We still have very little knowledge about how ourbrains decouple different sound sources, which is known assolving the cocktail party problem. Several approaches; includingERP, time-frequency analysis and, more recently, regression andstimulus reconstruction approaches; have been suggested forsolving this problem. In this work, we study the problem ofcorrelating of EEG signals to different sets of sound sources withthe goal of identifying the single source to which the listener isattending. Here, we propose a method for finding the number ofparameters needed in a regression model to avoid overlearning,which is necessary for determining the attended sound sourcewith high confidence in order to solve the cocktail party problem.
We investigate the unsupervised K-means clustering and the semi-supervised hidden Markov model (HMM) to automatically detect anomalous motion patterns in groups of people (crowds). Anomalous motion patterns are typically people merging into a dense group, followed by disturbances or threatening situations within the group. The application of K-means clustering and HMM are illustrated with datasets from four surveillance scenarios. The results indicate that by investigating the group of people in a systematic way with different K values, analyze cluster density, cluster quality and changes in cluster shape we can automatically detect anomalous motion patterns. The results correspond well with the events in the datasets. The results also indicate that very accurate detections of the people in the dense group would not be necessary. The clustering and HMM results will be very much the same also with some increased uncertainty in the detections.
A new approach to track bicycles from imagery sensor data is proposed. It is based on detecting ellipsoids in the images, and treat these pair-wise using a dynamic bicycle model. One important application area is in automotive collision avoidance systems, where no dedicated systems for bicyclists yet exist and where very few theoretical studies have been published.
Possible conflicts can be predicted from the position and velocity state in the model, but also from the steering wheel articulation and roll angle that indicate yaw changes before the velocity vector changes. An algorithm is proposed which consists of an ellipsoid detection and estimation algorithm and a particle filter.
A simulation study of three critical single target scenarios is presented, and the algorithm is shown to produce excellent state estimates. An experiment using a stationary camera and the particle filter for state estimation is performed and has shown encouraging results.
In this technical report, some derivations for the filter and smoother proposed in [1] are presented. More specifically, the derivations for the cyclic iteration needed to solve the variational Bayes filter and smoother for state space models with skew t likelihood proposed in [1] are presented.
In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is linearized with respect to the sufficient statistic of the prior distribution in exponential family such that the posterior obtains the same exponential family form as the prior. Similarities between the proposed method and the extended Kalman filter for nonlinear filtering are illustrated. Further, an extended target measurement update for target models where the target extent is represented by a random matrix having an inverse Wishart distribution is derived. The approximate update covers the important case where the spread of measurement is due to the target extent as well as the measurement noise in the sensor.
We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.
In this technical report, some derivations for the smoother proposed in [1] are presented. More specifically, the derivations for the cyclic iteration needed to solve the variational Bayes smoother for linear state-space models with unknownprocess and measurement noise covariances in [1] are presented. Further, the variational iterations are compared with iterations of the Expectation Maximization (EM) algorithm for smoothing linear state-space models with unknown noise covariances.
[1] T. Ardeshiri, E. Özkan, U. Orguner, and F. Gustafsson, ApproximateBayesian smoothing with unknown process and measurement noise covariances, submitted to Signal Processing Letters, 2015.
Prediction and filtering of continuous-time stochastic processes require a solver of a continuous-time differential Lyapunov equation (CDLE). Even though this can be recast into an ordinary differential equation (ODE), where standard solvers can be applied, the dominating approach in Kalman filter applications is to discretize the system and then apply the discrete-time difference Lyapunov equation (DDLE). To avoid problems with stability and poor accuracy, oversampling is often used. This contribution analyzes over-sampling strategies, and proposes a low-complexity analytical solution that does not involve oversampling. The results are illustrated on Kalman filtering problems in both linear and nonlinear systems.
Prediction and filtering of continuous-time stochastic processes often require a solver of a continuous-time differential Lyapunov equation (CDLE), for example the time update in the Kalman filter. Even though this can be recast into an ordinary differential equation (ODE), where standard solvers can be applied, the dominating approach in Kalman filter applications is to discretize the system and then apply the discrete-time difference Lyapunov equation (DDLE). To avoid problems with stability and poor accuracy, oversampling is often used. This contribution analyzes over-sampling strategies, and proposes a novel low-complexity analytical solution that does not involve oversampling. The results are illustrated on Kalman filtering problems in both linear and nonlinear systems.
