In this paper, a unified form for robust Gaussian information filtering based on M-estimate is proposed, which can incorporate robust weight functions with zero weight for large residues. The proposed information filtering framework can avoid the numerical problem introduced by the zero weight in the Kalman filtering framework. Simulation results show the efficiency and superiority of the proposed robust filters over the non-robust filter against heavy-tailed measurement noises.
Novel Student’s t based approaches for formulating a filter and smoother, which utilize heavy tailed process and measurement noise models, are found through approximations of the associated posterior probability density functions. Simulation results for manoeuvring target tracking illustrate that the proposed methods substantially outperform existing methods in terms of the root mean square error.
This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.
An improved Huber-Kalman filter approach is proposed based on a nonlinear regression model. The measurement nonlinearity is maintained in this approach, and the Huber-based filtering problem is solved using a Gauss-Newton approach. This modification is motivated by an equation in which the iterative extended Kalman filter (IEKF) is derived from the standpoint of nonlinear regression theory. The IEKF nonlinear regression model is extended to use Huber's generalized maximum likelihood approach to provide robustness to non-Gaussian errors and outliers. The nonlinear regression Huber-Kalman approach is also extended to the fixed-interval smoothing problem, wherein the state estimates from a forward pass through the filter are smoothed back in time to produce a best estimate of the state trajectory given all available measurement data.
Nonlinear Kalman filter and Rauch-Tung-Striebel smoother type recursive estimators for nonlinear discrete-time state space models with multivariate Student's t-distributed measurement noise are presented. The methods approximate the posterior state at each time step using the variational Bayes method. The nonlinearities in the dynamic and measurement models are handled using the nonlinear Gaussian filtering and smoothing approach, which encompasses many known nonlinear Kalman-type filters. The method is compared to alternative methods in a computer simulation.
In this paper, passive emitter localization using Time Difference of Arrival (TDOA) measurements within a sensor network is investigated. Contrary to the case of a moving sensor pair the fact of correlated measurements in a single time step arises dependent on the choice of the measurement set. In tracking simulations, the Cramer Rao Lower Bound (CRLB) and simulation results are often computed assuming constant standard deviations of the incoming measurements. Though, the measurement error is parameter dependent, it depends for example on the emitter-sensors-geometry. In Monte Carlo simulations, a comparison is performed between the localization in a static sensor network with three sensors and the localization using a moving sensor pair. Measurements are generated assuming additive white Gaussian noise with constant and parameter dependent variance. Results confirm the attainable localization accuracy and show the superior performance of an additional sensor compared to additional motion.
A robust derivative-free algorithm named outliers robust unscented Kalman filter (ORUKF) is proposed to handle both the state and measurement outliers. Based on the generalized maximum likelihood perspective on the Kalman filter, the state is first augmented with the measurement noise, then the covariance of the augmented state is reformulated by the M estimate methodology and embedded into a modified version of the iterated unscented Kalman filter (UKF) to detect and suppress the outliers. Attractive features of the novel robust derivative-free algorithm include ability to handle multiple outliers, ability to exhibit the accuracy and flexibility of the UKF for the nonlinear problems, and high statistical efficiency under nominal conditions and flexibility to encompass maximum likelihood estimate.
An efficient, timely, and accurate state estimation is a prerequisite for most energy management system (EMS) applications in power system control centers. The emerging wide-area measurement systems (WAMSs) offer new opportunities for developing more effective methods to monitor power system dynamics online. Recently, alternative methods for power system state estimation have caught much attention. Due to the nonlinearity of state transition and observation equation, linearization and Jacobian matrix calculation are indispensible in the existing methods of power system state estimation. This makes WAMS' high performance compromised by burdensome calculation. In order to overcome the drawbacks, this study tries to develop an effective state estimation method without the linearization and Jacobian matrix calculation. Firstly, unscented transformation is introduced as an effective method to calculate the means and covariances of a random vector undergoing a nonlinear transformation. Secondly, by embedding the unscented transformation into the Kalman filter process, a method is developed for power system dynamic state estimation. Finally, some simulation results are presented showing accuracy and easier implementation of the new method.
