Indoor Pedestrian Navigation Using PDR/Wi-Fi Integration Indoor Pedestrian Navigation Using PDR/Wi-Fi Integration

Positioning of pedestrians is a challenging problem, especially, in case of global positioning system (GPS) signal outage inside buildings. The inertial navigation systems (INS) are used to detect the motion of the human body by placing the inertial measurement unit (IMU) in a speci ﬁ c part of the human body. However, using IMU alone will not produce a proper navigation solution with suf ﬁ cient accuracy due to the gradually accumulated errors of IMU stochastic drift, noise, and state integration with time. This led researchers to enhance the performance of indoor navigation systems using aiding sources such as the received signal strength (RSS) from beacon sources recorded on a database, and maintained on a server for collecting signals from certain locations and then using classi ﬁ cation methods such as the k-nearest neighbors (KNN) and support vector machines (SVM) for identifying locations that are not in the database to provide ﬁ ngerprint system-based localization. However, it was discovered that this approach presents drawbacks such as low precision and excessive cost. In this paper, the proposed system is based on integrating both INS and Wi-Fi access to mitigate errors. Further, the Kalman ﬁ lter is used for optimally fusing the data from the INS and Wi-Fi signals. In addition, the algorithm is modi ﬁ ed by the bubble technique to build a more accurate Kalman ﬁ lter observation model to remove the need for a database to determine the position using the ﬁ ngerprint method. The proposed algorithm is validated using simulation and real experiments at the Faculty of Engineering in Mansoura. The proposed work presented a low-cost and less complex pedestrian indoor navigation system with suf ﬁ cient performance with an accuracy of less than 7.2905 cm.


