In the previous sections adapted standard and generalized PHD Intensity filters are compared using the BML framework for simulated data. The corresponding BML framework is presented in Section 5.1.3 and visualized in Figure 5.3. There, the mea-surement data is created in the following way. First, a ray tracer produces a set of predicted multipaths based on the OS and the ground truth position of the MS for all time instances. Afterwards, these multipaths are deteriorated by an antenna em-ulation and then used as measurement data by the tracking algorithms.
In this section, the second proposed BML framework from Figure 5.4 for the process-ing of real world data is used to compare the generalized PHD filter (see Section 6.3) to the adaption of the standard iFilter (see Section 6.1). The data was collected in the
Figure 6.30: Visualization of the MS trajectory for the real world experiment (city of Erlangen/Germany). The colors indicate the received field strength that is received by the observer for the hypothetical emitter positions. Map Data: GeoBasis–DE/BKG 2015.c Ray–Tracer Visualization: c2015 AWE Communications.
Figure 6.31:Zoom of the studied scenario. Map Data: cGeoBasis–DE/BKG 2015. Ray–
Tracer Visualization: c2015 AWE Communications.
Time in s
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RMSE in m
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Generalized PHD Standard iFilter
Figure 6.32:Comparison of the generalized PHD and the adapted standard iFilter in terms of the RMSE.
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AoA in rad
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Predicted Multipaths Measured Multipaths
Figure 6.33: Comparison of the received multipaths to the predicted multipaths coming from the ray tracer for the ground truth position in terms of the AoA.
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Predicted Multipaths Measured Multipaths
Figure 6.34: Comparison of the received multipaths to the predicted multipaths coming from the ray tracer for the ground truth position in terms of the relative path length.
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Mean Time Consumption in ms
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Generalized PHD Standard iFilter
Figure 6.35:Comparison of the generalized PHD and the adapted standard iFilter in terms of the mean computation time per iteration.
Figure 6.36:Picture of the OS c2013 Saab Medav Technologies GmbH. The antenna array is carried by a lifting platform with a height of 10m.
Figure 6.37: Picture of the antenna array (SYST-A0006 from Alaris Antennas) and the receiver setup c2013 Saab Medav Technologies GmbH.
city of Erlangen. The trajectory of the MS and the location of the OS are depicted in the Figures 6.30 and 6.31.
The MS is given by a car, which is equipped with a signal generator, a power ampli-fier and an ommidirectional antenna to generate the emitted electromagnetic signal.
Furthermore, the target is equipped with an GPS-recorder for evaluating the target state estimations of the data fusion algorithms with respect to accuracy. The emitted signal has a frequency of 475.560 MHz and a bandwidth of 5 MHz. Note that the bandwidth is small compared to the real world data evaluation carried out in [Alg10].
The power of the emitted signal is 10 Watt.
The five–element antenna array carried by the OS is a prototype from Alaris An-tennas (SYST-A0006, see http://www.alarisanAn-tennas.com/ and Figures 6.36, 6.37), which is mounted on a lifting platform in a height of 10 m (see Figure 6.36). Due to this setup the OS is fixed for the considered scenario. However, in general a moving OS and therefore an online processing of the ray tracing prediction is possible for the proposed data fusion algorithms. Furthermore, the OS carries signal processing equipment including a direction finding system (see Figure 6.37). The received signal is then processed by the blind channel estimation algorithm proposed in [HKT15], which outputs a set of multipaths characterized by the AoA and the RToA.
In Figures 6.33 and 6.34 the received multipaths are compared in terms of their AoA and their relative path length (RPL) (which is equal to the RToA multiplied by the speed of light), respectively, to the predicted multipaths generated by the MS. Using this real world data the two SMC-implementations of the generalized PHD and the adapted standard iFilter from Section 6.3.4.3 are numerically compared. The only difference is given by the parameterization of the filters and the fact that the EoA is not processed in this evaluation. Therefore, only the differences to Section 6.3.4.3 are explained in the following. The standard deviations are set to σϕ = 1.0 rad for the AoA andστ= 100.0c s for the RToA, wherecdenotes the speed of light.
