Severe cumulative errors signicfiantly limit the applicability and expansion of IMU -based indoor localization. A quantitative analysis is conducted showing the impact that heading estimation and step length estimation have on cumulative error. In response, this paper proposes a method that utilizes a few numbers of indoor landmarks to assist IMU localization. Specifi cally, a lightweight self-attention model is employed to classify behavioral sequences from training data, matching behaviors with landmarks to reconstruct indoor paths. By sequentially linking space-discrete landmarks through timecontinuous behaviors, a spatially reconstructed path is formed within the building, assisting PDR in correcting heading directions based on the resemblance between newly predicted and existing paths. When an activity matches a landmark, the positioning estimate is recalibrated to align with the identifi ed landmark, thereby rectifying cumulative errors. While doing heading estimation, a deep learning technique is applied to mitigate sensor yaw misalignment in the IMU data. The proposed indoor positioning method demonstrates exceptional performance.
PDR suefrs from serious cumulative errors (CE) which derive from the estimation of three parameters: heading, stride, and stride length. A lot of eofrts have been made to diminish it. One way is to improve algorithms, like Kalman Filter(KF) [1], Particle Filter(PF) [2] , and Deep Learning(DP) [3]. Heading estimation and Step length are corrected by these methods. However the measuring error is persistent, later corrections are based on positions with bias causing CE constantly. It seems necessary to have additional source data to assist, which is another way out. Correspondingly, diefrent sources of data, like Wi -Fi [4, 5], Bluetooth [6], vision [7], etc. are applied with PDR to improve the accuracy. And better results have been made by them. The problem is that there are unequal scale errors, which cost abundant ef orts, in additional data. More devices are also required which makes PDR lose its conciseness.
Additional information from other resources is necessary for CE correction of PDR. Auxiliary methods relying on wireless communication require data scales in the tens of thousands, while visual approaches demand even higher computational power, resulting in substantial human and nifancial costs. To mitigate these issues and enhance the convenience of PDR localization, we propose a method that combines a small number of landmarks with the extraction of behavioral information from IMU. Based on this idea, the path inside a building and human activity information are excavated from IMU. For the majority of indoor human physical activities, directly determining the position determination and navigation of the whole body is not essential because we can quickly visually learn and memorize the space layout to nfid out where we are and how to get to another location. Monitoring human movements has many more indirect benetfis, e.g., determining the quantity of human motion, building occupancy with respect to layout, optimizing human physical activities that are distributed, care in the community of less physically able people, etc. Firstly, a deep learning method is applied to mine the behavior characteristics in IMU data, such as stairs up and down, turning, walking, stopping, etc., and map them with landmarks. Then, the path inside the building is reconstructed by matching landmarks and the original PDR result. The reconstructed path can help PDR itself to correct the heading. The contributions of our work are as follows: 1. IMU data is used to extract behavior semantics based on a self-attention model we designed. And mapping the relationship between pedestrians’ behaviors and landmarks inside the building is built. This mapping relationship can update the position to the specicfi waypoints in the PDR positioning process. 2. The intrinsic nature of CE lies in the high autocorrelation of step sequences. The segmentation of this correlation through truncated approaches in behavior recognition constitutes a pivotal strategy for mitigating the CE. Furthermore, we discern that within disparate behavioral intervals, the state of motion remains constant, and this equilibrium state exerts a lesser impact on the CE compared to the transitional phases of behavior states. 3. Classicfiation models eefctively avoid noise interference in the data, whereas regression models are more susceptible to yaw misalignment, making them dicfiult to tfi accurately. Peak and valley detection are both applied based on a low-pass lfi ter and cooperate with vertex and interval threshold to clean the interference points shown in Figure.6 4. We designed a landmarks-based calibrating (shiiftng reference point to a new location related to an activity waypoint change) PDR location system based on activity information extracted from IMU data, which can alleviate the accumulated PDR error by mining the path information and behavior semantics hidden in the data. We compared the other two classic data fusion methods, PDR+WiFi and XMU_PDR, resulting in a 26.8% increase in real-time positioning.
