Yi Wang, Bhaskar Krishnamachari, Qing Zhao, and Murali Annavaram 1 The Tradeoff between Energy Efficiency and User State Estimation Accuracy in Mobile.

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Yi Wang, Bhaskar Krishnamachari, Qing Zhao, and Murali Annavaram 1 The Tradeoff between Energy Efficiency and User State Estimation Accuracy in Mobile Sensing Ming Hsieh Department of Electrical Engineering University of Southern California Department of Electrical and Computer Engineering University of California, Davis MobiCase ‘09 October 26, 2009

Motivation 2 The scenario for human- centric, mobile device based sensing: Sensors need to be managed intelligently to maintain device/application lifetime We study two essential but conflicting metrics: Energy consumption User state estimation accuracy

3 Problem modeling and assumptions The stationary deterministic sensing policy Estimation of user state for missing observations Visualizing the tradeoff: energy vs. accuracy Conclusion and Ongoing/future work Outline

4 Model Sensor samples the user state sequence according to some pre-defined policy Provide state estimation when observations are missing Assumptions Time is discretized User state transition is Markovian, with N states In each time slot, the sensor can be either “sampling” or “idle” If sensor samples User state is detected at that time slot A corresponding unit of energy is consumed Preliminaries

5 A stationary deterministic sampling policy “If the sensor detects user state i at some time t, it will stay idle for I i time slots, and is re-sampled at time slot t+I i.” The steady state probability of detecting state i in an observation Overall expected sampling interval Define the overall expected energy consumption as: The Sensing Policy

6 Method 1: Picking the most likely state for each time slot in the estimation interval, given neighboring observations Expected estimation error for time slot t Expected per-slot estimation error of the whole process E[W]: Expected number of incorrect estimations in one estimation interval E[N]: Expected number of time slots in one estimation interval ij tmtm t m + I i ? t Estimation interval State Estimation

Method 2: Estimate the most likely state sequence for the whole estimation interval, given a leading observation Always find the highest probability path Expected sequence error for one estimation interval Expected sequence error for the whole process 7 ij tmtm t m + I i ? Estimation interval State Estimation

8 Goal: Visualize the tradeoff between energy consumption and expected state estimation error By varying I i, the length of idle intervals Test policy on two-state discrete time Markov chains Different combinations of I 1 and I 2 are tested (1 ≤ I 1 ≤ 30, 1 ≤ I 2 ≤ 30) Six Markov chain transition probability matrices are investigated: Analytical result vs. Simulation result In simulation, user state data is generated based on Markov model Policy is applied through the simulation process 5000 time slots in each simulation run Case Study

9 Expected per-slot estimation error vs. Expected energy consumption Analytical Error range: [0, 1-max{π 1, π 2 }] Result: Method 1 Simulation

10 Expected sequence estimation error vs. Expected energy consumption Analytical Error range: [0, 1] Result: Method 2 Simulation

11 An energy budget is given The optimal stationary deterministic policy can be obtained by Searching through all sensing interval combinations The one producing the lowest error is selected Results for two-state Markov chains Picking the best policy Optimal sensing interval sizes vs. Energy budget

12 A stationary deterministic sensing policy State estimation mechanisms Energy efficiency vs. user state estimation accuracy The optimal stationary deterministic policy can be obtained by exhaustively search A more computationally efficient algorithm for optimal policy Performance of sensing policy on real data trace Conclusion & Ongoing/Future Work

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