A linear least square approach for navigation using ultrasonic waves

Abstract

This paper presents a method to locate a moving object with velocities in three dimensional (3D) spaces by echolocation. This method can determine the object’s position and velocity measurements, through computation from the original nonlinear model using a linear least square (LLS) - based approach. To satisfy the navigation problem and deal with the additive noise, Colored Gaussian Noise was considered as a performance parameter in computer simulations. The design system consisted of one loudspeaker and four acoustical microphones. An echo received from the microphone was converted into a one-bit stream, based on four channels, delta-sigmamodulation board. A field-programmable gate array (FPGA) was then applied to compute the recursive cross correlation, using one-bit signal processing. The object, considered as a fiying ball, was positioned in 3D space at x-y-z coordinates. The dilution of precision and the uncertainty in the object position were also studied. The velocity of the object was calculated using a pair of linear-period-modulated ultrasonic signals. The validity was evaluated by the probability density function (PDF) and the cumulative density function (CDF) from repeated experimental results. The results of this proposed system using an LLS-based method can provide better repeatability, when compared against the linearization-based method.