Sensor yaw misalignment inherently contributes to each localization result, propagating through the system with subsequent measurement. This necessitates precise interval alignment to accurately determine the IMU's relative position with respect to the carrier. Techniques typically involve nonlinear and linear Kalman lfiters or multi -vector solutions, which impose signicfiant computational loads [8-10]. Attitude error dynamics are leveraged to analyze this issue. The observability of yaw misalignment is assessed using Piecewise Constant Systems (PWCS) and Singular Value Decomposition (SVD) theory [11]. Furthermore, the observability of roll misalignment in high-speed motion scenarios is improved [12]. In [13], the author proposes a method to estimate the bias between the IMU and the carrier coordinate systems, considering IMU bias. The estimation problem is treated as a joint state and parameter estimation problem, resolved using an adaptive estimator system dependent on IMU measurements. Additionally, the eefctiveness of bias estimation can be evaluated by identifying the bias between high-precision INS/GNSS and the IMU and carrier coordinate systems.
The localization algorithm follows a Markov process, where errors in previous results propagate and accumulate through successive measurements. PDR is chain positioning mode, and each estimation depends on the last result. With the chain last, the error will be accumulated [14, 15]. To solve this problem, D. Yan et al. [16] proposed a deep belief network (DBN) focusing on the periodicity of angular rate while walking, peak–valley angular velocity detection, and zero-cross detection. Based on biomechanical models, N. Perukhov. et al. [17] minimized the length estimation error. In [16, 18], authors all use peak detection to determine one step, and they made ef orts to noise canceling of acceleration. Magnetometers and gyroscopes are used for heading estimation. M.Abadi. [19] tried to use deep learning to reduce the strong disturbance of Earth’s magnetic efild inside buildings. J.Tian [20] designed an adaptive adjustment mechanism of lfiter param eters based on measurement quality assessment to improve the applicability of the method to diefrent speeds and groups of people.
Additional data sources are also added to PDR to reduce the accumulated error. In [21, 22], authors use Wi-Fi to help PDR to improve its performance. Wi-Fi RSSI nfigerprint provides a blurred area which corrects deviation in PDR. The same theory is employed in BLE [23, 24], RFID [25, 26], and UWB[27, 28]. The oflor plan as another additional data source is also used to decrease error. Through the integration of data fusion, environmental data is procured to bolster PDR positioning by Ricardo Santos [29]. CE indeed requires additional information for correction, and a specicfi type of supplementary data limits the expansion of PDR across various data environments. Furthermore, IMU contains ample information that traditional PDR has not appropriately exploited. Based on these two key points, we propose a calibrating system based on the human physical activity information system.
The envisioned system bifurcates into two distinct stages: the oiflne phase and the online phase. In the preliminary oiflne phase, depicted in the yellow and blue sections of the diagram, IMU data serves as the initial input, feeding into the "HAR-Attention Network" to extract pertinent human behavior information. This data, once harvested, is synchronized with the traditional PDR outcomes in a temporal context. Subsequently, spatial matching of reference point coordinates with behavioral semantics ensues. Through a process of coordinate transformation, the original PDR results undergo a renfied correction, culminating in the reconstitution of the indoor pathway, as illustrated in the blue segment of the gfiure. Progressing to the online phase, considerabl e recticfiation of the heading is realized, leveraging the meticulously reconstructed path. This stage involves the strategic resetting of the original PDR positioning at critical nodes, facilitated by the identicfiation and alignment of specicfi behaviors . This intricate process ultimately yields real-time, high-accurate positioning results.
The self-attention mechanism, a trailblazing concept, has gained considerable acclaim in the domain of natural language processing. When applied to serialized datasets, such as IMU data, which is rich in human activity insights, it uncovers a multitude of semantic modules. Capitalizing on this compatibility, our research harnesses the self-attention mechanism to delve into and elucidate the subtle semantic layers embedded within the activities represented in IMU data.