Introduction
P edestrian indoor navigation is important for a variety of reasons.It can be used in complex public or commercial facilities such as airports, train stations, clinics, museums, fairgrounds, or conference centers to help people navigate their way around (Wang et al., 2022).Indoor navigation technology has also been widely considered and studied by scholars in disaster relief and rescue, medical search and rescue, public security, anti-terrorism, and other fields (El-Sheimy and Li, 2021).Indoor navigation technology is becoming increasingly important with the emergence of new chip-level micro-electromechanical system (MEMS) sensors, positioning big data, and artificial intelligence (AI) technology, as well as the increase of public interest and social potential.The global indoor positioning, localization, and navigation (PLAN) market is expected to reach $28.2 billion by 2024.Accurate PLAN can serve safety and medical applications and benefit special groups such as the elderly, children, and the disabled (Czogalla and Naumann, 2016).
Indoor navigation systems face several challenges.One of the main challenges is the lack of global positioning system (GPS) signals and line of sight with orbiting satellites in indoor environments, which makes navigation more challenging compared with outdoor environments (El-Sheimy and Li, 2021).To overcome this challenge, various technologies such as radio frequency (RF) signals, computer vision, and sensor-based solutions are being used for tracking users in indoor environments (El-Sheimy and Li, 2021).
Another challenge is the need for accurate and reliable indoor positioning and navigation systems.The accuracy of indoor positioning systems can be affected by various factors such as multipath propagation, signal attenuation, and interference (Kunhoth et al., 2020).To improve the accuracy and reliability of indoor positioning systems, researchers are exploring the use of advanced sensors, multiplatform/multi-device/multi-sensor information fusion, machine-learning systems, and the integration with artificial intelligence, 5G, IoT, and edge/ fog computing (Kunhoth et al., 2020).The machine learning used in indoor positioning confronts a formidable obstacle: it takes a protracted period to execute its task, as it instructs and evaluates this machine, through training and testing phases, ultimately ascertaining the veracity of its outcomes (Mahdi et al., 2022).
Inertial navigation is the concept of using inertial sensors to provide the information required to make observations about an object's movement and current location (Titterton and Weston, 2004).All inertial navigation systems (INS) require at least a gyroscope for sensing angular velocity and an accelerometer for measuring acceleration, which are packaged together in a device called an inertial measurement unit (IMU).Error grows because of accelerometer deficiencies that grow cubically with time (El-Sheimy and Li, 2021), meaning that unbounded errors in the sensors become damaging to the system quickly.Regarding gyro drift, another common type of error occurs when unaddressed errors are incorporated into the gyro measurements (Czogalla and Naumann, 2016).The yaw axis of the system in the navigation frame is the most vulnerable to gyroscope drift, while roll and pitch inaccuracies can be eliminated by combining an accelerometer and determining the gravity vector.This makes yaw correction methods essential for inertial navigation systems.The IMU is typically put on the foot to identify the location based on the movements of that foot, which is generalized to include the person.Systems can also be chestmounted (Kunhoth et al., 2020) or hip-mounted (Mahdi et al., 2022).It may use inexpensive sensors such as those exist in mobile devices.The accumulated errors can be eliminated in the pedestrian dead reckoning (PDR) system, where the IMU can be fixed on the leg, and using the zero-velocity update (ZUPT), and zero angular rate update (ZARU) methodologies can be applied to recalibrate the IMU, which helps reduce the INS drift errors.The foot is a good indicator of movement, so IMUs are often placed on the soles of shoes.PDR-based methods are beneficial; the positioning accuracy of PDR is determined by step detection (Titterton and Weston, 2004), step length estimation, and heading estimation (Skog et al., 2010).On the other side, most localization methodologies based on Wi-Fi rely on signal-to-noise ratio (SNR) or received signal strength (RSS) by fingerprinting methods.WLANs allow users to move around within a local area while remaining connected to the network.Some uses of Wi-Fi may be similar to Li-Fi (light fidelity), with Wi-Fi being better overall, because Wi-Fi uses radio waves that can pass through walls, while Li-Fi is limited to one room, and Li-Fi cannot cope with turbulence due to its lightweight signal (Hasanudin et al., 2023).The integration of the Wi-Fi positioning technique and INS, produces a synergistic effect that results in improved performance.The most common challenge of Wi-Fi positioning is the database of fingerprints.In this paper, it is necessary to provide a solution for improving indoor positioning using a combination of the RSS and PDR through sensor fusion and not relying on the database to determine the position instead of the fingerprint method.
Recently, the most commonly used techniques for developing pedestrian indoor navigation systems can be summarized as follows: (1) Zero velocity updating (ZUPT) is a core component of pedestrian-based inertial navigation systems, allowing for the use of human gait patterns to reduce errors within an INS (Skog et al., 2010;Foxlin, , 2005).(2) Kalman filter is a type of recursive linear filter.
The filter was developed by R. Emil Kalman in the 1960s (Kalman, 1960).It is used to provide an estimate of a state (desired information) from related measurements that contain noise, combined with information regarding the measurement noise and the process noise characteristics.
Prediction phase: In Eq. ( 1), b x À t is the new state estimation matrix; A represents the state transition matrix; b x À tÀ1 is the previous state; B is the input-control matrix; and U t is the control vector.
where in Eq. (2), P À t is the new state estimation covariance matrix, and Q is the modeling noise covariance.
Updating phase: In Eq. ( 3), K t denotes the Kalman gain; C is the sensors mapping matrix; and R is the sensor noise covariance.: In Eq. ( 4), z t is the sensor data matrix and b x t is the new system state: I is an identity matrix.Bubble algorithm method sorts a set of numbers by frequently comparing adjacent elements and changing them to a different sequence.If the first element is greater than the second element, the algorithm swaps the two elements.The algorithm then moves on to the next two elements and repeats the process.This continues until the algorithm reaches the end of the list.
In this paper, related work is explored in Section 2. The proposed method is explored in Section 3. The experiments and evaluation are introduced in Section 4. Section 5 provides the conclusion.

