PIR Sensor Based Indoor Locating and Tracking System EE209AS Course Project Report

Yicheng Wang SID: 804237453

Tairan Jin SID: 204589288

Longjia Niu SID: 304590762 Abstract—This paper presents an optimized indoor locating and tracking system based on PIR sensor module. The PIR sensors in one module are modeled as concentric rings and combinations of outputs are used for detection. In order to build the tracking system, methods of location and expansion are proposed. Then the system is proved in MatLab and Kalman filtering is used to eliminate the possible detection error in practice. Finally, the hardware prototype is tested to demonstrate the basic idea of the system. 1. Instruction With the rapid improvement of technology and the growth of people comfort level, smart home and indoor locating and tracking gradually become the hottest researching and application area. People are looking for a cost-effective, energy-saving indoor locating and tracking system with good performance serving to household appliances (lighting, HVAC, etc.). In our project, we proposed an indoor locating and tracking method with implementation of PIR sensors. And we optimized the tracking model considering the real situation of measurement. What’s more, we made comparisons among different implementation options and found a relatively cost-effective one with high accuracy and low cost. Finally, we made a prototype to achieve the basic one-object tracking. In the second chapter, we mainly talk about the background knowledge of indoor location system requirements and motion sensors. In the third chapter we talk about the project work, including locating modeling, tracking modeling with Kalman filtering, MATLAB simulation and hardware implementation. In the final part we make a conclusion of the job we have done. 2. Background 2.1 Indoor location system requirement First of all, in order to implement an indoor location system, several requirements need to be reached. Because many sensors will be installed in rooms of different sizes, the implementation has to be at a relatively low cost. And the installation must be flexible due to the different shapes of each room and the obstacles such as household appliances and furniture. Also importantly, the sensors used should be robust enough to environment noise. What’s more, the accuracy of location system should be high enough and adjustable according to room types. 2.2 Motion sensor An indoor location system needs to employ multiple motion sensors, and other indoor locating and communication technology such as WIFI, ZigBee, etc. Motion sensors can be sorted into active and passive motion sensor. Active motion sensors (such as microwave and ultrasonic sensors) emit energy to the detection field and receive reflected signals for analysis, however, passive motion sensors (such as PIR sensors and pressure sensors) only receive energy from the

detection field. 2.3 PIR sensor The structure of PIR sensors is shown in Figure 1. The PIR sensor can let a certain wavelength infrared radiation in and block other wavelengths. So the sensor let in the strongest radiation that human and animals can emit. And PIR sensor has two sensing elements inside and they are put opposite. When there is nobody or no movement in the detection field, the output from these two sensing elements is low voltage (0V); when PIR sees the movement of humans or animals, the output from these two sensing elements becomes high and the high voltage signal will be amplified and AD converted before final output.

Figure.1 PIR structure

PIR sensors have many advantages when utilizing in the indoor location system. First, it is robust to temperature, humidity, and electromagnetic noise. Second, it will not be affected by the structure of a room or any obstacles and easy to install on the ceiling. And no wearable or handheld devices are needed for PIR sensor based indoor location system. Finally, PIR sensors are cheaper than many other sensors and PIR sensors are energy saving because they do not emit any energy. Therefore, considering the good performance, low cost and energy efficiency of the PIR sensor, we eventually choose it as the motion sensor implemented in our location system. 3. Implementation 3.1 PIR Sensor Locating Model Usually PIR sensors are installed on the ceiling because there is no obstacle between the sensors and target person. Also it can save space in the room. The sensing area of a PIR is a circle as shown in Fig. 2. This is the original model. However, this model does not provide satisfying accuracy.

Fig.2 Model as A Circle

For example, it cannot detect a person’s location within the circle. In order to increase the accuracy, we combine several PIR sensors into one module to optimize this original model. 3.1.1 Basic Model Fig.3 shows our basic model to demonstrate the idea. In the basic model, the circle is divided into three concentric rings with equal distance one after another. White rings are un-shaded area which the relevant PIR can detect.