The Figure 2. illustrates the architecture of the model, with IMU data serving as the input which is initially subjected to a linear embedding. Utilizing an attention mechanism, the data undergoes a re-weighting process as delineated by the formula. This entails computing the dot-product results of the
and , which are subsequently multiplied by the matrix , thereby channeling heightened focus toward regions with greater weighted signicfiance, shown below:
( , , ) = = ∗ , ∈ ℝ ∗ = ∗ Where
is the recognition result, represents the fully connected layer.
Where ∈ ℝ ∗ , ∈ ℝ ∗
and ∈ ℝ ∗ are three inputs of the self-attention layer: queries, keys, and values, where , , and are the element numbers in diefrent inputs and , , and denote the corresponding element dimensions. The scalar prevents the Somftax func tion from falling into regions with tiny gradients. One query’s output is computed as a weighted sum of the values, where each weight of the value is computed by a designated function of the query with the homologous key.
Where represents the output of 1 ∗ 1 convolution layer weighted by and the attention
layer
. And the nfial output of this network is:
(
√
)
1
√
(
During the training phase, conventional PDR is used to generate the initial path which has a large cumulative error. Then, the timestamps of behavior recognition in section 3.2 are obtained to match the path nodes in the time domain. Aeftrward, coordinates transformations are made to the heading estimation of conventional PDR in diefrent time periods based on known reference points.
Figure 4. (a) shows the path generated by conventional PDR, and the lower part shows the
timestamps of diefrent behavior results recognized by the ‘self -attention network’ in the time
sequence. The time nodes of the behaviors are matched with the results of the generated path,
resulting in the visualization of the matching results shown in (b), where the red markers represent
the matching results. The indoor reference coordinates are used to correct the coordinate positions
of the matches. The angle at which each behavior landmark deviates from the reference point is
denfied as the formula (
θ = arccos [||(( ,, ))||∗∗||(( ,, ))||] (
The deviation angle can be used to correct the predicted path of PDR. The formula for correcting
each predicted point is as follows (
{ ′′ == ∗∗ scions +− ∗∗csoins (
Aeftr performing heading conversion on all coordinates in each time interval, the reconstruction of the indoor path is completed, as shown in the result in Figure 4. (c).
The main reason for the serious CE in conventional PDR is the deviation in heading estimation
explained later. To avoid errors in heading estimation, the reconstructed path in the indoor
environment is used as an eefctive basis for heading determination. The path between the behavior
recognition points is classiefid as the same heading, and the reconstructed path data is sliced and
used as training samples. An MLP is used to tfi the estimated heading with the training data,
completing an accurate estimate of the heading. To reduce time complexity, we used lightweight
weight parameters, with the number of nodes in each hidden layer being (
are the measurements from the three-axis accelerometers, and denotes the sum values of these three-axis accelerometer measurements.
For this part, the main problem is to nfid out the peak value and valley accurately, and the peak
value or valley value is exactly a complete gait. Due to the inuflence of noise, the traditional method
can detect the peak value, but the peak value needs to be lfitered twice , because the detected peak
value always contains some interference, and these interference points are random. A low path lfiter
is applied to straining high-frequency noise and the setting is:
(
= = 2 ∗
is Nyquist frequency, represents sampling rate and
Peak and valley detection is then applied to the lfitered accelerated data. There is also low frequency noise caused by the physical shaking which will be also detected in peaks or valleys as shown in the red circle in Figure 6. To avoid this detection error, vertex, and interval threshold is used.
Generally, a linear frequency model or empirical model is used to calculate the step length. The linear frequency model mainly uses height and step frequency to establish a linear relationship with the step length. This method generally has low calculation cost, but a high error rate. At present, most of the step estimation methods using PDR for positioning generally use parametric models. The parametric model is proposed in this paper [30], using an empirical model. Where is the coecfiient which can reduce the impact of mutation values.
() represents the Earth coordinate calculation algorithm. = ℎ( ), where is the ℎ estimated Heading. = ℎ(
), where is the ℎ estimated Step length.
Where
End if End while ℎ = ∗ √4 − Where ,
represent the maximum and minimum of accelerate, is the rate index and it represents the inuflence of the high, step direction and step rate to step length.