This paper summarizes previous work on tool position estimation on industrial manipulators, and emphasize the problems that must be taken care of in order to get a satisfied result. The acceleration of the robot tool, measured by an accelerometer, together with measurements of motor angles are used. The states are estimated with an extended Kalman filter. A method for tuning the covariance matrices for the noise, used in the observer, is suggested. The work has been focused on a robot with two degrees of freedom.
The performance of a non-linear filter hinges in the end on the accuracy of the assumed non-linear model of the process. In particular, the process noise covariance $Q$ is hard to get by physical modeling and dedicated system identification experiments. We propose a variant of the expectation maximization (EM) algorithm which iteratively estimates the unobserved state sequence and $Q$ based on the observations of the process. The extended Kalman smoother (EKS) is the instrument to find the unobserved state sequence. Our contribution fills a gap in literature, where previously only the linear Kalman smoother and particle smoother have been applied. The algorithm will be important for future industrial robots with more flexible structures, where the particle smoother cannot be applied due to the high state dimension. The proposed method is compared to two alternative methods on a simulated robot.
The performance of a non-linear filter hinges in the end on the accuracy of the assumed non-linear model of the process. In particular, the process noise covariance Q is hard to get by physical modeling and dedicated system identification experiments. We propose a variant of the expectation maximization (EM) algorithm which iteratively estimates the unobserved state sequence and Q based on the observations of the process. The extended Kalman smoother (EKS) is the instrument to find the unobserved state sequence. Our contribution fills a gap in literature, where previously only the linear Kalman smoother and particle smoother have been applied. The algorithm will be important for future industrial robots with more flexible structures, where the particle smoother cannot be applied due to the high state dimension. The proposed method is compared to two alternative methods on a simulated robot.
The correct spatial registration between virtual and real objects in optical see-through augmented reality implies accurate estimates of the user’s eyepoint relative to the location and orientation of the display surface. A common approach is to estimate the display parameters through a calibration procedure involving a subjective alignment exercise. Human postural sway and targeting precision contribute to imprecise alignments, which in turn adversely affect the display parameter estimation resulting in registration errors between virtual and real objects. The technique commonly used has its origin incomputer vision, and calibrates stationary cameras using hundreds of correspondence points collected instantaneously in one video frame where precision is limited only by pixel quantization and image blur. Subsequently the input noise level is several order of magnitudes greater when a human operator manually collects correspondence points one by one. This paper investigates the effect of human alignment noise on view parameter estimation in an optical see-through head mounted display to determine how well astandard camera calibration method performs at greater noise levels than documented in computer vision literature. Through Monte-Carlo simulations we show that it is particularly difficult to estimate the user’s eyepoint in depth, but that a greater distribution of correspondence points in depth help mitigate the effects of human alignment noise.
The EM algorithm and two MCMC algorithms are applied to manoeuvre detection in target tracking. These statistical methods are off-line and the intended use is to compute upper performance limits of on-line algorithms as well as for off-line analysis. A consequence of the MCMC theory is that an approximation of the a posteriori distribution for the manoeuvre times is obtained.
The nonlinear estimation problem in navigation using terrain height variations is studied. The optimal Bayesian solution to the problem is derived. The implementation is grid based, calculating the probability of a set of points on an adaptively dense mesh. The Cramer-Rao bound is derived. Monte Carlo simulations over a commercial map shows that the algorithm, after convergence, reaches the Cramer-Rao lower bound.
The performance of terrain-aided navigation of aircraft depends on the size of the terrain gradient in the area. The point-mass filter (PMF) described in this work yields an approximate Bayesian solution that is well suited for the unstructured nonlinear estimation problem in terrain navigation. It recursively propagates a density function of the aircraft position. The shape of the point-mass density reflects the estimate quality; this information is crucial in navigation applications, where estimates from different sources often are fused in a central filter. Monte Carlo simulations show that the approximation can reach the optimal performance, and realistic simulations show that the navigation performance is very high compared with other algorithms and that the point-mass filter solves the recursive estimation problem for all the types of terrain covered in the test. The main advantages of the PMF is that it works for many kinds of nonlinearities and many kinds of noise and prior distributions. The mesh support and resolution are automatically adjusted and controlled using a few intuitive design parameters. The main disadvantage is that it cannot solve estimation problems of very high dimension since the computational complexity of the algorithm increases drastically with the dimension of the state space. The implementation used in this work shows real-time performance for 2D and in some cases 3D models, but higher state dimensions are usually intractable.
