# Conditional Dependencies and Position Fixing
## 2 Understanding Position Fixing  
Making a fix is an inference scheme that involves evidence and hypotheses [6; 7]. One can reason as to the particular location of the truth that represents the observer's position given all the available observations, as well as to the knowledge regarding each of them [8]. I illustrate the idea in Figure 1a, in which I display two pieces of evidence (o1 and o2), with the sets of instances indicating their dispersions. I also present the single-hypothesis point labelled H1. The statement that a given location (H1) is the true position gains some support from each piece of available evidence. I assumed that the involved data were diversified regarding their quality. For the situation presented in Figure 1, Observation o1 seems to be more reliable than Observation o2. The density of the instances that fall close to o1 is greater than that of the ones that fall close to o2. I present the results of the processing, including the instance sets, in Figure 1b. Statistical evaluations of the example system indications are missing. Instead, I converted the raw data to histograms, which I further transformed to injective diagrams of the density functions. Local injection is required to obtain solutions for many problems that engage random variables [9]. I present the basic scheme followed during the position fixing and imprecise data handling in Figure 1. The general pattern of the presented rational also fits the arrangement. In order to calculate the support measure of the truth that a point represents the true location, we need to define and solve the partially related tasks, evaluate the trustworthiness of the observations at hand, and propose the methodology of the support estimation included in each observation. Taking advantage of fuzzy sets and Bayesian conditional dependencies enables an adequate approach proposal. Finally, we need to upgrade the basic probability assignments and their combinations. The results of the conjunctive associations embed the sought support measures. Researchers have performed many studies on the modified concept of random data handling [10], which represents a shift towards the discrete space of solutions and the mathematical theory of evidence as the basic platforms of processing schemes. The broad scope of consequences includes the verified approach to the meaning of the accuracy. A natural feature of the new approach is the ability to evaluate the truth attributed to the obtained solutions. A supporting measure of a ship's fixed location at a particular position  
Figure 1: (**a**) Two observations with examples of their dispersions and single-hypothesis locations; (**b**) horizontal-axis distributions converted to histograms and their continuous versions. is embedded in the processing scheme. Most researchers start from statistical evaluations of the random instance behaviour, and they often encounter Gaussian distributions. The included uncertainty usually refers to a variety of available standard deviations. Self-contained modern applications should contain initial data processing modules. Their lifecycles should contain a learning phase, while the raw input data should be analysed to mine the necessary initial items. Bayesian conditional dependencies deliver a unique opportunity to evaluate the hypothesis truth based on the related evidence at hand. In nautical science, observations and the linked knowledge are the main constituents of the evidence. The widely known information on the taken observation represents an instance of random variables, and usually sets of samples are available. The data distribution functions need to be identified to render the sets useful. Attempts to consider the Gaussian functions as density patterns dominated in the traditional approach. However, raw sets are forgotten and statistical measures, such as standard deviations and elliptic or circular errors, are used instead. The informative context of the initial raw data is rather rich; thus, the method of using them should be reconsidered.