Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter
Abstract
:1. Introduction
2. Problem Formulation
3. Review of Distance Partitioning and Distance Partitioning with Sub-Partitioning
3.1. Distance Partitioning (DP)
3.2. Distance Partitioning with Sub-Partitioning (DPSP)
4. The Proposed SNN Partitioning
4.1. SNN Similarity
4.2. SNN Partitioning Algorithm
4.2.1. SNNSP
- Step 1: Select the Mahalanobis distance as the distance measure , and then compute the distance between each pair of measurements.
- Step 2: Find K nearest neighbors for each measurement, and then compute the SNN similarity between each pair of measurements.
- Step 3: Decide the similarity threshold set . The similarity threshold set can be selected from its effective range, which is between the minimum and maximum of the SNN similarity, i.e., belonging to . K is usually small, and so is the number of partitions by the SNNSP. Note that the neighborhood list size will decide the maximum of the upper similarity threshold.
- Step 4: For each given , leave all pairs of measurements satisfying in the same cell. partitions of the measurement set Z can be generated by selecting different similarity thresholds. Some resulting partitions might be identical, and hence, need to be discarded so that each partition at the end is unique.
4.2.2. SNNDP
- Step 4: For a given , compute the SNN density of every measurement. Measurements whose SNN densities are not less than a given SNN density threshold are considered as core measurements, while those that are less than but larger than 0 are considered as border measurements.
- Step 5: Leave all pairs of core measurements satisfying in the same cell. For the border measurement , if the measurement is the nearest core point according to the SNN similarity, will be put in the cell where is.
4.3. Parameterizations
5. Simulation Results
5.1. Simulation Setup
5.2. Scenarios and Results
5.2.1. Differing Densities
5.2.2. High Clutter
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Require: , , , |
Initialize: CoreBound(i) = 0, CellNumber(i) = 0, |
CellId = 1 the current cell id to 1 |
% Find the core measurements and boundary measurements |
for |
num = 0 |
for |
if |
num = num + 1 |
end if |
end for |
if num |
CoreBound(i) = 1 |
else if |
CoreBound(i) = −1 |
end if |
end for |
% Find cell numbers for core measurments |
for |
if CellNumber(i) = 0 & CellBound(i) = 1 |
CellNumber(i) = CellId |
CellNumbers = FindNeigbors(i,CellNumbers,CellId) |
CellId = CellId + 1 |
end if |
end for |
% Find the cell of boundary measurements |
for |
if CellNumber(i) = 0 & CellBound(i) = −1 |
if |
CellNumber(i) = CellNumber(m) |
end if |
end if |
end for |
% the function FindNeigbors() |
function CellNumbers = FindNeigbors(i,CellNumbers,CellId) |
for |
if & & CellNumber(j) = 0 & CellBound(j) = 1 |
CellNumber(j) = CellId |
CellNumbers = FindNeigbors(j,CellNumbers,CellId) |
end if |
end for |
Expected Number of Measurements per Target | Desirable Range of K |
---|---|
10 | 4–6 |
15 | 6–12 |
20 | 6–16 |
30 | 6–16 |
40 | 6–18 |
50 | 6–22 |
100 | 8–45 |
Value of K | Desirable Range |
---|---|
K | of |
8 | 2–5 |
12 | 2–8 |
16 | 2–10 |
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Han, Y.; Han, C. Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter. Sensors 2019, 19, 2665. https://doi.org/10.3390/s19122665
Han Y, Han C. Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter. Sensors. 2019; 19(12):2665. https://doi.org/10.3390/s19122665
Chicago/Turabian StyleHan, Yulan, and Chongzhao Han. 2019. "Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter" Sensors 19, no. 12: 2665. https://doi.org/10.3390/s19122665
APA StyleHan, Y., & Han, C. (2019). Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter. Sensors, 19(12), 2665. https://doi.org/10.3390/s19122665