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Therefore, an analytical evaluation of the sensor placement for the propagation of the sensor variance is provided here.
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However, as shown in Table2, DcPF has a slightly lower processing cost when the sensor variances are known.
To achieve this duality, we propose transformations which can be used to convert sensor failure probabilities into equivalent sensor variances and vice versa.
We assessed the performance of the proposed algorithms using 100 Monte Carlo runs with simulated data in three distinct scenarios assuming both unknown and known sensor variances.
As expected, the DcPF algorithm assuming known sensor variances has the same communication requirements as in the scenario with unknown variances since DcPF locally computes the likelihood functions and then broadcasts them to the entire network.
In the first scenario, we assumed unknown sensor variances and evaluated the performance of the Rao-Blackwellized ReDif-PF and two consensus-based PF trackers using respectively iterative minimum consensus (CbPFa) and flooding (CbPFb) (see also[11]).
Figure8 shows the evolution of the RMS error norm assuming known sensor variances for the ReDif-PF algorithm in Section 4.1 with a single-mode GMM parametric approximation and the MCDPF algorithm in[9] for J ∈ {10,30,50,100} iterations.
In the second scenario, the sensor variances are perfectly known and the ReDif-PF tracker is compared both to the optimal centralized PF and to a linearized random exchange extended Kalman filter (ReDif-EKF), which is summarized in Appendix 3. In the simulations, we assumed a non-informative prior for the sensor's initial position that is uniform in the entire surveillance space.
Table1 summarizes the communication cost for each algorithm in the first scenario (unknown sensor variances) in terms of average transmission (TX) and average reception (RX) rates per node and also quantifies the processing cost for each algorithm in terms of average duty cycle per node, measured in a Intel Core i5 machine with 4GB RAM.
In the third scenario, the ReDif-PF tracker is compared to two iterative algorithms from the literature - the MCDPF and the selective gossip from[9] and[23], respectively - assuming perfectly known sensor variances as in the second scenario and the same Gaussian priors for the emitter's initial position and velocity used in the first scenario.
Figure7 shows the evolution of the RMS error norm assuming known sensor variances respectively for the ReDif-PF algorithm in Section 4.1 with a two-Gaussian GMM parametric approximation and the ReDif-EKF algorithm in Appendix 3. We also show the RMS curve for the optimal centralized PF tracker as a benchmark.
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