**1. Introduction**

Inertial navigation systems (INSs) are widely used with price being a crucial factor predeter‐ mining the application. In case of unmanned vehicles, "low-cost" or "cost-effective" systems are preferred in general applications. As long as low-cost inertial measurement units (IMUs) use micro-electro-mechanical system (MEMS)-based inertial sensors, they are small in dimen‐ sion and light and are low power consuming, and thus their presence can be found for in‐

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stance inmobilephones,terrestrialvehicles,robots, stabilizedplatforms aswell as inunmanned aerial vehicles (UAVs), small aircraft, and satellites. Even if the applications are cost-effective, theperformancecommonlyrequiresdatafusionfromvarious sourcesduetotheinertial sensors' imperfections, such as insufficient resolution for navigation purposes, bias instabilities, noise, etc. Therefore, special data treatment is required. In sense of aerial applications, the usage of UAVs has increased rapidly in recent years. UAVs can be used in many applications [1, 2] fulfilling a broad spectrum of assignments in fields of reconnaissance, surveillance, search and rescue, remote sensing for atmospheric measurements, traffic monitoring, natural disaster response, damage assessment, inspection of power lines, or for aerial photography [2, 3]. These applicationsgenerallyrequirenavigationtobe carriedoutwhichincludes theposition,velocity, andattitude(PVA)estimation[4],andthuscost-effectivesolutionshavebeencommonlystudied and implemented with advantage.

Current research and development in the area of low-cost navigation systems are focused on small-scale and integrated solutions [5]. As mentioned, as long as MEMS-based IMUs are used, the evaluation process requires data fusion from other aiding sources available. These sources stabilize errors in navigation solutions and thus increase navigation accuracy. Over the last few years, a solution for vehicle navigation without absolute position measurements provided by global positioning system (GPS) or radio frequency beacons has become very popular. For indoor or low-altitude navigation, it can use for example cameras, laser scanners, or odometers in terrestrial navigation [6, 7]. However, the solutions fusing inertial and GPS measurements are still preferable for aerial vehicles operating outside in large areas simply because of unblocked GPS signals. The implementation of other aiding sensors, such as magnetometer or pressure sensors, can further enhance the overall accuracy, reliability, and robustness of a navigation system [8, 9]. Attention is also paid to data processing algorithms used for PVA estimation, so that many literature sources can be found dealing with filtering techniques used for instance complementary filters [10], particle filters [11], or Kalman filters (KFs) [12, 13]. In the last named case, the extended KF (EKF) is used most of the time since it provides an acceptable accuracy with a reasonable computational load. Therefore, KF represents one of the most used algorithms for UAV attitude estimation (see comprehensive survey of estimation techniques in [14]) and is often complemented by other algorithms and decision-based aiding [15]. Since the accuracy of navigation systems is always directly related with the choice of sensors, the chapter also includes a short introduction on sensors suitable for cost-effective navigation systems as well as topics concerning stochastic sensor parameter evaluation methods and data pre-processing.

The contribution of this chapter is dedicated to comparison of two approaches suitable for navigation solutions and thus provides a clear understanding of the differences in the studied approaches. These approaches are tuned to satisfy a certain level of accuracy and applied on real flight data. The results are compared to an accurate referential attitude obtained from a multi-antenna GPS receiver. Such comparison with an independent referential system provides a thorough evaluation of performances of the studied approaches and shows their capabilities to handle sensors' imperfections and vibration impacts of harsh environment on the accuracy of attitude estimation in aerial applications.


*2.4. Statistical Analysis*

We assessed all variables for normality with the Shapiro–Wilk test and considered a variable to have a normal distribution if the probability value for a test was greater than or equal to 0.05. To describe riders' demographic characteristics, we computed the means, standard deviations, and 95% confidence intervals of rider age, BMI, Spanish foot size, height, and weight.

We measured intra-trial reliability with the three records for each CFI for each rider. To evaluate reliability within trials in each rider, we computed intra-class correlation coefficients. For interpreting ICC values, we considered values less than 0.40 as poor, values between 0.40 and 0.59 as fair, values between 0.60 and 0.74 as good, and values 0.75 or greater as excellent [30,31]. Portney and Watkins [32] proposed that reliability coefficients greater than 0.90 were sufficient for clinical measurement. We also calculated the mean scores and the standard error of measurement (SEM) [30]. We used Brand and Altman's [33] formula for the SEM as follow: SEM = SD × sqrt (1 − ICC).

The minimal detectable change (MDC) can be used to assess the minimal magnitude of change required to be 95% confident that the observed change between the 2 tests reflects the true change and not measurement error [34]. The MDC was calculated as: 1.96 × SEM × √2.

For demonstrating the effect size of the comparisons, the Cohen d coefficient was calculated. Cohen's d effect size can be interpreted as follows: values ≤0.20 indicate slight effects, values between 0.20 and 0.49 indicate fair effects, values between 0.50 and 0.79 indicate moderate effects, and values larger than 0.79 indicate large effects [35].

We computed nonparametric Mann–Whitney U tests to assess differences among CFIs groups. For all tests, we considered *p* values < 0.05 to be statistically significant. We used SPSS 19.0 for Windows (IBM, Chicago, IL, USA) to perform all analyses.