In aircraft navigation the demands on reliability and safety are very high. The importance of accurate position and velocity information becomes crucial when flying an aircraft at low altitudes, and especially during the landing phase. Not only should the navigation system have a consistent description of the position of the aircraft, but also a description of the surrounding terrain, buildings and other objects that are close to the aircraft. Terrain navigation is a navigation scheme that utilizes variations in the terrain height along the aircraft flight path. Integrated with an Inertial Navigation System (INS), it yields high performance position estimates in an autonomous manner, ie without any support information sent to the aircraft. In order to obtain these position estimates, a nonlinear recursive estimation problem must be solved on-line. Traditionally, this filtering problem has been solved by local linearization of the terrain at one or several assumed aircraft positions. Due to changing terrain characteristics, these linearizations will in some cases result in diverging position estimates. In this work, we show how the Bayesian approach gives a comprehensive framework for solving the recursive estimation problem in terrain navigation. Instead of approximating the model of the estimation problem, the analytical solution is approximately implemented. The proposed navigation filter computes a probability mass distribution of the aircraft position and updates this description recursively with each new measurement. The navigation filter is evaluated over a commercial terrain database, yielding accurate position estimates over several types of terrain characteristics. Moreover, in a Monte Carlo analysis, it shows optimal performance as it reaches the Cramér-Rao lower bound.
When the systems evolved from analog to digital, the performance was improved by the use of power control on the one hand and different modulations and coding schemes on the other. Condensing the available information we are able to propose a new concept of power control. The concept is applicable to real systems, since it uses the available measurements for estimating parameters necessary for the power control. It also supports the use of an adequate quality measure together with a quality specification supplied by the operator. We will use frequency hopping GSM as an example and the resulting control algorithm is ready for implementation in the software in the base stations where the output powers are computed. No modifications are needed in the GSM standard, the mobile terminals, the radio interfaces or in the base station transmitters. Finally we provide simulation results confirming the benefits of using the new concept for power control.
The problem to track time-varying parameters in cellular radio systems is studied, and the focus is on estimation based only on the signals that are readily available. Previous work have demonstrated very good performance, but were relying on analog measurement that are not available. Most of the information is lost due to quantization and sampling at a rate that might be as low as 2 Hz (GSM case). For that matter a maximum likelihood estimator have been designed and exemplified in the case of GSM. Simulations indicate good performance both when most parameters are varying slowly, and when subject to fast variations as in realistic cases. Since most computations take place in the base stations, the estimator is ready for implementation in a second generation wireless system. No update of the software in the mobile stations is needed.
A method and system for quality-based transmission power control in a cellular communications system (100) are disclosed, whereby a network operator can specify the transmission quality requirements using a measurement that better reflects the actual quality perceived by the users. All transmitter power levels in the network can be controlled by identical power regulators (200), each of which can adapt to individual traffic situations in order to achieve the specified quality. For example, in a GSM frequency-hopping network, the FER together with the parameters estimated from the current traffic situation (54), are mapped onto a target C/I (56), which in turn, the power control algorithm strives (16) to achieve (58, 60). Consequently, the power regulators can adapt to the traffic situation experienced by each receiver.
Time delays reduces the performance of any controlled system. If neglected in the design phase, the system may even become unstable when using the designed controller. Several power control strategies have been proposed in order to improve the capacity of cellular radio systems, but time delays are usually neglected. Here, it is shown that the problems can be handled by considering the time delays in the design phase in order to choose the appropriate parameter values. Most popular algorithms can be seen as special cases of an integrating controller. This structure is extended first to a proportional integrating (PI)-controller and then further on to a general linear controller of higher orders. Corresponding design procedures are outlined based on techniques, such as pole placement, from the field of automatic control. The PI-controller is a very appealing choice of structure, with better performance compared to an I-controller and less complex than a higher order controller. The benefits are further illuminated by network simulations.
