### A linear least square approach for navigation using ultrasonic waves

#### Abstract

In this paper, we present an optional method for position and velocity measurements of navigation by means of echolocation. The proposed idea can localize a moving object with various velocities in three dimensional (3D) spaces. In addition, this method can determine the object’s position and velocity with one-time computation from the original non-linear model using the linear least square-based method. To satisfy the navigation problem dealing with the additive noise, Color Gaussian Noise is considered mainly for the performance study in computer simulations. The designed system consists of one loudspeaker and four acoustical microphones. An echo received from the microphone is converted into a one-bit stream based on a four-channel delta-sigma-modulation board. Next, FPGA is applied to compute the recursive cross correlation using one-bit signal processing. The object considered as a flying ball is positioned in x-y-z coordinates. Study of position dilution of precision involving with the uncertainty in the object position is also studied. The object’s velocity is calculated using a pair of linear-period-modulated ultrasonic signals. The validity is evaluated by the probability density function (PDF) and the cumulative density function (CDF) from the repeated experimental results.

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