Related works
In (Ciurana et al., 2007), the author uses only a pair of access points (APs) for estimating the position of a smartphone terminal.The TOA-based positioning method works by measuring the period required for a radio signal to travel from an AP to the mobile terminal.The travel distance between the AP and the mobile device can then be calculated using the speed of light.Once the distance to two APs are known, the mobile terminal's position can be estimated using a simple geometric triangulation algorithm.The results can achieve an accuracy of up to 2 m.In (MA et al., 2003), the author used a combination of clustering and probability distributions to estimate the location of a mobile terminal.This approach works by first clustering the APs in the environment into groups based on their signal strength.Once the APs have been clustered, the probability distribution of signal strength is calculated for each cluster.The mobile terminal's location is then estimated by finding the cluster with the highest probability of containing the mobile terminal.In (Rubiani et al., 2019), the author uses support vector machines (SVMs) to predict the position of a mobile device based on the signal strength of adjacent APs.SVMs are a form of machine learning technique that can be used in regression and classification issues.In this scenario, SVMs are used to categorize signal strength values into different geographic classes.The location classes are formed by the signal strength measurements of APs at recognized locations.This method was evaluated using actual data collected in a university building.The results revealed that the proposed method can reach an accuracy of up to 2 m.In (Wang et al., 2019), the author uses a neural network to enhance the accuracy of fingerprinting-based localization methods.Fingerprinting-based localization methods work by building a fingerprint database of signal strength measurements at locations that are known.When the location of a mobile device is to be predicted, the signal strength measurements from the mobile device are compared with the fingerprint database in search of most locations.A neural network is used for enhancing the accuracy of fingerprinting-based localization methods by learning the relationship between the signal strength measurements and the location.The neural network is trained using a set of data that includes signal strength measurements and their corresponding locations.The results showed that the proposed method can achieve an accuracy of up to 1 m.In (Qu et al., 2020), the author obtains raw amplitude data from several subcarriers of IEEE 802.11n protocol that access points by adjusting the 5300 network interface card driver.In addition, a Hampel filter is used to manage amplitude signals, and a four-hidden-layer convolutional neural network is built to learn and train the properties of the calibrated amplitude values.In (Micheletti and Godoy, 2021), the author depended on the communication Long Range (LoRa) protocol and the altimeter for applications in indoors even though wireless communication technology for long-distance applications is a sort of low-power wide-area network (LPWAN) that has recently gained popularity.To improve positioning operation, the author additionally used the classic trilateration approach mixed with the signal strength indicator (RSSI).In (Hu and Hu, 2023), the researcher has discovered a resolution to the issue concerning the fixed K value when employing the K-nearest neighbor approach.The authors introduce an innovative algorithm, commonly known as static continuous statistical characteristics-soft range limited-self-adaptive WKNN (SCSC-SRL-SAWKNN).The researchers were distinguished in that the enhancement of localization is achieved through the utilization of prolonged periods of inactivity's ongoing statistical characteristics, However, the authors encountered the challenge of equipment heterogeneity.In (Zhang et al., 2021), the author managed to deal with the problem of neighboring locations that occur when RSS values for nearby locations are similar, so the location accuracy of RSS-based techniques is restricted, where he used a reconfigurable intelligent surface (RIS) for the RSS-based multiuser localization.RIS can adjust the radio channel by changing the phase shift of the reflected signal.It can be improved by selecting an adequate phase shift and a suitable difference in RSS values between adjacent locations.In (Poulose et al., 2019), the author estimates position using the combined characteristics of IMU sensor's acceleration transducer, magnetometer, and gyro data to overcome the poor GPS signal received.The author discussed the accumulation of errors in PDR localization.In addition to a comparison of different step detection approaches, the results show that a pitch-based procedure performs better.In (Lu et al., 2019), the authors used a regression approach for estimating stride length with only acceleration while usig IMU data to correctly calculate stride displacement.The author presented the PDR system based on a chestmounted IMU.In addition, it is used as a barometer to measure pedestrian height.In (Bai et al., 2020), the author uses motion-based adaptive error compensation and step detection-based up/downstairs tracking to improve positioning precision without the use of more sensors.In (Zhou and Franklin, 2020), the author also confronted the same problem of indoor positioning using an IMU, which that the inertial sensors show faults and the errors increases with time, and noise from reading IMU.For solving them, he suggested an edge detection method based on the pruned exact linear time (PELT) model.The author includes a map-aided system that uses map features to help fix the user's position.He assessed the system when the smartphone was in the user's hand or in the pocket of the bag.In (He et al., 2020), The author referred that the majority of researchers use nine degrees of freedom (9-DOF) inertial sensor for indoor positioning.In contrast, when a person moves quickly and regularly, it is evident that using a 9 DOF sensor necessitates a substantial amount of processing.In addition, when performing data fusion for inertial sensors, the Kalman filtering process is always timeconsuming.He used zero-velocity update (ZVU) algorithm to solve this problem and improve the cumulative error due to double integral Table 1.
Then, it can be identified that the IMU and WLAN technologies are the best because they provide high accuracy and low cost.This research paper contributes to finding the lowest error value from the real path considering the reduction of the cost that results from the creation of fingerprint databases and the creation of servers that will save these signals.In the next section, the concept and method for combining these two sensors will be discussed, as well as how to acquire satisfactory results.
The contribution of this paper can be summarized as follows: (1) Design of low-cost indoor navigation system for pedestrians (2) Utilizing bubble technique for enhancing the Kalman filter observation model (3) Implementation and testing of the proposed algorithm using embedded board and applying field test for system evaluation.

