AR-P Experimental Results

In our experiments, the positioning effect factors of proposed positioning algorithms, View Angle and Similar Triangle algorithm, are analyzed according to combinations of AR objects, user’s location and the effective focal length that is the result of section 5.1. The proposed positioning algorithms are tested at 7 locations with 7 POIs. 7 test locations and 7 POIs are distributed on the second floor of a building as illustrated in Fig. 5.7, where blue points 1, 2 . . . and 7 are the test locations and red points 1, 2 . . . and 7 are the POIs known in databases. Test locations are distributed according to distances. There is one meter between each test location. POIs are marked on flat walls according to distance, height and plane as illustrated in Fig. 5.8, where numbers, located on the walls, represented the POIs and black blocks are used to match the AR objects. A coordinate system in which test location 4 is the origin, the east of Earth’s magnetic field is the x-axis, North Magnetic Pole is the y-axis and z-axis points to sky, is setup.

1,2 3

Figure 5.7: Experiment locations in map

6

Figure 5.8: AR-P experiment environment

Fig. 5.9 illustrates the system interface. Red cubes are AR objects used to match the POIs. The number in AR objects represents its POI number. The first button on the upper left side is refresh button used to return the type of taking picture; positioning button located the second button is used to perform AR-P algorithm to position.

Since the positioning effects of focal lengths calculated by different focal length exper-iments are still unknown, we need to compare or verify them with different focal lengths.

Proposed positioning algorithms are performed according to ranges of focal length from 7.5cm to 8.5cm, and unit interval is 0.1cm. 7.76cm of average focal length has the smallest positioning error in the positioning result of View Angle algorithm as illustrated in Fig. 5.9, where line 1, 2, ..., 7 represent test position 1, 2, ..., 7, and the average focal length of previous focal length experiment of View Angle algorithm is 7.69cm. There are closed positioning errors between focal length 7.76cm and 7.69cm in Fig. 5.9, so we use 7.69cm as the focal length in View Angle algorithm. Fig. 5.10 gives the positioning result of Similar Triangle algorithm, where line 1, 2, ..., 7 represent test position 1, 2, ..., 7. Compared with focal length converged in range from 7.5cm to 7.65cm of previous focal length experiment of Similar Triangle algorithm, focal length 8.08cm has the smallest positioning error. Since there are a gap of positioning error between focal length calculated by previous focal length experiment of Similar Triangle algorithm and focal length 8.08cm, we use focal length 8.08cm as the focal length in Similar Triangle algorithm.

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Figure 5.9: View Angle algorithm result: positioning error affected by focal length

Fig. 5.11 gives the positioning result of proposed algorithm according to different

dis-0

Figure 5.10: Similar Triangle algorithm result: positioning error affected by focal length

tances, where “VAGIG” represents ”View Angle Good Initial Guess” that means the View Angle algorithm with initial point (0, 0, 0), “VABIG” represents ”View Angle Bad Initial Guess” that means the View Angle algorithm with initial point (−500, −500, −500) and

“ST” is the Similar Triangle algorithm. Fig. 5.12 illustrates the positioning result of pro-posed algorithm according to the POI combination numbers. The problems of local minima exist in View Angle algorithm. Average positioning error of View Angle algorithm is 88.9cm when selecting the better initial point, but 245.95cm in poor initial points. Similar Triangle algorithm has the 74.34cm of average positioning error.

Experiment Analysis

In this section, position effect factors that may affect the accuracy of the proposed positioning algorithm are analyzed. These factors include the initial point, combinations of AR objects, user’s locations and focal lengths. To reach the highly accuracy positioning result, we show how to select these factors. Finally, the positioning results of View Angle and Similar Triangle

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Figure 5.11: Average positioning results with different test locations

Combination Numbers

Figure 5.12: Positioning result affected by combinations number algorithm are compared.

View Angle algorithm

Local minima: The existence of local minima of the evaluation function is an inevitable problem. This problem could be alleviated when the POI number we picked is more. To verify this problem, we find all local minima in evaluation function by set that −1400 <=

blue points represent the local minima, read points means POIs and the real locations is green point. From the result, poor initial point converged to local minima easily when POI numbers we picked is few and difficultly when POI numbers we picked is more. However, there still has change to converge to local minima even more POIs are selected. The selection of the initial point significantly affects the answer given by the View Angle algorithm.

Figure 5.13: Local minima with 3 points

Figure 5.14: Local minima with 7 points

Combinations of AR objects: Positioning result are affected by the combinations of AR objects due that the relation between user and AR objects provides the information of user’s location. The more combinations of AR objects we pick, the more accuracy of user’s location we get as illustrated in Fig. 5.15. Even the problem of local minima could be alleviated.

Figure 5.15: View Angle algorithm: Positioning error affected by combination numbers

Combinations of AR objects are also an important factor. The near AR objects provide the closed information of user’s location. The experiment results of the POI combinations of same plane illustrates in Fig. 5.16, where column 34 represents the combinations of P OI{3, 4}

and other columns follow this rule. POI 3, 4 and 5 are in the same plane as illustrated in Fig. 5.8. POI combinations {3, 4}, {3, 5} and {4, 5} are nearly the same in positioning relations and POI combinations{3, 4, 5} are the sum of those of POI combinations, therefore POI combinations {3, 4, 5} have closed positioning result with POI combinations {3, 4}, {3, 5} and {4, 5}. Average positioning errors of those combinations are above 150cm. POI combinations{1, 5, 6} and {2, 3, 7} have 50cm of the average positioning error due to the POI

selections of diversity. The more diversity the POI combinations have, the more information of user’s location they provide and there would have the better position results.