For certain types of sensor-target configurations, a point target model or approach is not suitable and the physical extent of the target is accounted for during processing. An extended target track-before-detect (TBD) algorithm is presented and the performance is compared to an algorithm based on the point target assumption. Simulations illustrate the gain in performance obtained by using the extended target model where a particle filter is used for the TBD implementation.
This paper presents a distributed online method for joint state and parameter estimation in a Jump Markov NonLinear System based on a distributed recursive Expectation Maximization algorithm. State inference is enabled via the use of Rao-Blackwellized Particle Filter and, for the parameter estimation, the E-step is performed independently at each sensor with the calculation of local sufficient statistics. An average consensus algorithm is used to diffuse local sufficient statistics to neighbors and approximate the global sufficient statistics throughout the network. The evaluation of the proposed algorithm is carried out on a Terrain Based Navigation problem where the unknown parameters of the observation noise model contain relevant information about the terrain properties.
This work evaluates a previously introduced algorithm called Particle-Based Rapid Incremental Smoother within the framework of state inference and parameter identification in Jump Markov Non-Linear System. It is applied to the recursive form of two well-known Maximum Likelihood based algorithms who face the common challenge of online computation of smoothed additive functionals in order to accomplish the task of model parameter estimation. This work extends our previous contributions on identification of Markovian switching systems with the goal to reduce the computational complexity. A benchmark problem is used to illustrate the results.
This paper is concerned with cooperative Terrain Aided Navigation of a network of aircraft using fusion of Radar Altimeter and inter-node range measurements. State inference is performed using a Rao-Blackwellized Particle Filter with online measurement noise statistics estimation. For terrain coverage measurement noise parameter identification, an online Expectation Maximization algorithm is proposed, where local sufficient statistics at each node are calculated in the E-step, which are then distributed to neighboring nodes using a random gossip algorithm to perform the M-step at each node. Simulation results show that improvement on positioning and calibration performance can be achieved compared to a non-cooperative approach.
The global positioning system (GPS) is a Global Navigation Satellite System (GNSS) uses a constellation of between 24 and 32 Medium Earth Orbit satellites that transmit precise microwave signals, which enable GPS receivers to determine their current location, the time, and their velocity [1]. Initially, the GPS was developed for military applications, but very quickly became the most used technology in positioning even for end-user applications run by individuals with no technical skills. GPS reading are used also as reference points for many positioning techniques such as the techniques that depend on the transmitted electromagnetic signal to determine the position of the transmitter or the receiver, due to their superior accuracy comparing to such techniques. But how accurate are those readings, and how to obtain accurate reference points starting from raw GPS observations even when they are corrupted with errors. In this paper, a practical study about GPS positioning is provided. Generating the ground-truth reference points depending on GPS observations is also provided and discussed in details.
This paper considers the problem of fingerprinting localization in wireless networks based on received-signal-strength (RSS) observations. First, the performance of static localization using power maps (PMs) is improved with a new approach called the base-station-strict (BS-strict) methodology, which emphasizes the effect of BS identities in the classical fingerprinting. Second, dynamic motion models with and without road network information are used to further improve the accuracy via particle filters. The likelihood-calculation mechanism proposed for the particle filters is interpreted as a soft version (called BS-soft) of the BS-strict approach applied in the static case. The results of the proposed approaches are illustrated and compared with an example whose data were collected from a WiMAX network in a challenging urban area in the capitol city of Brussels, Belgium.
A localization algorithm based on cell identification (Cell-ID) information is proposed. Instead of building the localization decisions only on the serving base station, all the detected Cell-IDs (serving or nonserving) by the mobile station are utilized. The statistical modeling of user motion and the measurements are done via a hidden Markov model (HMM), and the localization decisions are made with maximum a posteriori estimation criterion using the posterior probabilities from an HMM filter. The results are observed and compared with standard alternatives on an example whose data were collected from a worldwide interoperability for microwave access network in a challenging urban area in the Brussels capitol city.
