a sparse undersea sensor network decision support system based on spatial and temporal random field...
TRANSCRIPT
A Sparse Undersea Sensor Network Decision Support System Based on Spatial and Temporal Random Field
April 10, 2007
Defense and Security Symposium 2007
Dr. Bo LingMigma Systems, Inc.
Dr. Mike TraweekOffice of Naval Research
Dr. Tom WettergrenNaval Undersea Warfare Center
Presentation Outline
- Problem Statement
- Forward & Backward Mapping Mitigation
- Spatial & Temporal Layering Discrimination
- A Simulation Tool for Target Detection and Tracking
- Random Field Estimation of Undersea Sensor Network
- Conclusion
Problem Statement
A Large Surveillance Region
In a passive submarine detection system, we need to consider:
- Number of sensors required in the sparse sensor network
- Probability of submarine detection when a submarine might be detected by only one sensor at one particular time instance
- False alarm mitigation
No Overlapping
Problem in Motion Based Detection
In a sparse sensor network, targets can be detected and tracked over a period of time.
As a target moves, although it may not be detected by any sensors at certain time instance, it will be detected by a number of sensors over a period of time.
When positive and negative reports co-exist, it is difficult to determine if targets actually exist!
Basic System Architecture
Although targets in a surveillance region may not always be detected, as they move, sensors can collectively detect, classify and track them.
Random Field for Undersea Sensor Network
A typical random field model can be described by the following difference equation:
Random Field Estimation
In random field modeling setting, it is always assumed that Z = {Zij | (i, j) } is stationary and Gaussian distributed with known or empirical mean and variance.
Gaussian Random Field (GRF) or Gaussian-Markov Random Field (RMRF) modeling has been widely used in image processing.
In undersea sensor network, the assumption of stationary process and Gaussian or Markov distribution needs to be carefully verified.
Our Approach for Random Field Estimation
Based on the continuation of sensor outputs, the random field zf over two consecutive samples must be similar provided that the sampling rate is large enough or the sampling time is small enough.
Mathematically, suppose and are the random fields at the sampling time instants k and k+1. Then, based on the continuation property, the quantity of || - || is small.
Minimize:
Forward & Backward Mapping Mitigation
FBMM Technology (Patented)
It can be used to reduce false reports while keeping the positive reports.
A Simulated Network
2020 sq. miles
Two targets at 180 m/h
200 sensors
Detections after 2 hours
Both true and false detections co-exist
Difficult to Find Targets Visually
What an operator will see after two-hour monitoring.
Are there any targets?
Random Field Estimation
Random field estimated using our LMI-based optimization
Mathematical Morphological Operation
Morphological operators can be applied to reduce false detections
Backward Mapping
Backward Mapping for refined situation awareness.
Spatial & Temporal Layering Discrimination
STLD Technology (Patented)
STLD technology applies temporal patterns to further reduce the false reports.
Gap Statistics Based Clustering
Gap Statistic (Robert Tibshirani, Guenther Walther, Trevor Hastie, “Estimating the number of clusters in a data set via the gap statistic”, J. R. Statist. Soc. B (2001), 63, Part 2, pp. 411-423) is a technique used to estimate the number of clusters in the data.
Individual Clusters in Temporal Patterns
Temporal & Spatial Mitigation
Detections in each cluster are checked for both temporal and spatial patterns.
Temporal Pattern - True detections must show temporal trend
Spatial Pattern - True detections must be relatively close spatially
False Reports Reduction Using STLD
After FBMM Processing After STLD Processing
Combine FBMM & STLD
FB
MM S
TL
D
Target Synthetic Tracks
Groundtruth Synthetic Tracks
A Simulation Tool
Conclusion
- In a sparse undersea network, targets can be detected and tracked based their motion
- Our patented Forward & Backward Mapping Mitigation technology and Spatial & Temporal Layering Discrimination technology can help operator make better decisions
- The mixture of both positive and negative reports makes it difficult for an operator to determine whether or not targets are actually present