David Lindgren

Shooter localization in wireless microphone networks

Shooter localization in a wireless network of microphones is studied. Both the acoustic muzzle blast (MB) from the gunfire and the ballistic shock wave (SW) from the bullet can be detected by the microphones and considered as measurements. The MB measurements give rise to a standard sensor network problem, similar to time difference of arrivals in cellular phone networks, and the localization accuracy is good, provided that the sensors are well synchronized compared to the MB detection accuracy. The detection times of the SW depend on both shooter position and aiming angle and may provide additional information beside the shooter location, but again this requires good synchronization. We analyze the approach to base the estimation on the time difference of MB and SW at each sensor, which becomes insensitive to synchronization inaccuracies. Cramér-Rao lower bound analysis indicates how a lower bound of the root mean square error depends on the synchronization error for the MB and the MB-SW difference, respectively. The estimation problem is formulated in a separable nonlinear least squares framework. Results from field trials with different types of ammunition show excellent accuracy using the MB-SW difference for both the position and the aiming angle of the shooter.

Multi-target tracking with PHD filter using Doppler-only measurements

In this paper, we address the problem of multi-target detection and tracking over a network of separately located Doppler-shift measuring sensors. For this challenging problem, we propose to use the probability hypothesis density (PHD) filter and present two implementations of the PHD filter, namely the sequential Monte Carlo PHD (SMC-PHD) and the Gaussian mixture PHD (GM-PHD) filters. Performances of both filters are carefully studied and compared for the considered challenging tracking problem. Simulation results show that both PHD filter implementations successfully track multiple targets using only Doppler shift measurements. Moreover, as a proof-of-concept, an experimental setup consisting of a network of microphones and a loudspeaker was prepared. Experimental study results reveal that it is possible to track multiple ground targets using acoustic Doppler shift measurements in a passive multi-static scenario. We observed that the GM-PHD is more effective, efficient and easy to implement than the SMC-PHD filter.

Sensor models and localization algorithms for sensor networks based on received signal strength

Received signal strength (RSS) can be used in sensor networks as a ranging measurement for positioning and localization applications. This contribution studies the realistic situation where neither the emitted power nor the power law decay exponent be assumed to be known. The application in mind is a rapidly deployed network consisting of a number of sensor nodes with low-bandwidth communication, each node measuring RSS of signals traveled through air (microphones) and ground (geophones). The first contribution concerns validation of a model in logarithmic scale, that is, linear in the unknown nuisance parameters (emitted power and power loss constant). The parameter variation is studied over time and space. The second contribution is a localization algorithm based on this model, where the separable least squares principle is applied to the non-linear least squares (NLS) cost function, after which a cost function of only the unknown position is obtained. Results from field trials are presented to illustrate the method, together with fundamental performance bounds. The ambition is to pave the way for sensor configuration design and more thorough performance evaluations as well as filtering and target tracking aspects.

Distributed localization using acoustic Doppler

It is well-known that the motion of an acoustic source can be estimated from Doppler shift observations. It is however not obvious how to design a sensor network to efficiently deliver the localization service. In this work a rather simplistic motion model is proposed that is aimed at sensor networks with realistic numbers of sensor nodes. It is also described how to efficiently solve the associated least squares optimization problem by Gauss-Newton variable projection techniques, and how to initiate the numerical search from simple features extracted from the observed frequency series. The methods are evaluated by Monte Carlo simulations and demonstrated on real data by localizing an all-terrain vehicle. It is concluded that the processing components included are fairly mature for practical implementations in sensor networks. HighlightsWe consider a distributed network of acoustic Doppler sensors.We model an acoustic source motion with parameterized models.The motion parameters are estimated based on the Doppler.A tailored Gauss-Newton algorithm with robust initialization is described.Computational and numerical efficiencies are showed for realistic noise levels.

A novel feature extraction algorithm for asymmetric classification

A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By asymmetric classification is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not, in general, have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well-known LDA is the assumption of symmetric classes with separated centroids. The ACP, in contrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from an array of semiconductor gas sensors with the purpose of distinguish bad grain from good.

Clustered regression analysis

Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regression explained variables onto the explaining variables, or vice-versa, is not arbitrary. Numerical experiments indicate that the classical statistical model is more powerful than the inverse regression approach.

Generalization Ability of a Support Vector Classifier Applied to Vehicle Data in a Microphone Network

Audio recordings of vehicles passing a microphone network are studied with respect to the classification ability under different weather and local conditions. The audio data base includes recordings in different seasons, recordings at various sensor locations and also recordings using different microphones. A support vector machine (SVM) is used to classify vehicles from normalized, low-frequency spectral features of short time chunks of the audio signals. The classification performance using individual time chunks is estimated, as well as the accuracy of fusing data from the different microphones in the network. The study shows that, combining temporal and spatial data, a vehicle traversing a microphone network can be correctly classified in up to 90 percent of all runs. A more demanding test, classifying data from a totally independent measurement equipment, yields 70 percent correct classifications

Interactive Visualization as a Tool for Analysing Time-Varying and Non-Linear Systems

This paper shows how 3-dimensional interactive visualization can be used as a tool in system identification. Non-linear or time-dependent dynamics often leave a significant residual with linear, ti ...

Nonlinear Dynamics Identified by Multi-Index Models

For a class of nonlinear systems, the residual of a well fitted model has low intrinsic dimensionality. For these systems, a particular low-dimensional linear projection of the regressor will facil ...

Nonlinear dynamics isolated by delaunay triangulation criteria

Inspired by an idea by Q. Zhang, we show that Delaunay triangulation of data points sampled from a system with an additive nonlinearity gives a criterion by which a linear projection can be found that isolates the nonlinear dependence, leaving out the linear one. This isolation means the nonlinear modeling can be confined to a regressor space of lower dimensionality, which in turn means over-parameterization can be avoided. Monte Carlo simulations indicate that a particular criterion built on triangle asymmetries has a minimum that coincides with the sampled system nonlinear part. The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.