Tracking in WiMax networks is gaining a lot of interest; especially after the mobile WiMax became one of the emerging technologies that promote low-cost deployment and evolving to provide IP-based services of high mobility including providing location-based services (LBS). Therefore, locating users in a cheap way thatdepend on the available network resources is becoming more and more interesting and an active topic for researchers. In this paper we consider the problem of tracking in WiMAX networks depending on SCOREobservations. The provided examples show that with efficient measurement data processing and with the help of already available data (street maps), plausible results can be achieved.
In this paper, we analyze the performance of the Gaussian mixture probability hypothesis density (GM-PHD) filter in tracking multiple non-cooperative targets using a passive sensor network. Non-cooperative transmissions from illuminators of opportunity like GSM base stations, FM radio transmitters or digital broadcasters are exploited by non-directional separately located Doppler measuring sensors. Clutter, missed detections and multi-static Doppler variances are incorporated into a realistic multi-target scenario. Simulation results show that the GM-PHD filter successfully tracks multiple targets using only Doppler shift measurements in a passive multi-static scenario.
Sensor localization is a central problem for sensor networks. If the sensor positions are uncertain, the target tracking ability of the sensor network is reduced. Sensor localization in underwater environments is traditionally addressed using acoustic range measurements involving known anchor or surface nodes. We explore the usage of triaxial magnetometers and a friendly vessel with known magnetic dipole to silently localize the sensors. The ferromagnetic field created by the dipole is measured by the magnetometers and is used to localize the sensors. The trajectory of the vessel and the sensor positions are estimated simultaneously using an Extended Kalman Filter (EKF). Simulations show that the sensors can be accurately positioned using magnetometers.
Indoor localization in unknown environments is considered, using inertial measurements from accelerometers, gyroscopes and magnetometers. Foot-mounted inertial sensors allow for stand-still detection triggering zero velocity updates that reduces the inertial navigation system (ins) drift in distance traveled from cubical to linear in time. We present a statistical framework, based on an navigation model. The standard stand-still mode is complemented with binary modes of magnetic disturbances. Test statistics for these two mode estimation problems are derived. Instead of making hard decisions, a hidden Markov model filter is used to compute the mode probabilities, leading to soft measurement updates in the Kalman filter.
Based on this, a robust smoothed heading estimate is computed in a second stage using the magnetometer. The final position estimate is then obtained by fusing the ins output with the robust heading in a standard dead-reckoning filter. Experiments demonstrate that the robust heading decreases the relative error in position from 10% to less than 1%, despite large magnetic disturbances.
We consider stand still detection for indoor localization based on observations from a foot-mounted inertial measurement unit (IMU). The main contribution is a statistical framework for stand-still detection, which is a fundamental step in zero velocity update (ZUPT) to reduce the drift from cubic to linear in time. First, the observations are transformed to a test statistic having non-central chi-square distribution during zero velocity. Second, a hidden Markov model is used to describe the mode switching between stand still, walking, running, crawling and other possible movements. The resulting algorithm computes the probability of being in each mode, and it is easily extendable to a dynamic navigation framework where map information can be included. Results of first mode probability estimation, second map matching without ZUPT and third step length estimation with ZUPT are provided.
Indoor positioning in unknown environments is crucial for rescue personnel and future infotainment systems. Dead-reckoning inertial sensor data gives accurate estimate of distance, for instance using zero velocity updates, while the heading estimation problem is inherently more difficult due to the large degree of magnetic disturbances indoors. We propose a Kalman filter bank approach based on supporting a magnetic compass with gyroscope turn rate information, where a hidden Markov model is used to model the presence of magnetic disturbances. In parallel, we suggest to run a robust heading estimation system based on data from a sliding window. The robust estimate is used to detect filter divergence, and to restart the filter when needed. The underlying assumptions and the heading estimation performance are supported in field trials using more than 500 data sets from more than 50 venues in 5 continents.