Fig.3 FOV of PIRs in Basic Model Gray rings are shaded area which the relevant PIR cannot detect. Therefore, three PIRs in one module have different FOVs and there is no overlap between different FOVs. In this way, we can use the different combination of outputs from three PIRs to detect the target person. For example, if the target person is in the middle ring, PIR No.1 and PIR No.3 will output low voltage and PIR No.2 will output high voltage. The output of the module will be (0, 1, 0). If we regard different outputs of the module as different codes, there are three codes in the basic model (1, 0, 0) (0, 1, 0) (0, 0, 1). 3.1.2 Location Detection In the model, the location of the target can be represented as the middle point of concentric rings. As Fig.4 has shown, if the target is in B, the distance between the target and center is d which equals to rA+0.5rB.

Fig.4 Location Detection (1) If the radius is divided into N equal parts by N concentric rings, the location of target can be estimated as

1 ∗ /2 (1)

in which d means distance between target and center, n means the number of the sensing area starting from 1 from center to the boarder, m means max radius. For example, in Fig.5, N is

Fig.5 Location Detection (2) 3, with (1) we have

1 ∗ /2 (2)

if target is in area No.2, which means n=2, we will get

(3)

3.1.3 Location and Expansion With one PIR module, the ring where the target person is in can be detected, but the exact location cannot be provided. Trilateration is a simple but effective way for locating. (2) can provide d within one module and three PIR modules need to be used to estimate the exact location. As Fig.6 has shown, if we assume

1 1, 1 , 2 2, 2 , 3 3, 3 and the target person’s location is

,

Fig.6 Trilateration Location then we have

1 1 1 (4)

2 2 2 (5)

3 3 3 (6) With (4) (5) (6) we have

(7) In which

22 1 2 13 2 3 23 1 3 1

(8)

(9)

1 2 2 1 2 12 3 3 2 3 21 3 3 1 3 1

(10)

With (7)(8)(9)(10)we can calculate the location (11)

Three PIR modules can detect the exact location in grey area. If the room has bigger area, it can expand into locating network as Fig.7 has shown. Every regular triangle is a small function block and they detect different regions.

Fig.7 Location Network

A second way to provide the exact location is to calculate all the intersection points of different concentric rings first and then calculate the target person’s location with the intersection points closest to the person.

Fig.8 Location with Intersection Points

As Fig.8 has shown, if the target person is in the unit detection regionⅠ, the closest intersection points are A B C D. If we assume

1, 1 , 2, 2 , 3, 3 , 4, 4 and the target person’s location is

, then we can estimate the location by

x (11)

y (12)

3.1.4 Multi-FOV for One PIR In the basic model, one PIR sensor has one FOV. As Fig.9 has shown, PIR No.1’s FOV is A, PIR No.2’s FOV is B and PIR No.3’s FOV is C.

Fig.9 FOV of PIR in Basic Model In this case, the output signals are A(1,0,0) B(0,1,0) C(0,0,1) in which 1 means the PIR sensor in the module outputs high voltage. However, one PIR sensor may have more than one FOV and we can use the overlap between FOVs. In this case, the number of PIR sensors may be reduced to 2. For example, PIR No.1’s FOVs are A and C. PIR No.2’s FOVs are B and C.

A B C can also be detected and output signals are A(1,0) B(0,1) and C(1,1). In this way, the cost will be lower because of reduced number of PIR sensors in a module. The FOVs of PIR sensors need to be designed carefully in order to avoid error signal. If we assume that the number of PIR sensor in a module is N, the total number of output combinations of all PIR sensors, or the number of codes we can use is 2N-1. For example, if there are 2 PIR sensors in a module, the 3 codes are (1,0) (0,1) and (1,1). If we use M to represent the number of areas which need to be detected, then we have

2 1 (13)

log 1 (14) Also the number of PIR sensors shall not exceed the number of areas which need to be detected.