Proposed method
In this paper, Kalman filter is proposed for data fusion of INS measurements and received signal strength from the Wi-Fi receiver, to realize optimal positioning.The PDR includes the solution of the navigation equations by estimating the user's position, velocity, and attitude in a reference navigation frame from sensor measurements in the body frame which is mounted on foot.PDR methods explore the kinematics of human gait with the travelled distance and heading information.The pedestrian dead reckoning is the determination of a new position from the knowledge of a previous position using current distance and heading information.
Regarding the system modeling for our integrated system, the system state vector x is composed of position r, velocity v, and attitude J in the navigation frame.The INS mechanization model is defined as the system process model (Titterton and Weston, 2004).For low-cost MEMS-based IMUs, the effects from the earth rotation cannot be observed, so the Coriolis and centrifugal terms are not considered in the INS process model.In this model, the gravity is assumed as a constant and the transport rate is no longer considered for simplicity (Zhou et al., 2010).The simplified mechanization model in discrete time can be expressed in navigation frame as follows: are the preestimated accelerometer and gyroscope bias error terms; w terms represent the corresponding white noise of the model; C n b is the frame rotation matrix from the body frame to navigation frame; and F n b is the transformation between body frame and navigation frame: cos 4 cos f cos 4 sin 4 sin q À sin 4cos q cos 4sin fcos q þ sin 4sin q sin 4cos f sin 4sin f sin q þ cos cos q sin 4 sin f cos q À cos 4 sin q À sin f cos 4 sin q cos f cos 4  1 sin q tan f cos q tan f 0 cos q À sin q 0 sin q cos q cos q cos f 3 7 7 7 7 7 5 ð10Þ q ; f; 4 represent the roll, pitch, and yaw.The process model defines the evolution of the state from time t-1 to time t as follows: As for Wi-Fi positioning, the measurement equation for the position of the object from the Wi-Fi propagation model is rewritten as follows: In Eq. ( 15) S OB;L is the received signal strength measurements from AP(L); r and r APðLÞ represent the position vectors of the object and AP l, respectively; h s;L is the additional Gaussian noise term; a n and U L are the Wi-Fi signal-related parameters, which can be pre-estimated.Work was done on four access points to improve positioning accuracy, and then all readings from four AP installed in equal dimensions, their area is 4 m * 4 m, and the readings were recorded by a Wi-Fi antenna receiver connected through a computer.These readings are recorded on a computer with a decibel unit, and the three equations of the three strongest signals will be solved to find the location of the person x n ; y n ; z n , knowing that the altitude z n in this experiment is constant and does not change for both the AP and Wi-Fi, where n is the total number of the survey points as shown in Fig. 1, which illustrates stages of extracting the position by Wi-Fi, and Fig. 2 shows the proposed method of positioning using Wi-Fi.To facilitate the calculation process, four routers have been selected with the same parameter U and h can neglect this parameter while solving the three equations together: After sorting the received signals from four access points, bubble technique is used, to rearrange the signals from the largest to the smallest in terms of received signal strength to determine the first three strong signals, whereas leaving the fourth and solving these three equations using methods such as Gaussian elimination or Cram er's rule or inverse matrix method.The observation model equation with respect to the position can be rewritten as In Eq. ( 19), Z t is the measurement vector; H is the measurement matrix; and v t is the measurement noise vector that is assumed to be zero-mean Gaussian: where T t À T tÀ1 is the different time between two consecutive points on path.

