Accurate assessment of the degree of liver fibrosis is important for estimating prognosis and deciding on an appropriate course of treatment for cases of chronic liver disease (CLD) with various etiologies. Because of the inherent limitations of liver biopsy, there is a great need for non-invasive and reliable tests that accurately estimate the degree of liver fibrosis. Ultrasound (US) elastography is considered a non-invasive, convenient, and precise technique to grade the degree of liver fibrosis by measuring liver stiffness. There are several commercial types of US elastography currently in use, namely, transient elastography, acoustic radiation force impulse imaging, supersonic shear-wave imaging, and real-time tissue elastography. Although the low reproducibility of measurements derived from operator-dependent performance remains a significant limitation of US elastography, this technique is nevertheless useful for diagnosing hepatic fibrosis in patients with CLD. Likewise, US elastography may also be used as a convenient surveillance method that can be performed by physicians at the patients’ bedside to enable the estimation of the prognosis of patients with fatal complications related to CLD in a non-invasive manner.

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The odometry information used in mobile robot localization can contain a significant number of errors when robot experiences slippage. To offset the presence of these errors, the use of a lowcost gyroscope in conjunction with Kalman filtering methods has been considered by many researchers. However, results from conventional Kalman filtering methods that use a gyroscope with odometry can unfeasible because the parameters are estimated regardless of the physical constraints of the robot. In this paper, a novel constrained Kalman filtering method is proposed that estimates the parameters under the physical constraints using a general constrained optimization technique. The state observability is improved by additional state variables and the accuracy is also improved through the use of a nonapproximated Kalman filter design. Experimental results show that the proposed method effectively offsets the localization error while yielding feasible parameter estimation.