System and method for optimal sensor placement

A method for determining an arrangement of sensors for monitoring a space, comprising:

• receiving, from a first sensor of at least two sensors, a first sensor data comprising at least one time-series observation representing at least a first activity and a second activity;
• receiving, from a second sensor of the at least two sensors, a second sensor data comprising at least one time-series observation representing the first activity and the second activity;
• generating, by a processor, a first model for the first activity involving a first progression through a plurality of states indicated by at least a portion of the first sensor data;
• generating, by the processor, a second model for the second activity involving a second progression through a plurality of states indicated by at least a portion of the first sensor data;
• generating, by the processor, a third model for the first activity involving a third progression through a plurality of states indicated by at least a portion of the second sensor data;
• generating, by the processor, a fourth model for the second activity involving a fourth progression through a plurality of states indicated by at least a portion of the second sensor data;
• receiving, from the first sensor, a third sensor data comprising at least one time-series observation representing at least the first activity and the second activity;
• receiving, from the second sensor, a fourth sensor data comprising at least one time-series observation representing at least the first activity and the second activity;
• determining, using the processor, a likelihood that the first model generated at least a portion of the third sensor data, a likelihood that the second model generated at least a portion of the third sensor data, a likelihood that the third model generated at least a portion of the fourth sensor data, and a likelihood that the fourth model generated at least a portion of the fourth sensor data;
• calculating, using the processor, a pair-wise distance between each sensor-specific determined likelihood to obtain calculated distances;
• grouping, using the processor, the calculated distances for the likelihoods involving the first sensor, and grouping, using the processor, the calculated distances for the likelihoods involving the second sensor, to obtain grouped calculated distances;
• and
• determining, using the processor, a first relevance of the first sensor and a second relevance of the second sensor for capturing the first activity and the second activity by executing a regression model using the grouped calculated distances,
• wherein one of the first sensor and the second sensor is included in an arrangement of sensors used to monitor the space based on the first relevance and the second relevance determined using the processor, and the other of the first sensor and the second sensor is excluded in the arrangement of sensors used to monitor the space based on the first relevance and the second relevance determined using the processor.

A system for determining an arrangement of sensors for monitoring a space, comprising:

• a communication interface used to communicate over a communications network;
• a user interface;
• and
• a controller comprising a memory that stores instructions, and a processor that executes the instructions,
• wherein, when executed by the processor, the instructions cause the system to execute a process comprising:
• receiving, from a first sensor of at least two sensors, a first sensor data comprising at least one time-series observation representing at least a first activity and a second activity;
• receiving, from a second sensor of the at least two sensors, a second sensor data comprising at least one time-series observation representing the first activity and the second activity;
• generating, by the processor, a first model for the first activity involving a first progression through a plurality of states indicated by at least a portion of the first sensor data;
• generating, by the processor, a second model for the second activity involving a second progression through a plurality of states indicated by at least a portion of the first sensor data;
• generating, by the processor, a third model for the first activity involving a third progression through a plurality of states indicated by at least a portion of the second sensor data;
• generating, by the processor, a fourth model for the second activity involving a fourth progression through a plurality of states indicated by at least a portion of the second sensor data;
• receiving, from the first sensor, a third sensor data comprising at least one time-series observation representing at least the first activity and the second activity;
• receiving, from the second sensor, a fourth sensor data comprising at least one time-series observation representing at least the first activity and the second activity;
• determining, using the processor, a likelihood that the first model generated at least a portion of the third sensor data, a likelihood that the second model generated at least a portion of the third sensor data, a likelihood that the third model generated at least a portion of the fourth sensor data, and a likelihood that the fourth model generated at least a portion of the fourth sensor data;
• calculating, using the processor, a pair-wise distance between each sensor-specific determined likelihood to obtain calculated distances;
• grouping, using the processor, the calculated distances for the likelihoods involving the first sensor, and grouping, using the processor, the calculated distances for the likelihoods involving the second sensor, to obtain grouped calculated distances;
• and
• determining, using the processor, a first relevance of the first sensor and a second relevance of the second sensor for capturing the first activity and the second activity by executing a regression model using the grouped calculated distances,
• wherein one of the first sensor and the second sensor is included in an arrangement of sensors used to monitor the space based on the first relevance and the second relevance determined using the processor, and the other of the first sensor and the second sensor is excluded in the arrangement of sensors used to monitor the space based on the first relevance and the second relevance determined using the processor.