(15) Therefore, we have

log 1 (16) This means that the number of PIR sensors can be determined by the number of areas which need to be detected. In our model, the areas are concentric rings. For example, if there are 5 rings A B C D E, according to (16), we need 3 PIR sensors in one node. There are 7 codes for use ( 1, 0, 0 ) ( 0, 1, 0 ) ( 0, 0, 1 ) ( 1, 1, 0 ) ( 1, 0, 1 ) ( 0, 1, 1 ) ( 1, 1, 1 ). We can choose five from them to determine the FOVs of PIR in a node. If we choose ( 1, 0, 0 ) ( 0, 1, 0 ) ( 0, 0, 1 ) ( 1, 1, 0 ) ( 1, 0, 1 ) for 5 different rings, A ( 1, 0, 0 ) B ( 0, 1, 0 ) C ( 0, 0, 1 ) D ( 1, 1, 0 ) E ( 1, 0, 1 ), PIR No.1’s FOVs are A D E, PIR No.2’s FOVs are B D and PIR No.3’s FOVs are C E. This is the way to determine the FOVs of PIR sensors in a module. If we do not use the code to determine FOVs of PIR sensors, error signals may be easily generated. In the above case, if PIR No.2’s FOVs are A B D instead of B D, there output signals for detected A and D are the same (1, 1, 0), which means detection fails. 3.1.5 Whole Process of Model Building

Fig.10 Accuracy determines ring number The whole process for building the model is following. As Fig.10 has shown, if the max radius of PIR sensing area is 3m and design accuracy of location system is 0.5m, the circle need to be divided in to at least 6 rings.

6 (17) With (16) and (17), the number of PIR sensors in a node will be determined.

2.81 6 (18) For minimum cost, N is the minimum

3 (19) Then we will get the code we can use ( 1, 0, 0 ) ( 0, 1, 0 ) ( 0, 0, 1 ) ( 1, 1, 0 ) ( 1, 0, 1 ) ( 0, 1, 1 ) ( 1, 1, 1 ). If we represent 6 rings as A B C D E F, from inside to outside, we

can choose six code for them A ( 1, 0, 0 ) B ( 0, 1, 0 ) C ( 0, 0, 1 ) D ( 1, 1, 0 ) E ( 1, 0, 1 ) F ( 0, 1, 1 ). Finally FOVs of PIR sensors will be determined. PIR No.1’s FOVs are A D E, PIR No.2’s FOVs are B D F and PIR No.3’s FOVs are C E F. Influence From Height In practice the target person may not be represented as a point and person’s height may influence the system. As Fig.11 has shown, B C D will all detect the target person.

Fig.11 Influence From Height

We call this multi-output. For multi-output, we can locate the target person in the active sensing area which is closest to the center. In this case, output is B C D and B is closest to the center. Thus the location systems output that the target person is in B, which is the correct detection. 3.2 Kalman Filter Tracking Model 3.2.1 Why Need Kalman Filter The PIR locating system may produce some measurement errors resulting in inaccurate locating in some specific scenario. See the examples in figure 12 and figure 13.

Figure.12 Uncertain Measurement Border Because of the unavoidable manufacture errors, the width of the shaded circles on the Fresnel lens is more or less than 1mm (the theoretical blind area caused by the shaded circle is the yellow ring however the real blind area is yellow plus red one (shown in Figure 12), so the detection areas of two adjacent shaded circles may have overlap, which makes the locating result incorrect. Meanwhile, because objects are seen as radiation sources with specific cross sectional area, when an object is crossing the border of two adjacent detection areas, wrong locating result may also be output. See figure 13. When the object (blue circle) has almost entered the detection area 2, but PIR modules can find the object in both detection area 1 and 2. And because detection area 1 is more closed to the center point of the left PIR module, the final detection result is the object is in detection area 1 based on our locating

algorithm, which is not accurate.

