Comparison of Kalman and Least Squares Filters for Locating Autonomous Very Low Frequency Acoustic Sensors

Under the Office of Naval Research sponsorship, the Marine Physical Laboratory has designed, fabricated, and taken to sea self-contained, freely drifting acoustic sensors which can measure signal propagation and ambient ocean noise in the 1 to 20 Hz band for up to 25hour periods. The deployment of several freely drifting floats forms an array of sensors whose outputs can be combined after the experiment with a beamformer. Float locations must be known in order to beamform their outputs. The floats generate and receive acoustic pulses and thereby measure float-to-surface and float-to-float travel times. A Kalman filter and a least squares estimator have been developed to estimate float positions from travel time measurements. Computer simulation is used to compare filter performance under several deployment scenarios. The effects of increasing the randomness of float movement and the measurement error are also investigated. Results show that the Kalman filter performs better than the least squares filter when the floats are subjected to small magnitude accelerations between measurements. This is true even when there are large measurement errors. Neither filter was sensitive to relatively major changes in deployment geometry as long as the sound-speed profile is known exactly. However, deploying the floats in a vertical array did degrade the performance of both filters for the bottom baseline geometry considered.