A minimax approach to sensor fusion for intrusion detection

The goal of sensor fusion is to combine the information obtained by various sensors to make better decisions. By better, it is meant that the sensor fusion algorithm provides, for example, better detectability or lower false alarm rates compared to decisions based upon a single sensor. This work is motivated by combining the data gathered by multiple passive infrared (PIR) sensors to detect intrusions into a room. Optimal decision theoretic approaches typically include statistical models for both the background (non-event) data, and intrusion (event) data. Concurrent work by the author has shown that by appropriately processing multiple PIR data streams, a statistic can be computed which has a known distribution on the background data. If the distribution of the statistic during an event is known, optimal decision procedures could be derived to perform sensor fusion. It is shown, however, that it is difficult to statistically model the event data. This paper thus focuses on using minimax theory to derive the worst-case event distribution for minimizing Bayes risk. Because of this, using the minimax distribution as a surrogate for the unknown true distribution of the event data provides a lower bound on risk performance. The minimax formulation is very general and will be used to consider loss functions, the probability of intrusions events and consider non-binary decisions.