Figure.13 Crossing Between Two Adjacent Detection Areas

These measurement errors can be maximally eliminated by utilizing Kalman filter theory. Kalman filter regards these measurement errors as unavoidable system noise, white and Gaussian. And the filter can produce more accurate results by combining and reconfiguring the measurement values and predicted values. And the predicting ability of Kalman filter plays an important role in object tracking. So we choose Kalman filter as our tracking model. 3.2.2 Kalman Filter Tracking Model Kalman filter estimates process states by feedback control method. The working procedure of Kalman filter is as follow. Firstly the filter estimates the process state at moment k, i.e. the predicted values at moment k, based on the process state information at moment k-1. For our tracking problem, the process state includes the position coordinates and moving velocity of the object. Secondly the filter will combine the predicted values with the measurement values at moment K to produce a new estimate state as the process state at moment k. The model is shown below. State equation:

, , 20

, , (21)

Where , and , are the current state in x direction and y direction separately. And , and , are the estimate next state in x-coordinate and y-coordinate separately.

, ,, , ,

A=[10 1

], B= ∗

Where and , are the coordinate and velocity of the object in x direction; and , are the coordinate and velocity of the object in y direction. T is the sampling period.

is an error deviation, white and Gaussian, with zero and covariance matrix , caused by the random acceleration of the object.

~ 0, Measurement equation:

, , 22

, , 23

, and , are the measurement state in x direction and y direction separately.

H=[1 0] is a measurement error of PIR locating system, also white

and Gaussian, with zero and covariance matrix .

~ 0, Kalman filter can be divided into two main parts: time update and measurement update. We do a priori estimate and can get the values of next state and error covariance Matrix

in time update part:

, , , 24

, , , 25

|

And we do a posteriori estimate by combining the values from the priori estimate with measurement value and Kalman gain matrix in measurement update part:

, , , 26

, , , 27

|

And iteration procedure of the Kalman filter tracking model is shown in Table 1.

State model:

, ,

, ,

, ,

, ,

Where and are independent white Gaussian

noise with covariance matrix and separately.

Initialization: For k=0, we assume the initial

velocity of the object is 1m/s in both x and y

direction (1.4m/s in total), and set

,01, ,

01

|0 00 1

Calculation: For k = 1,2,…, calculate:

Kalman gain matrix:

State estimate update:

, , , ,

, ,

Error covariance update:

Error covariance propagation:

Q

Table 1 Iteration Procedure of Kalman Filter Tracking Model 3.3 MATLAB Simulation Setup 3.3.1 Sensors Placement Setup In our model, the simulated test area is a 20*20 square area, 4 sensors covering and 8 sensors covering cases are considered, as shown in Fig.14. PIR Sensors aggregations are represented by black nodes. Each of them forms an equilateral triangle with other two. Each node is the center of 3 or 5 concentric rings, indicating the number of sensors in an aggregation. For example, if there are 5 concentric rings surrounding a node, then there are 5 PIR sensors locating at that node which has the detection area corresponding to concentric rings.

Fig.14. 4 Sensors Covering Model (Left) and 8 Sensors Covering Model (Right)

3.3.2 Test Routes Setup We also setup up three types of test routes to simulate the actual human being's walking path. They include square routes, reverse Z route and Z route, as shown in Fig.15. Each of them will be tested carefully and thoroughly to gain a better understanding of multi-sensor tracking.

Fig.15. Square Type of Route (Left), Reverse Z Type of Route

(Middle) and Z Type of Route(Right) 3.3.3 Impact of White Gaussian Noise (WGN) In telecommunications and computer networking, communication channels can be affected by Gaussian noise which is statistical noise having a probability density function equal to that of the normal distribution, which is also known as the Gaussian distribution. White Gaussian Noise (WGN) is a special case in which the values at any pair of times are identically distributed and statistically independent. We add WGN into our model and compare the prediction precisions without and with WGN, as shown in Fig. 16. Intuitively, PIR sensors without WGN have better resolution than those with WGN, as estimated locations (Red Nodes) diverge from actual locations (Black Nodes) less in the case without noise than with noise. This is also confirmed by statistics in Table 2, where we can see that, given the same number of concentric rings and the number of circles covering the area, we get at most 21% average error reduction for PIR sensors without noise. As a result, Kalman Filter is integrated in our model to relieve the effects of WGN and get better prediction result.