In this book, the extended Kalman filter (EKF) has been used as the standard technique for performing recursive nonlinear estimation. The EKF algorithm, however, provides only an approximation to optimal nonlinear estimation. In this chapter, we point out the underlying assumptions and flaws in the EKF, and present an alternative filter with performance superior to that of the EKF. This algorithm, referred to as the unscented Kalman filter (UKF), was first proposed by Julier et al [24, 22, 23], and further developed by Wan and van der Merwe [54, 53, 49, 50]. The basic difference between...
The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.
The classical filtering and prediction problem is re-examined using the Bode-Sliannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinitememory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the coefficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.
A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation
Detection, estimation and linear modulation theory, Part 1, covering random processes, signal detection in noise and continuous waveforms
While conventional sensor networks have revealed their vast potentials, simple and special purposed data doubtlessly limits their expansion into information hungry domains. Video sensor networks present an unprecedented opportunity to annex rich information with distributed sensor networks. However, directional sensing range and high data rate unique to video sensors also demands novel solutions, especially for reducing data amount and individual sensor's workload. Toward this end, this paper proposes a method for cooperative video processing in video sensor networks bused on sensor correlations. By pairing up highly correlated nodes and divide sensing tasks among them, each sensor only needs to cover a fraction of the targeted area. Compared to the non-cooperative approach, video sensor's image processing and transmission workload is significantly reduced. We design efficient algorithms to calculate the correlations, partition sensing areas, and fuse partial images. A set of experiments are also performed to prove the concept.
An algorithm, the bootstrap filter, is proposed for implementing
recursive Bayesian filters. The required density of the state vector is
represented as a set of random samples, which are updated and propagated
by the algorithm. The method is not restricted by assumptions of
linearity or Gaussian noise: it may be applied to any state transition
or measurement model. A simulation example of the bearings only tracking
problem is presented. This simulation includes schemes for improving the
efficiency of the basic algorithm. For this example, the performance of
the bootstrap filter is greatly superior to the standard extended Kalman
filter
We consider the problem of correlated data gathering in sensor networks with multiple sink nodes. The problem has two objectives. First, we would like to find a rate allocation on the correlated sensor nodes such that the data gathered by the sink nodes can reproduce the field of observation. Second, we would like to find a transmission structure on the network graph such that the total transmission energy consumed by the network is minimized. The existing solutions to this problem are impractical for deployment because they have not considered all of the following factors: (1) distributed implementation; (2) capacity and interference associated with the shared medium; and (3) realistic data correlation model. In this paper, we propose a new distributed framework to achieve minimum energy data gathering while considering these three factors. Based on a localized version of Slepian-Wolf coding, the problem is modeled as an optimization formulation with a distributed solution. The formulation is first relaxed with Lagrangian dualization and then solved with the subgradient algorithm. The algorithm is amenable to fully distributed implementations, which corresponds to the decentralized nature of sensor networks. To evaluate its effectiveness, we have conducted extensive simulations under a variety of network environments. The results indicate that the algorithm supports asynchronous network settings, sink mobility, and duty schedules.
In target tracking systems that utilize Doppler radar (or sonar),
the measurements consist of range, range rate, and one or two angles,
When multiple sensors are used in the proper geometry, the final
accuracy is determined primarily by each sensor's range estimation
accuracy. In this case it is particularly important to extract the most
accurate state estimate in the range direction by processing optimally
the range and range rate measurements. The usual assumption in the
design of tracking filters is that the measurement errors in range and
range rate are uncorrelated. However, in the case of the commonly used
upsweep chirp (linear FM) waveforms, there can be a significant negative
correlation between the range and range rate measurement noises. The
purpose of this note is to quantify the performance improvement one can
obtain when this correlation is present, as it is in certain waveforms,
and accounted for
The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearises all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterise mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet general...
Kalman filter, sensor fusion, and constrained regression: Equivalences and insights
- Jahja