AN IMPROVED PDR INDOOR LOCAION ALGORITHM BASED ON PROBABILISTIC CONSTRAINTS

In this paper, we proposed an indoor pedestrian positioning method which is probabilistic constrained by "multi-target encounter" when the initial position is known. The method is based on the Pedestrian Dead Reckoning (PDR) method. According to the PDR method of positioning error size and indoor road network structure, the buffer distance is determined reasonably and the buffer centering on the PDR location is generated. At the same time, key nodes are selected based on indoor network. In the premise of knowing the distance between multiple key nodes, the forward distance of pedestrians which entered from different nodes can be calculated and then we sum their distances and compared with the known distance between the key nodes, which determines whether pedestrians meet. When pedestrians meet, each two are seen as a cluster. The algorithm determines whether the range of the intersection of the buffer meet the conditions. When the condition is satisfied, the centre of the intersection area is taken as the pedestrian position. At the same time, based on the angle mutation of pedestrian which caused by the special structure of the indoor staircase, the pedestrian's location is matched to the real location of the key landmark (staircase). Then the cumulative error of the PDR method is eliminated. The method can locate more than one person at the same time, as long as you know the true location of a person, you can also know everyone’s real location in the same cluster and efficiently achieve indoor pedestrian positioning. * Corresponding author


INTRODUCTION
With the rapid development of positioning technology, people have put forward higher and higher requirements of positioning.Seventy percent of the people's daily activities are indoors, so the indoor positioning has been the most pressing demand for modern people.In recent years, there are more and more researches which are closely related with indoor positioning technology, such as the application of ultrasonic positioning technology (Priyantha, 2000), but the ultrasonic attenuation is obvious, and the cost is expensive.Based on WiFi positioning technology (Kawaguchi, 2009), but because of the complex indoor environment and diverse interference, the accuracy of positioning is not high.It is difficult to be widely used in the daily life.Based on the RSSI range study (Noh, 2013) the signal which is received by the positioning system is also unpredictable due to the uncertainty of the environment.Bluetooth-based positioning technologies (Munoz-Mari, 2007) are only suitable for small-scale positioning and still rely on external signal.Besides, the costs what are spent on the layouts of the signal source infrastructure and maintenance are also higher.
The above positioning methods cannot be used in large-scale due to all kinds of reasons.And single positioning method is difficult to meet people's positioning needs.In this case, some researchers propose a fusion of Bluetooth and map method (Zhao, 2016).Although it improves the accuracy, it still has to rely on external equipment, universality is not strong.
The popularity of smart phones brings people a new way of thinking.Low-cost and fast positioning technology has become the pursuit of many researchers in recent years.How to rely on a mobile phone for high-precision positioning is an urgent problem need to be solved.In the circumstances, Pedestrian dead reckoning (PDR) method (Park, 2016) makes use of only a smart phone, without the need for other ancillary equipment, to carry out indoor pedestrian positioning.
However, single PDR positioning method in short distance, positioning accuracy of which is acceptable.With the increase of distance, the cumulative error increases.Some other problems also exist such as inaccurate positioning, low positioning speed.It is difficult to meet the indoor positioning needs.Therefore, based on the PDR algorithm, this paper presents a "multi-target encounter" probability constraint indoor positioning algorithm.To a certain extent, it can achieve multitarget simultaneous positioning, and effectively reduce the rate of error accumulation.It aims to achieve a high efficiency indoor positioning, and position better.

PEDESTRIAN DEAD RECKONING
For the main error of PDR positioning method comes from the error of step size and angle, resulting in increased cumulative error (Zhou, 2014).According to the stature and the number of steps, we can determine the step size, the regression equation as the formula (1) shows (Li, 1999): Where H = pedestrian height l = pedestrian step length Because of the limit of the built-in sensor accuracy of the mobile phone, and in order to prevent the accumulation of error of the forward distance obtained by the secondary integration of the acceleration, the pedestrian forward distance is calculated as: Where L = the distance forward n = the number of steps When pedestrian take the n-step is coordinates as: As shown in Figure 1.
Since there is a lot of noise in the original acceleration data, in order to correctly detect the number of steps, we use the Chebyshev low-pass filter for denoising.We apply the peak detection algorithm (Mladenov, 2009) to avoid the error of step detection.No. 1 experimenter walked straight forward some 15 steps, as shown in Figure 2. No. 2 experimenter went straight and then made a turn for 22 steps in total, as shown in Figure 3. No. 3 experimenter went straight 14 steps, and the detection can be shown as Figure 4:

Probability constraint
The outdoor positioning initial position serves as a known starting position for the positioning target.Indoor positioning can be studied under the condition of knowing initial position and indoor road network.
The experimenter can be tracked according to "multi-target encounter" probability constraint method under the condition that the entrance is one-way street and has known forward direction.
Based on the principle of PDR, forward direction can be detected when the entrance has several roads, as shown in Figure 5.According to the network structure, the entrance and corners are selected as the key nodes, and the distance of each node is known.Take initial position of entrance of the building as the first node, the distance is recorded according to the principle PDR method.The condition is that A, B are two entrances and it has more than one subject.There is no doubt that person P1 heads to the direction 1 and P2 heads to the direction 3. The forward direction is 1,2,3,4.
According to the PDR method of positioning error size and indoor road network structure, the buffer distance is determined reasonably and the buffer centring on the PDR location is generated.Then we detect whether there is a buffer intersection between P1 and P2.When the buffers intersect, we calculate the sum of the forward distances of the two persons and the distance between the entrance A and the entrance B, and determine whether the distance is equal.The formula is shown as following: Where So = overlapping region Sp = the generated buffer area The formula (7) shows that the probability that the pedestrian in the intersection area is greater than the probability in the other location.
As long as overlapping buffer is detected, the sum of distances of the pedestrian forward distance and the available distance can be compared, according to (5), ( 6).Then the formula ( 7) is used to judge the probability.If it satisfies the requirement, it can locate the geometric centre of the overlapping area.
The positioning flow chart for this paper is shown in Figure 6. Step

Indoor map matching constraint
In order to prevent from positioning exterior space of the building or some non-accessible place, this paper uses the constraints of indoor map, that is, marking the all accessible roads directly.When the PDR positioning drifts to the wall or outside the building, the position can be corrected and be located in the middle of the identified roads again according to the indoor map constraint.

Eliminate cumulative errors
Personal Dead Reckoning (PDR) has little cumulative error in the initial time.With the accumulation of distance, the error increases.In this way, it causes large degree of drift (Jekeli, 2000) and positioning accuracy is also greatly reduced.The error comes mainly from the azimuth error which caused by the electronic compass susceptibility and the distance error is caused by the acceleration.If you can identify the key indoor landmarks and the location of pedestrians, you can match the location of key landmarks and pedestrians to eliminate the accumulation of errors.In the research of the indoor map, pedestrians seldom have continuous angle reversal behaviour when they go straight in the short distance.When you go up the stairs, it has repeatedly appeared in this behaviour, and the azimuth difference of 180 °.As shown in Figure 7. Based on this unconventional change of angle, it is possible to match known points (stairs) based on indoor map constraints, pedestrian's location as well as angle mutations.In this way, the errors that are accumulated before can be eliminated and positioning accuracy can be greatly improved.

CONCLUSIONS
Through the way of PDR, we can locate the approximate location of indoor pedestrians.The error accumulation problem of PDR method is effectively improved according to the method of probability constraint and the matching of indoor landmarks.Moreover, we can efficiently and accurately locate the true location of other clusters when the true location of one is known.When the crowd is dense, the positioning speed is greatly improved.Experiments have shown that the margin of error is controlled in the range of 2 meter to 3 meters for it has about 1meter reasonable distance among people when they meet.At the same time, there is a time interval detected when pedestrians go upstairs.During this interval, the pedestrian of the first cluster keep on moving for some distance, which results in offset error.But it eliminates the cumulative error of the second cluster.In general, the PDR-based probabilistic constraint method proposed in this paper is fast and stable, and it does not lead to large-scale location errors with the increase of steps.

Figure 5 .
Figure 5. Probabilistic constraints for multi -target positioning forward distance of P1 S2 = the forward distance of P2 SAB = the accessible distance between the entrance A and the entrance B When the sum of S1 and S2 is less than SAB, the means of PDR positioning is used.When the sum of S1 and S2 is greater than or equal to SAB, overlap region can be estimated, according to the formula Figure 6.Technical roadmap

Figure 7 .
Figure 7. Azimuth changes of up and down