Fig.16 Locations Estimated by PIR Sensors (Red Nodes)

Without Noise (Left) and With White Gaussian Noise (Right)

Table.2 Average Estimation Error Without and With WGN In

Given Conditions 3.3.4 Impact of Concentric Rings The number of concentric rings for a node center indicates the number of PIR sensors aggregated at that center. We compare the estimation result between 3 and 5 concentric rings model, as shown in Fig.17. Intuitively, 5 concentric rings model has better resolution than 3 concentric rings model, as estimated locations (Red Nodes) diverge from actual locations (Black Nodes) less in the former case. This is also confirmed by statistics in Table 3, where we can see that, given the same condition of noise impact and the same number of circles covering the area, we get at most 37% average error reduction for PIR sensors without noise. As a result, Kalman Filter is integrated in our model to relieve the effects of WGN and get better prediction result.

Fig.17 Locations Estimated by PIR Sensors (Red Nodes) in 3 Concentric Rings Model (Left) and 5 Concentric Rings Model

(Right)

Table.3 Average Estimation Error for 5 or 3 Concentric Rings Model In Given Conditions

3.4 MATLAB Simulation Results 3.4.1 Type One Route Simulation With MATLAB simulation setup completed, we integrated white Gaussian Noise and 5 concentric rings into our model, and get all three types of test routes thoroughly tested. An example of type one route estimation is shown in Fig.18. Black nodes are actual paths, red nodes are estimation locations before Kalman Filters, and green nodes are estimation locations after Kalman Filters. From the simulated graph, green nodes diverge from black nodes less than red nodes, which shows us the effectiveness of Kalman Filters intuitively. We also get some statistical results, as shown in Table 4. From the table we can see that given the same conditions, locations predicted after Kalman Filters can have over 50% reduction on average error than before Kalman Filters, which indicates that Kalman Filters have successfully relieved the average error of estimation locations.

Fig.18 Locations Predicted by PIR Sensors Before Kalman

Filters (Red Nodes) and After Kalman Filters (Green Nodes)

Table.4 Average Error for 5 Concentric Rings, 8 or 4 Circles Covering Model Before and After Kalman Filters for Type

One Route 3.4.2 Other Routes Simulation The results of reverse Z routes and Z routes are shown in Fig.19 Table.5 and Fig.20 Table.6.

Fig.19 Locations Predicted by PIR Sensors Before Kalman Filters (Red Nodes) and After Kalman Filters (Green Nodes)

for Type Two Route

Table.5 Average Error for 5 Concentric Rings, 8 or 4 Circles Covering Model Before and After Kalman Filters for Type

Two Route

Fig.20 Locations Predicted by PIR Sensors Before Kalman

Filters (Red Nodes) and After Kalman Filters (Green Nodes) for Type Three Route

Table.6 Average Error for 5 Concentric Rings, 8 or 4 Circles Covering Model Before and After Kalman Filters for Type

Three Route 3.4 Cost-effective Implementation In industrial field we care much about how to achieve a highly accurate locating system with lower price. From last chapter we have discussed 4 implement options (8 PIR modules with 3 PIR in one each; 8 PIR modules with 2 PIR in one each; 4 PIR modules with 3 PIR in one each; 4 PIR modules with 2 PIR in one each). We try to find the optimal one from the dimension of the number of PIR sensors in a module and the dimension of the m=number of modules. And the result is drawn in fig.21.