Experiments and evaluations
In this section, the performance of the proposed model is evaluated through a procedure in the laboratory of the Faculty of Engineering at Mansoura University.The experiment is divided into two parts: PDR and Wi-Fi positioning.To conduct the first part of the experiment, a dedicated path is drawn on the laboratory floor so that the path is the real path that we will measure through the errors that occur in the parts of the experiment, as shown in Fig. 3.
The PDR includes the solution of the navigation equations by estimating the user's position, velocity, and attitude in a reference navigation frame of the user.PDR consists of three components: stride detection, stride length (L strd ) estimation of the S OB;2 ¼ À10:a L :log Fig. 3(a).The path along which the experiment will be conducted: (b) dimensions of the path.A person moves from point A to point B, passes through point C, and then comes to point A.
distance traveled by the user since previous step t-1 and the user's heading (j) during the step t-1 to t. consequent.The coordinates (r x;t ; , r y;t ) of a new position with respect to a position of the previous stride (r x;tÀ1 ; r y;tÀ1 ) can be computed as follows: r x;t ¼r x;tÀ1 þL strd;tÀ1 cos j tÀ1 ð23Þ r y;t ¼r y;tÀ1 þL strd;tÀ1 sin j tÀ1 ð24Þ The step detection is based on pedestrian gait model cycle.In contrast, a gait cycle includes four sequential phases, namely push-off, swing, heel strike, and stance as in the figure.Therefore, the percentage of each phase in a gait cycle is user dependentin (Fig. 4).The IMU(MPU-6050) is installed on a personal foot and connected by wire into PCs Fig. 5.The steps and gait phases can be detected from the IMU measurement using a sliding window.
Fig. 6 shows the trajectory estimation results, the PDR using zero velocity update (ZUPT) and zero angular rate update (ZARU) techniques can significantly improve the heading estimation accuracy of a pedestrian dead reckoning (PDR) system using the IMU raw data.The IMU(MPU6050) measurements are extracted on MATLAB to be plotted.Also, one of the most important parameters of the threshold of ZUPT is the value that is used to determine whether the IMU is in a state of zero velocity.If the magnitude of the IMU's velocity is less than the threshold, and therefore the ZUPT algorithm will assume that the IMU is in a state of zero velocity and will update the IMU's position and heading estimates accordingly.The threshold of ZUPT is typically a function of the IMU's noise level and the desired accuracy of the ZUPT algorithm, then A higher threshold will result in a less accurate ZUPT algorithm, but it will also be less susceptible to noise.A lower threshold will result in a more accurate ZUPT algorithm, but it will also be more susceptible to noise.Many experiments are conducted to determine the ideal values that give the lowest error value, where we found the minimum error to the optimum threshold ¼ 2E^-3.
In IMUs, gyro bias and accelerometer bias are a gradual change offset in the output signal of IMU.This offset is caused by imperfections in the gyroscopes or accelerometer construction and manufacturing process.Consequently, this bias can cause errors in the IMU's output, which can degrade the accuracy of the IMU's measurements.
In Figs. 7 and 8 show an estimate of the offset value in the accelerometer and gyroscope, whereas there are two types of bias: static bias and drift.Static bias is the constant offset in the accelerometer's output signal.As for drift bias it is the gradual change in the accelerometer's output signal over time.Consequently, ZUPT methods are proposed for bias correction by assuming that the accelerometer is not accelerating when the velocity is zero.The accelerometer bias can be estimated by averaging the output signal over a period when the velocity is zero.Therefore, this drift bias can be compensated by subtracting from actual IMU reading for enhancement performance of PDR.
In Figs. 9 and 10 illustrate the estimated attitude and position; then position, velocity, and attitude can be illustrated, which represents ( r PDR    form of the error equation depends on the type of inertial sensors (accelerometers and gyroscopes), and the navigation algorithm utilized.The error of position can be computed as follows: D _ r ¼ DvÀ 1 sin q tan f cos q tan f 0 cos q À sin q 0 sin q cos q cos q cos f In Eq. ( 25), Dr is the error vector in the navigation frame and Dv is the error vector in the navigation frame.F n b is given by Eq. ( 10).Fig. 11 shows the effect of ZUPT in improve error due to drift bias, but the value of this error is considered unsatisfactory compared with the accuracy reached by the researchers, that the average error in PDR without  ZUPT is 11.8138 cm and in PDR with ZUPT is 9.42 cm.However, these results are not as precise as required.
However, the technology of the RSS will be used that depends on receiving the signal from four access points (VDSL ZXHN H188A) fixed on equal distances as shown in the following Fig. 12.
In this part, a special antenna (Alfa AWUS036NH 802.11nWireless USB Wi-Fi Adapter) is used to receive power signals as shown in Fig. 13 and send this data to the computer.The fixing position is suggested to be at the shoulder from above as it is not affected by swinging hands while walking as shown in Fig. 13.By choosing the three strongest signals and solving this equation together.Therefore, to facilitate calculations, the height is assumed to be not changed to facilitate the calculation.r z is constant, as the receiver antenna is fixed on the shoulder and does not move and there are four available APs with known positions.
In Fig. 14 shows the values of RSS on the period in which the person moved on the drawn path.The received signal from the access point (AP) undergoes fluctuations as the individual approaches or  moves away from it.To investigate this phenomenon in Fig. 16 we conducted an experiment where we traversed a triangular trajectory.This approach was chosen because the proximity to the AP correlates positively with the RSS.The error between the estimated path and the real path is calculated.The average error is ~8.5216 cm, when using Wi-Fi, the RSS value will change according to the above equation.The observed error value is close to the PDR method, but not as accurate as required; therefore, a Kalman filter is proposed to enhance the performance by considering the accuracy and reliability of each source.Then the integration of PDR and Wi-Fi is a powerful technique that can be used to achieve more accurate and reliable positioning in a variety of environments.
Fig. 15 shows the basic architecture of an INS/Wi-Fi integration system.The system consists of INS,  which provides the initial position estimate and the velocity estimate.It is also used to track the errors in the position and velocity estimates.Second, the Wi-Fi positioning system is used to estimate the position of the device.Also it uses the known locations of Wi-Fi access points to estimate the position of the device.Finally, the Kalman filter is used to combine the position estimate from the INS with the position estimate from the Wi-Fi positioning system to estimate the position of the device.
Finally, the results of the experiment show that using fusion between Wi-Fi positioning and INS provides accuracy more than using only Wi-Fi positioning or using only INS.The results showed that when subtracting the output trajectory of the proposed method from the actual trajectory it becomes almost 7.2905 cm as shown in Fig. 16.
Fig. 17 presents the cumulative distribution function (CDF) of the position error rate of each INS under evaluation.The CDF indicates the probability that the position error rate is equal to or smaller than a given value.Fig. 17 shows that in approximately 75 % of the cases, the position error rate of both PDR and the fusion method is equal to or below 3.2 cm/s, i.e., 3.2 cm per stride.If a higher probability is considered, e.g., 95 %, it can be seen from Fig. 19 that the position error rate of the fusion is equal to or below 5 cm/s, i.e., 5 cm/stride Table 2.

