# Compensation of Measurement Uncertainty in a Remote Fetal Monitor
When developing new technology, guaranteeing precision and reliability for the chosen environment contributes to achieving safer results and sound medical attention. Under these conditions, the main problem is to reassure the reliability of the data obtained by the remote fetal monitor, since health-care professionals would not be present, and there would be only a few samples of variables (heart rate (HR), uterine activity) that lead to the detection of anomalies. Therefore, the analysis of measurement uncertainty becomes necessary. For reliable estimation of measurement uncertainty, it is necessary to guarantee some properties (distribution independence, a large sample size, and a normal distribution). Health-care professionals are not familiar with the measurement process carried out by remote fetal monitoring, and, in general, only have a few samples. This means it is not possible to verify the hypotheses required so that the evaluator may have the properties required by a good estimator. By means of a statistical approach, several works related to uncertainty estimation have been conducted, for cases where the hypothesis of classical theory is not verified. A fetal monitor is a stochastic process that has few samples available. Therefore, it is very difficult to model by using conventional methods. Different approaches have been used when the hypothesis of the classical theory is not verified, including the Monte-Carlo method (MCM) [12], parametric and non-parametric theory formulation [13], adaptive estimators [14], spectrum-based estimation [15], stochastic gradient [16], and mean square error [17] estimators with Cramer-Rao type restriction and reliability estimation under measures degradation [18]. The MCM is a widely used tool for modeling stochastic systems since with a large enough sample, the probability that an estimator will deviate from the expected value can be as small as required. The MCM is used to get information related to estimator properties. The parameters of softening and form of estimating function are adjusted to modify the performance of maximum probability estimators. The MCM can be used for modeling unknown distribution functions. The parametric and non-parametric models are wide probability function estimation methods; theory formulation has been developed considering local asymptotic length and restrictions in sample size. Adaptive estimators that guarantee the consistency in finite samples for any distribution function are helpful in the fetal monitor application. The term adaptive integrates the concept that such estimators adapt to the sample using data to estimate a non-parametric density function. Adaptive estimators have been applied using the least-squares method with finite samples, reaching substantial increases in efficiency, but with hypotheses that are difficult to verify for applications with a few samples. The spectrum-based method is useful when the relationship between observations and parameter model is noisy, potentially non-linear, and not invertible. The stochastic gradient estimation is a numeric method that is stable and robust for fitting parameters and predicting standard errors well. Even though only the typical case, with some modifications, was considered, the hypothesis that let the Cramer-Rao type limit such estimators have been changed. The mean square error can be improved by implementing estimatorswith parametric restrictions that do not satisfy certain conditions. With a new definition of bias in restricted surroundings, a Cramer-Rao restriction type was determined for the pondered mean square error estimators, for normal distribution only. Correlated perturbations were not considered. The reliability estimation for a system whose degradation measures are monotonous, can obtain the fault time distribution, and, therefore, system reliability. The remote fetal monitor has a context application.