*4.3. Data Evaluation*

Several parameters were measured in both sets of scenario experiments. The most important were the ranges and relative bearings, i.e., relative azimuth angles. In general, the range of the first detection and last detection for each target was recorded. These were direct relative measurements of the sensor in the local coordinate system, related to sensor position. Measurements from several iterations (up to 11) were collected for each scenario to obtain good statistical evaluations. The Student's t-distribution was assumed because of the small sample size. The results showed that in this particular case it was a reasonable approach. Based on this statistical analysis, the average (Equation (1)), standard deviation (Equation (2)), and standard error (Equation (3)) were calculated for each scenario.

$$
\overline{\mathbf{x}} = \frac{\sum\_{i=1}^{n} \mathbf{x}\_i}{n} \tag{1}
$$

$$
\sigma\_{\mathbf{x}} = t\_{n-1, \alpha} \sqrt{\frac{\sum\_{i=1}^{n} (\mathbf{x}\_i - \overline{\mathbf{x}})}{n-1}} \tag{2}
$$

$$S\_{\overline{\mathbb{Z}}} = \frac{\sigma\_{\overline{\mathbb{Z}}}}{\sqrt{n}} \tag{3}$$

where:

*x* represents the measured value,

*xi* represents measurement in *i-th* iteration,

*n* represents the number of iterations (number of measurements),

*x* is the mean value of *x* for *n* measurements,

σ*<sup>x</sup>* is the standard deviation for *n* measurements of *x,*

*tn*−1,<sup>α</sup> is the critical value in Student's t-distribution for *n* degrees of freedom and confidence, level α (68.3% in this study), and

*Sx* is the standard error of *x* (the standard deviation of the mean value).

Using this method, the minimum and maximum detection range can be obtained for various bearings, which provides an empirical field of view.

#### **5. Results and Discussion**

#### *5.1. Stationary Scenario*

In this scenario, measurements were performed individually for the five targets presented in Figure 5. The object travelled along the moving lane; this target was observed on the screen and the detection data were recorded. The measurement numbers varied from four to six, depending on the detection observation and results achieved; the results are compiled in Table 2. At least four in/out iterations were made for each artificial target. If the results were coherent, performing more measurements was pointless. The results achieved were very cohesive and as such, the number of observations performed was reduced. The data achieved were enough to determine if the particular object was well or poorly detected. The exemption to this rule were the swans, which are live animals and could not be steered. They approached the vehicle twice and moved away. Thus, two measurements for the minimum detection range and two for the maximum detection range were measured.

**Table 2.** Minimum and maximum detection distance results from the Stationary Scenario.


Table 2 presents the minimum and maximum distances of detection along the moving lane. The mean values as well as standard deviations and standard errors are provided for the minimum detection and the maximum detection range. The fender was not detected at all and thus it is not included in the table. The swans were observed for a few minutes and during this time two measurement lines were chosen. The best detection results were achieved for the radar reflector, wherein the maximum distance was determined at the end of measurement line although the real maximum distance was larger. The measured minimum distance was the best for all the analyzed targets. Despite the complicated direct target observations on the screen and the target being mixed with others, the post-processing of data allowed the airtoy detection to be extracted and good data

were obtained. The lifebuoy target visibility was very good and the target was easily distinguishable. The swans were visibly distorted but observable.

The results indicate that most objects were visible at a distance of approximately 13–17 m. The minimum distance was generally 3–4 m based on a geometrical distribution. In summary, this stage of research shows that the radar can detect even small targets for anti-collision. However, small floating targets, such as fenders and small buoys, are not detected.
