This letter considers the problem of detecting and tracking objects in a sequence of images. The problem is formulated in a filtering framework, using the output of object-detection algorithms as measurements. An extension to the filtering formulation is proposed that incorporates class information from the previous frame to robustify the classification. Further, the properties of the object-detection algorithm are exploited to quantify the uncertainty of the bounding box detection in each frame. The complete filtering method is evaluated on camera trap images of the four large Swedish carnivores, bear, lynx, wolf, and wolverine. The experiments show that the class tracking formulation leads to a more robust classification.

The particle filter (PF) approximates the posterior distribution of the states in filtering problems, and it is well-known that it converges to the true posterior when the number of particles tends to infinity. It would be natural to assume that measures such as mean square error (MSE) decreases monotonically as the number of particles increases. This is, however, not always true. We present a simple two-dimensional linear Gaussian system where the MSE grows initially before it starts to decrease to eventually reach the optimal filter performance, which in this case is provided by the Kalman filter (KF). Other indicators such as the efficient number of particles and trace of the particle covariance show a similar strange behavior.

Inspired by this, we derive a condition for what we term projected instability, which means that the particle in the standard SIR PF that gives the best prediction actually increases the state estimation error. For linear systems, this gives an explicit condition in terms of the state space matrices when this situation occurs. Monte Carlo simulations of a large number of random linear systems indicate that everything works as expected as long as the system does not have a projected instability, otherwise the particle filter can perform badly or even diverge.

As human settlement expands into the natural habitats of wild animals, the conflicts between humans and wildlife increases. The human-elephant conflict causes a tremendous amount of damage, often to poor villages close to the savannah. In this paper, we continue our earlier reported research on a geophone network aimed for elephant localisation by focusing on the detection challenge. We have now collected larger sets of seismic data with footsteps from both elephants and other big animals including humans. To detect the footsteps, a method is developed that analyses features of the geophone signal, which are then compared to those of an elephant footstep. The method detects 54 % of the footsteps and has a classification accuracy of 89 %. Subsequently, the detected elephant footstep is used to calculate the direction of arrival (DOA) angle using a delay-and-sum beamformer. The direction to an elephant is estimated with good precision on distances ranging from 8 to 30 meters. This research, not only, showcases a practical solution for mitigating human-elephant conflicts, but also underscores the potential of seismic technology in wildlife management and conservation efforts.

This paper considers fusion of dimension-reduced estimates in a decentralized sensor network. The benefits of a decentralized sensor network include modularity, robustness and flexibility. Moreover, since preprocessed data is exchanged between the agents it allows for reduced communication. Nevertheless, in certain applications the communication load is required to be reduced even further. One way to decrease the communication load is to exchange dimension-reduced estimates instead of full estimates. Previous work on this topic assumes global availability of covariance matrices, an assumption which is not realistic in decentralized applications. Hence, in this paper we consider the problem of deriving dimension-reduced estimates using only local information. The proposed solution is based on an estimate of the information common to the network. This common information estimate is computed locally at each agent by fusion of all information that is either received or transmitted by that agent. It is shown how the common information estimate is utilized for fusion of dimension-reduced estimates using two well-known fusion methods: the Kalman fuser which is optimal under the assumption of uncorrelated estimates, and covariance intersection. One main theoretical result is that the common information estimate allows for a decorrelation procedure such that uncorrelated estimates can be maintained. This property is crucial to be able to use the Kalman fuser without double counting of information. A numerical comparison suggests that the performance degradation of using the common information estimate, compared to having local access to the actual covariance matrices computed by other agents, is relatively small.

Human-wildlife conflicts are a global problem which is central to the Global Goal 15 (life on land). One particular case is elephants, that can cause harm to both people, property and crops. An early warning system that can detect and warn people in time would allow effective mitigation measures. The proposed method is based on a small local network of geophones that sense the seismic waves of elephant footsteps. It is known that elephant footsteps induce low frequency ground waves that can be picked up by geophones in the ground. First, a method is described that detect the particular signature of such footsteps, and then the detections are used to estimate the direction of arrival (DOA). Finally, a Kalman filter is applied to the measurements in order to track the elephant. Field tests performed at a local zoo shows promising results with accurate DOA estimates at 15 meters distance and acceptable accuracy at 40 meters.

The uncertainty in the prediction calculated using the delta method for an over-parameterized (parametric) black-box model is shown to be larger or equal to the uncertainty in the prediction of a canonical (minimal) model. Equality holds if the additional parameters of the overparameterized model do not add flexibility to the model. As a conclusion, for an overparameterized black-box model, the calculated uncertainty in the prediction by the delta method is not underestimated. The results are shown analytically and are validated in a simulation experiment where the relationship between the normalized traction force and the wheel slip of a car is modelled using e.g., a neural network.

Network-centric multitarget tracking under communication constraints is considered, where dimension-reduced track estimates are exchanged. Previous work on target tracking in this subfield has focused on fusion aspects only and derived optimal ways of reducing dimensionality based on fusion performance. In this work we propose a novel problem formalization where estimates are reduced based on association performance. The problem is analyzed theoretically and problem properties are derived. The theoretical analysis leads to an optimization strategy that can be used to partly preserve association quality when reducing the dimensionality of communicated estimates. The applicability of the suggested optimization strategy is demonstrated numerically in a multitarget scenario.

Conventional direction of arrival (DOA) estimators are based on array processing using either time differences or beam-forming. The proposed approach is based on the received power at each microphone, which enables simple hardware, low sampling frequency and small arrays. The problem is recast into a linear regression framework where the least squares method applies, and the main drawback is that different sound sources are not readily separable.Our proposed approach is based on a training phase where the directional sensitivity of each microphone element is estimated. This model is then used as a fingerprint of the observed power vector in a real-time estimator. The learned power vector is here modeled by a Fourier series expansion, which enables Cramér-Rao lower bound computations. We demonstrate the performance using a circular array with eight microphones with promising results.

In this paper, we present a study on using weightedtotal least squares method for parameter estimation of errorsin-variables models with quadratic regressors. The statistics oferror is analyzed to fill in the gap between basic assumptions inweighted total least squares and our case. A modified Cram´er-Rao lower bound is introduced for error quantification in theproposed method. We perform evaluations based on simulationswith comparisons to standard least squares and generalized totalleast squares. Numerical results show that the proposed methodoutperforms the others in terms of estimation accuracy

The Particle filter can in theory estimate the state of any nonlinear system, but in practice it suffers from an exponential complexity in terms of the number of particles as the dimension of the state increases. The marginalized particle filter can potentially reduce this problem by improving the estimates, particularly for lower number of particles. However, it turns out that for certain systems, it does not provide any improvement in the accuracy of the estimate. The core cause of degeneracy is linked to when the uncertainty of the linear state conditioned on the nonlinear state is 0. Conditions for determining when this occurs are presented and applied to common constant velocity, constant acceleration and constant jerk models with various sampling methods. Interestingly, some combinations are useful while others should be avoided. These findings are supported using simulated systems.