Conclusion
This paper presents a new technology in indoor positioning that combines points strength of inertial navigation systems (INS) and Wi-Fi positioning to achieve more accurate and reliable positioning.This paper has contributed by presenting a novel approach for fingerprint-based motion estimation systems, and present an algorithm to remove the need for preparing a database which is always timeconsuming, and also can be expensive because it requires specialized hardware and software.In this work, the simulation results and the implemented hardware system presented sufficient positioning results with a resolution of around 7.2905 cm in 4 Â 4 [m 2 ].
3. The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript.

where
Dt is the sampling time; f b is the acceleration measurement vector from IMU (accelerometers); wb represents the measurement vector of angular rate from IMU (gyroscopes);

Fig. 7 .
Fig. 7.Estimated gyro bias [rad/s] after the zero update position and timing method is applied.

Fig. 11 .
Fig. 11.A comparison of the effect of zero update position and timing in pedestrian dead reckoning on error distance [Cm].

Fig. 12
Fig. 12.(a) Experimental scenario and the places of concentration of APs: (b) four APs installed in the heads of a square shape in an area of 4 Â 4 m 2 .

Fig. 13 .
Fig. 13.Wi-Fi antenna receiver connected through a computer and mounted on the shoulder.

Fig. 14 .
Fig. 14.Received signal strength values captured by the receiver antenna.

Table 1 .
Comparative analysis of preceding research endeavors.