The problem of estimating heading is central in the indoor positioning problem based on measurements from inertial measurement and magnetic units, Integrating rate of turn angular rate gives the heading with unknown initial condition and a linear drift over time, while the magnetometer gives absolute heading, but m here long segments of data are useless in practice because of magnetic disturbances. A basic Kalman filter approach with outlier rejection has turned out to be difficult to use with high integrity. Here, we propose an approach based on convex optimization, where segments of good magnetometer data are separated from disturbed data and jointly fused with the yaw rate measurements. The optimization framework is flexible with many degrees of freedom in the modeling phase, and we outline one design. A recursive solution to the optimization is derived, which has a computational complexity comparable to the simplest possible Kalman filter. The performance is evaluated using data from a handheld smartphone for a large amount of indoor trajectories, and the result demonstrates that the method effectively resolves the magnetic disturbances.
The problem of estimating heading is central in the indoor positioning problem based on mea- surements from inertial measurement and magnetic units. Integrating rate of turn angular rate gives the heading with unknown initial condition and a linear drift over time, while the magnetometer gives absolute heading, but where long segments of data are useless in prac- tice because of magnetic disturbances. A basic Kalman filter approach with outlier rejection has turned out to be difficult to use with high integrity. Here, we propose an approach based on convex optimization, where segments of good magnetometer data are separated from disturbed data and jointly fused with the yaw rate measurements. The optimization framework is flexible with many degrees of freedom in the modeling phase, and we outline one design. A recursive solution to the optimization is derived, which has a computational complexity comparable to the simplest possible Kalman filter. The performance is evaluated using data from a handheld smartphone for a large amount of indoor trajectories, and the result demonstrates that the method effectively resolves the magnetic disturbances.
A vessel navigating in a critical environment such as an archipelago, requires very accurate movement estimates. Intentional or unintentional jamming makes gps unreliable as the only source of information and an additional independent navigation system should be used. In this paper we suggest estimating the vessel movements using a sequence of radar images from the preexisting body-fixed radar. Island landmarks in the radar scans are tracked between multiple scans using visual features. This provides information not only about the position of the vessel but also of its course and velocity. We present here a complete navigation framework that requires no additional hardware than the already existing naval radar sensor. Experiments show that visual radar features can be used to accurately estimate the vessel trajectory over an extensive data set.
It is important to detect a change in the echo path quickly but not confuse it with double talk, since the echo canceler should react differently for these two phenomena. In this chapter, a sequential detection scheme is presented and, based on model assumptions, the maximum a posteriori probabilities of the occurrence of double talk and abrupt changes in the echo path are derived. By utilizing the fact that the most active part of a typical impulse response of a telephone channel is short and by using a low complexity time-delay estimation algorithm to find these most active taps and not estimating the rest of the taps, low computational complexity of the proposed detection method is achieved. The scheme is veried experimentally in computer simulations using a real speech signal and impulse responses created from measured impulse responses from real hybrids of a telephone channel.
The problem of detection and discrimination of double talk and change in the echo path in a telephone channel is considered. The phenomenon echo path change requires fast adaptation of the channel model to be able to equalize the echo dynamics. On the other hand, the adaption rate should be reduced when double talk occurs. Thus, it is critical to quickly detect a change in the echo path while not confusing it with double talk, which gives a similar effect. The proposed likelihood based approach compares a global channel model with a local one over a sliding window, both estimated with the recursive least squares algorithm.
In order to insert a virtual object into a TV image, the graphics system needs to know precisely how the camera is moving, so that the virtual object can be rendered in the correct place in every frame. Nowadays this can be achieved relatively easily in post-production, or in a studio equipped with a special tracking system. However, for live shooting on location, or in a studio that is not specially equipped, installing such a system can be difficult or uneconomic. To overcome these limitations, the MATRIS project is developing a real-time system for measuring the movement of a camera. The system uses image analysis to track naturally occurring features in the scene, and data from an inertial sensor. No additional sensors, special markers, or camera mounts are required. This paper gives an overview of the system and presents some results.
In order to insert a virtual object into a TV image, the graphics system needs to know precisely how the camera is moving, so that the virtual object can be rendered in the correct place in every frame. Nowadays this can be achieved relatively easily in postproduction, or in a studio equipped with a special tracking system. However, for live shooting on location, or in a studio that is not specially equipped, installing such a system can be difficult or uneconomic. To overcome these limitations, the MATRIS project is developing a real-time system for measuring the movement of a camera. The system uses image analysis to track naturally occurring features in the scene, and data from an inertial sensor. No additional sensors, special markers, or camera mounts are required. This paper gives an overview of the system and presents some results.