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Figure 5.16: Positioning error affected by POI combinations of same plane

Distance between user and POI combinations would affected the position result due that the evaluation functions of View Angle algorithm are the relation of view angle between POIs and user. Tiny touch error when drag-and-drop AR objects may cause the error of view angle calculation and then the positioning error. Fig. 5.17 gives the experiment result of distant POI combinations. POI 1 and 2 are at the near plane; POI 3, 4 and 5 are at the far plane as illustrated in Fig. 5.8. Experiment results show the POI combinations {1, 2, 7}

have better positioning result than the result of POI combinations {3, 4, 7}, {3, 5, 7} and {4, 5, 7}. The positioning effect factor of distant POI combinations can be explained in a

simple formula as illustrated in Fig. 5.4 and 5.1 For each ∆d^′_i, the positioning error ∆d_i is determined by ^D_f^c. Under the fixed focal length, the positioning error would be worse when D_cgoes up. The position effect factor of user’s location has the same meaning. As illustrated in Fig. 5.11, when user is far from the POIs, the positioning errors goes up.

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Figure 5.17: Positioning error affected by combinations of distant POI Similar Triangle algorithm

Combinations of AR objects: Positioning results are affected by the combinations of AR objects as previous analysis in View Angle algorithm section. Fig. 5.18 is the aver-age positioning result compared with combination numbers. Total positioning errors have significantly decreased from 112cm with 2 POIs to 48cm with 7 POIs.

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Figure 5.18: Positioning result affected by POI combinations

Distances are also the positioning effect factor as View Angle algorithm Fig. 5.19 lists {1, 2} and {6, 7}

at the near plane have better positioning result than POI combinations{3, 4}, {3, 5}, {4, 5}

Figure 5.19: Positioning error affected by combinations of distant POI

POI combinations that POIs are closed or nearly in the same line would affect the posi-tioning result due that the similar relation is used in Similar algorithm. POI 1 and 3 and POI 5 and 6 are the examples as illustrated in Fig. 5.20. POI combinations that have POI 1 and 3 or POI 5 and 6 would have poor positioning result compared to other combinations.

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Figure 5.20: Poor positioning results due to closed combinations

Focal length: Positioning results of Similar Triangle algorithm are affected by the focal length as illustrated in the Fig. 5.10. Tiny difference of focal length would have an impact significantly in positioning result as the distance between user and POIs goes up. The scope of Similar Triangle algorithm is given in Fig. 3.4. According to the Similar Triangle algorithm, Fig. 5.21 lists 4 relation formulas between user and 2 POIs and the solution of user’s location is given in Fig. 5.22. Focal length locates at denominator in solution of x and y, and locates at numerator in solution of z. When the focal length goes up, x and y would be decreased until converge into a fixed value and z would be increased into infinity.

On the inverse condition, when the focal length goes down, x and y would be increased into infinity and z would be decreased until converge into a fixed value. The effects of x, y and z is illustrated in Fig. 5.23 and Fig. 5.24 gives the experiment formula. The experiment result shows z would be increased significantly and x y decreased slightly. The focal length would affect the z value of user’s location significantly.

a^′_x

Figure 5.21: Position function with 2 points, A and B.

Comparison of two proposed positioning algorithm: Fig. 5.11 and Fig. 5.12 com-pared the View Angle algorithm with Similar Triangle algorithm. View Angle algorithm is affected by the problems of local minima but Similar Triangle algorithm has no such prob-lems. When the combination numbers go up, positioning errors of both proposed positioning algorithms have significantly decreased. When combination numbers of proposed algorithms increase and proposed algorithms have a better initial point, the positioning result of View Angle algorithm are better than the positioning result of Similar Triangle algorithm. Gener-ally, Similar Triangle algorithm has a steady and good positioning result than the positioning result of View Angle algorithm.

From the experiment result, The focal length of View Angle algorithm is 7.69cm and 8.083cm is average focal length of Similar Triangle algorithm that have lowest average posi-tioning error. Users should avoid selecting the combinations that POIs are closed or in the same line or plane and user should be near to POIs. Compared to the View Angle algo-rithm, Similar Triangle algorithm do not have problem of local minima and have a better positioning result.

X =

Figure 5.22: Solutions of equations.

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Figure 5.23: The x, y, z result of test Location 1 in AR frame



X = ^240.50558_f + 17.222198 Y = ^77.857063_f − 165.863

Z = f ∗ (−50.886617) + 722.35833

Figure 5.24: Solution formula of experiment

Chapter 6

Conclusions

Most current commercial positioning solutions could not meet the requirement of high-precision positioning for LBS application with AR. In this paper, two AR-based positioning methods, View Angle and Similar Triangle algorithm, are proposed. The average positioning error of View Angle algorithm is from 88.9cm to 245.9cm caused by the local minima issue of gradient method. The Similar Triangle algorithm does not have local minima problems and have a better average positioning error of 74.34cm. In the future work, matching POIs by hand can be replaced with automation such as vision-based or laser detection. Then, the AR-P system will be more fast, easy and accurate without human interaction. The problems of local minima of View Angle algorithm should be solved by the closed form solution or a new method to converge the solution to the global minima. Our system can be combined with feedback information routing and other positioning technique such as GPS or WiFi positioning to implement an real-time and high accuracy evacuation system.

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