Fig.21 Cost-effective Analysis

From fig.21 we can see the relatively optimal one is the option in red (4 PIR modules with 3 PIR in one each). 3.5 Hardware Prototype Implementation In our project we implement a hardware prototype to test the working parameters of single PIR sensor and combined working of multiple PIR sensors. 3.5.1 PIR Sensor Benchmarking After did the benchmarking of PIR sensors in the market. We found there are mainly 3 kinds of PIR sensors. The first kind is shown in Fig.22. This PIR module is built

with a PIR sensor and a PIR motion detector IC. This module can achieve PIR detection function easily with the help of the IC but the output of this module has minimum 5s delay, which means when it sees a person in detection field, it outputs a high voltage signal with 5s delay no matter the person is still inside the field or not in this 5s. This feature brings a lot inconvenience for our real time detection.

Fig.22 PIR Sensor with Micro Power PIR Motion Detector IC Second kind PIR sensor is shown in Fig.23. The output signal of this kind of PIR sensor is an analog at very low voltage. And the signal can only be used after amplifying and AD converting. This PIR sensor with a circuit board can achieve real time detection and with no delay, however, we should layout a circuit board by ourselves.

Fig.23 PIR Sensor with a circuit board (Based on Datasheet from Murata)

The third kind PIR sensor is shown in Fig.24. This PIR sensor is designed by Panasonic. It integrates the amplifier and converter circuit inside PIR sensor. So the PIR sensor can achieve real-time detection in a small size. Finally we choose this kind of PIR sensor for our hardware implementation. And the model number of the Panasonic PIR sensor is EKMC160111.

Fig.24 Panasonic PIR Sensor (Based on Panasonic PIR sensor Datasheet)

3.5.2 Hardware Prototype Implementation We did the test of the detection range of Panasonic EKMC160111 PIR. The hardware implementation is shown in fig.25, including an Intel Edison board, a PIR sensor and an indicator light.

Fig.25 Working Parameters Testing

And the testing result of max detection distance and angle are shown in Table.7. From the table we can see that the theoretical values and test values are almost the same. The design and simulation in our project are based on the test values of these parameter.

Theoretical Value Test Value

Max Distance 5m 5.3m

Max Angle 94° 90°

Table.7 Detection Range Test Then we combined 3 PIR sensors in a module to achieve a basic tracking test. The hardware prototype is shown in fig.26. We use 2 clapboards between every two adjacent PIR sensors to divide the detection areas of the 3 PIR sensors into 3 different regions (similar function as the shaded rings on the Fresnel lens). And we use a servo to show the location of the object. The tracking video can be found on YouTube. URL: https://youtu.be/0cNfHSquj08

Fig.26 (1) Front of The Hardware Prototype

Fig.26 (2) Back of The Hardware Prototype

4. Conclusions In our project, firstly we have done an investigation of the normally used sensors in the locating and tracking fields. Compared with other sensors, we finally choose PIR sensors for its good performance, low cost and energy efficiency. Then we combine multiple PIR sensors together in a module and cover their Fresnel lens by distributed shaded concentric rings. We implement the modules on the ceiling and build a locating model to detect the location of objects with the accuracy of 0.5m. Considering the unavoidable measurement errors, we employ Kalman filter to maximally eliminate the measurement noise. Next we utilize MATLAB to simulate the locating and tracking model we build and the results show that our models can achieve locating and tracking in high accuracy. And the tracking results are improved by using Kalman filter. What’s more, we find a relatively cost-effective (high accuracy with low cost) implementation after comparing 4 implementation options of locating system we have simulated. Finally we achieve a prototype to test the locating and tracking based on PIR sensors. References [1] Plett G L. Kalman-filter SOC estimation for LiPB HEV cells[C]//Proceedings of the 19th International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium & Exhibition (EVS19). Busan, Korea. 2002: 527-538. [2] Luo R C, Chen O, Lin C W. Indoor human monitoring system using wireless and pyroelectric sensory fusion system[C]//Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on. IEEE, 2010: 1507-1512. [3] Rahimi A, Dunagan B, Darrell T. Simultaneous calibration and tracking with a network of non-overlapping sensors[C]//Computer Vision and Pattern Recognition, 2004. CVPR 2004. Proceedings of the 2004 IEEE Computer Society Conference on. IEEE, 2004, 1: I-187-I-194 Vol. 1.