The generalized PHD filter is implemented including the approximations proposed in (6.85) and (6.86), where Nmin≡min(m,3),Nmax ≡6 and the threshold for signifi-cance of a partitionτ≡1.0·1010. Here,mdenotes the number of received multipaths.
The FOV, that is, the area of possible MS locations which is predicted by the ray tracer is given by
FOV≡[644489.0,646999.0]×[5494207.0,5497557.0]. (6.114) The probability of detection of the adaption of the iFilter is given bypD(x) ≡0.75 for allx∈X, whereX ≡FOV×R2. For the generalized PHD filter the probability of detection is modeled by (6.94), whereq ≡pD. The occurrence of clutter in a set of multipaths is modeled by λΦ ≡0.01, which is equal to the clutter density of the generalized PHD filter. The adaption of the standard iFilter estimates this quantity.
The probability of detection in the hypothesis space Xφ is set topD(φ) = 0.3. The
adaption of the standard iFilter uses the following transition probabilities. The tran-sition probability fromXφ to the target state space X is set to Ψ(x|φ) = 0.3, the transition probability inXφis defined as Ψ(φ|φ) = 0.1 and the transition probability from X to Xφ is given by Ψ(φ|x) = 0.3. For the adaption of the standard iFilter the maximal number of particles is set to 1500 and for the generalized PHD filter the maximal number of particles is restricted by 700.
It can be seen from the RMSE–values after 50 MC runs (using the same data set) (see Figure 6.32) that both filters show a comparable performance until iteration 30.
This is caused by the information quality of the received measurements (see Figure 6.33 and Figure 6.34), which is sufficient, such that the small number of particles used by the generalized PHD filter and the approximation criteria (6.85) and (6.86) do not decrease the performance of the generalized PHD filter compared to the stan-dard iFilter adaption. In some iterations the criteria (6.85) and (6.86) imply that no partition is significant, which is caused by the small number of particles and the small width of the likelihood function defined in (6.107) and thus the computation time of the generalized PHD filter is smaller for these iterations than the computation time of the adaption of the standard iFilter. Furthermore, it can be seen from the RMSE visualization in Figure 6.32 that the RMSE of the generalized PHD filter is larger than the RMSE of the adapted iFilter for the iterations 30–80. For some MC runs of the evaluation the generalized PHD filter yields for this time period a smaller (around 200m) RMSE–value than the mean–RMSE of the adapted standard iFilter.
However, due to product form of its likelihood function the generalized PHD filter is more restrictive than the adapted standard iFilter, which implies in combination with the small number of particles an instable behavior for these iterations. Additionally, in this time period the number of clutter in the received multipaths is rather high and due to non–adaptive clutter rate of the generalized PHD filter the adaption of the standard iFilter yields a more accurate estimate and is more stable, since it is able to estimate the clutter online. The situation changes drastically after iteration 85, when the generalized PHD filter is able to estimate the target state more accurately than the adapted standard iFilter. This is implied by the fact that the estimated multi-paths better match to the predicted multimulti-paths of the ground truth position coming from the ray tracer (see Figures 6.33, 6.34). The restrictive likelihood function of the generalized PHD filter then filters out rigorously hypothetical emitter positions with non–matching multipath predictions. This is the reason why the generalized PHD filter outperforms the standard iFilter adaption for the last ten iterations, even though the number of particles used by the generalized PHD filter is smaller than half the number of particles used by the adapted standard iFilter.
In summary it is shown that the proposed generalized and standard PHD intensity filter can be successfully applied to real world BML data, which is collected under demanding boundary conditions (small number of antenna arrays and small
band-width). The generalized PHD filter would clearly benefit from enlarging the number of particles and decreasing the approximation significance–threshold defined in (6.86).
However, due to the high numerical complexity these approximating conditions are needed and imply an instable behavior of the generalized PHD filter under real world conditions. Future work therefore should concentrate on reducing the numerical plexity without approximating the update equation. One approach is parallel com-putation of the update equation of the generalized PHD filter for different particles and/or partitions.