This paper proposes a diagonal covariance matrix approximation for Wide-Sense Stationary (WSS) signals with correlated Gaussian noise. Existing signal models that incorporate correlations often require regularization of the covariance matrix, so that the covariance matrix can be inverted. The disadvantage of this approach is that matrix inversion is computational intensive and regularization decreases precision. We use Bienayme's theorem to approximate the covariance matrix by a diagonal one, so that matrix inversion becomes trivial, even with nonuniform rather than only uniform sampling that was considered in earlier work. This approximation reduces the computational complexity of the estimator and estimation bound significantly. We numerically validate this approximation and compare our approach with the Maximum Likelihood Estimator (MLE) and Cramer-Rao Lower Bound (CRLB) for multivariate Gaussian distributions. Simulations show that our approach differs less than 0.1% from this MLE and CRLB when the observation time is large compared to the correlation time. Additionally, simulations show that in case of non-uniform sampling, we increase the performance in comparison to earlier work by an order of magnitude. We limit this study to correlated signals in the time domain, but the results are also applicable in the space domain.
This paper presents a new robustified data-driven fault detection approach, connected to closed-loop subspace identification. Although data-driven detection methods have recently been reported in the literature, attention has not yet been given to a robust solution coping with identification errors. The key idea of this paper is to analytically quantify the effect of the identification errors on the residual generator of a new data-driven detection approach, namely FICSI. The comparisons of the proposed robust FICSI detection scheme with both its nominal counterpart and the nominal data-driven PSA solutions have verified the effectiveness of accounting the identification errors in improving the performance of the data-driven detection scheme.
Detection of faults that appear as additive unknown input signals to an unknown LTI discrete-time MIMO system is considered. State of the art methods consist of the following steps. First, either the state space model or certain projection matrices are identified from data. Then, a residual generator is formed based on these identified matrices, and this residual generator is used for online fault detection. Existing techniques do not allow for compensating for the identification uncertainty in the fault detection. This contribution explores a recent data-driven approach to fault detection. We show first that the identified parametric matrices in this method depend linearly on the noise contained in the identification data, and then that the on-line computed residual also depends linearly on the noise. This allows an analytic design of a robust fault detection scheme, that takes both the noise in the online measurements as well as the identification uncertainty into account. We illustrate the benefits of the new method on a model of aircraft dynamics extensively studied in literature.
This correspondence is a companion paper to [J. Dong, M. Verhaegen, and F. Gustafsson, "Robust Fault Detection With Statistical Uncertainty in Identified Parameters," IEEE Trans. Signal Process., vol. 60, no. 10, Oct. 2012], extending it to fault isolation. Also, here, use is made of a linear in the parameters model representation of the input-output behavior of the nominal system (i.e. fault-free). The projection of the residual onto directions only sensitive to individual faults is robustified against the stochastic errors of the estimated model parameters. The correspondence considers additive error sequences to the input and output quantities that represent failures like drift, biased, stuck, or saturated sensors/actuators.
A GM-PHD filter is used for pedestrian tracking in a crowdsurveillance application. The purpose is to keep track of thedifferent groups over time as well as to represent the shape ofthe groups and the number of people within the groups. In-put data to the GM-PHD filter are detections using a state ofthe art algorithm applied to video frames from the PETS 2012benchmark data. In a first step, the detections in the framesare converted from image coordinates to world coordinates.This implies that groups can be defined in physical units interms of distance in meters and speed differences in metersper second. The GM-PHD filter is a Bayesian framework thatdoes not form tracks of individuals. Its output is well suitedfor clustering of individuals into groups. The results demon-strate that the GM-PHD filter has the capability of estimatingthe correct number of groups with an accurate representationof their sizes and shapes.
Detection and tracking of other vehicles and lane geometry will be required for many future intelligent driver assistance systems. By integrating the estimation of these two features into a single filter, a more optimal utilization of the available information can be achieved. For example, it is possible to improve the lane curvature estimate during bad visibility by studying the motion of other vehicles. This paper derives and evaluates various approximations that are needed in order to deal with the non-linearities that are introduced by such an approach.