Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the probability hypothesis density (PHD) and the cardinalized probability hypothesis density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples.

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters.

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The Probability Hypothesis Density (PHD) is a well-known method for single-sensor multi-target tracking problems in a Bayesian framework, but the extension to the multi-sensor case seems to remain a challenge. In this paper, an extension of Mahler's work to the multi-sensor case provides an expression of the true PHD multi-sensor data update equation. Then, based on the configuration of the sensors' fields of view (FOVs), a joint partitioning of both the sensors and the state space provides an equivalent yet more practical expression of the data update equation, allowing a more effective implementation in specific FOV configurations.

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The dynamics of a close-loop electrostatic MEMS resonator, proposed as a platform for ultra sensitive mass sensors, is investigated. The parameter space of the resonator actuation voltage is investigated to determine the optimal operating regions. side each of the potential wells and around both wells. The optimal region in the parameter space for mass sensing purposes is determined. In that region, steadystate chaotic attractors develop and spend most of the time in the safe lower well while occasionally visiting the upper well. The robustness of the chaotic attractors in that region is demonstrated by studying their basins of attraction. Further, regions of large dynamic amplification are also identified in the parameter space. In these regions, the resonator can be used as an efficient long-stroke actuator.