Noise performance of a novel total least squares approach to source location estimation.
Wm. Garth Frazier, Kenneth E. Gilbert, Xiao Di · The Journal of the Acoustical Society of America · 2009
One of the advantages of the time-of-arrival (TOA) representation for the source location problem is that it can be formulated such that the unknown variables appear linearly in the describing equations. It is known that to obtain a unique three-dimensional solution four measurements are required in the TOA case. Typically, more measurements than the minimum are available and this naturally leads to an over-determined problem for which an optimal estimate is sought. One method of solution is weighted least-squares (LS). The noisy measurements include the TOAs of the impulse at each acoustic receiver as well as the locations of the receivers. In the linear formulation these measurement values appear on both sides of the equation Ax=b, and not just on the right side. Application of a linear total least-squared (TLS) error method permits representation of the uncertainty on both sides of the equation. Moreover, the additional computations required in the TLS approach are not significantly greater than the LS approach. In this paper, we examine the noise performance of TLS solutions and demonstrate the significant reduction in bias obtained over the LS approach at the expensive increased sensitivity. Results from simulation and field experiments are provided.