Indeed, the precision of this method for estimating step length is notably inconsistent. This
variability largely stems from the substantial oscillation in the diefrential between peak an d trough
values. As discernible from the equation, this uflctuation diminishes somewhat when raised to the
fourth power. Nonetheless, even minor discrepancies, once magniefid by the coecfiient
in signicfiant deviations in step sizes. Conver sely, employing the reconstructed path as a corrective
measure for step estimation markedly enhances the stability, eefctively mitigating the cumulative
, can result
error in PDR attributable to inaccuracies in step calculations.
(
The algorithm outline is shown in Table 2. If there is a new movement, the rfist step is to use low pass lfitering and peak detection methods to process the accelerometer data, then update the peak point list and record the peak point time. Second, obtain the maximum and minimum values of the accelerometer within 0.2s before and aeftr the peak point, and then calculate the step size. The third step is to estimate the heading using the data from the gyroscope, accelerometer, and magnetometer. Finally, return the location result and update the location.
The preceding chapter delineated the entire algorithmic workoflw along with the intricacies of its implementation. This section is dedicated to applying the algorithm across diverse datasets, collected from within various architectural structures, thereby substantiating the algorithm's ecfiacy.
The data is ocfiially provided by IPIN 2021 and IPIN 2022 Conference. A variety of sensor data collected in mobile phones, such as Wi-Fi, BLE, light, sound, barometric pressure, acceleration, gyroscope, and magnetometer, are used to complete indoor positioning tasks in the IPIN 2022 Track 3 competition. The data used in this stage are mainly from barometers, accelerometers, gyroscopes, and magnetometers. Their data format is shown in the following Table 3. The sampling frequency of diefrent sensors is diefrent. The sampling frequency of the barometer is below 10Hz, and that of the accelerometer, gyroscope, and magnetometer is about 50Hz.
The format of the dataset [31].
MAGN: the local magnetic efild, as measured by the 3 -axis magnetometer in the phone Format Example Format Example Format Example
MAGE; AppTimestamps(s); SensorTimestamp(s); Mag_X(uT); Mag_Y(uT); Mag_Z(uT); AMcAcGurEa;c0y.(0i0n3te5g;8e9r0)2.708;-20.700;-34.02000;-19.20000;3 ACCE: the phone’s acceleration, as measured by the 3-axis accelerometers in the phone GYRO: measure the phone’s rotation, as measured by the 3-axis magnetometer in the phone ACCE; AppTimestamps(s); SensorTimestamp(s); Acc_X(uT); Acc_Y(uT); Acc_Z(uT); AACccCuEra;c0y.0(i0n3t5e;g8e9r0)2.708;-1.8004;6.41464;-7.17303;3 GYRO; AppTimestamps(s); SensorTimestamp(s); Gyr_X(uT); Gyr_Y(uT); Gyr_Z(uT); GAcYcRuOr a;0c.y0(0i3n5te;8g9e0r2).708;-0.22846;-0.22930;-19.20000;3 PRES: the atmospheric pressure Format
PRES; AppTimestamps(s); SensorTimestamp(s); Pres(bar); Accuracy(integer) Example PRES;0.0035;8902.708; 2.20000;3
In the process of data analysis, data over a long period is used to verify the eefctiveness of the algorithm. For example, in gait detection algorithm, acceleration data up to ten minutes is used to test the eefcts of low -pass lfitering and peak detectio n. The proposed algorithm is a real-time positioning algorithm, so it is necessary to specify how much of the positioning frequency is in realtime. Although, under diefrent requirements, the requirements for "real -time" are diefrent, and in human indoor activities, the positioning frequency of 2Hz and above can be considered as a realtime state.
Figure 7. shows the data collection process and the way to hold the device. The user may have done other realistic movements such as stopping, sitting, attending a phone call, taking an elevator, among others. The focus is more on ocfie buildings as they cater to a larger audience, and moreover, the behavior of individuals in ocfie spaces is more purposeful, meaning that the pathways are more organized.
During the training phase, data collection is imperative for the test area. The self-attention mechanism is then applied to this training data, facilitating the extraction of behavioral information from the sequential data. Concurrently, PDR is employed to garner initial path information. Following this, a correlation is established between the behavioral data and key nodes, leading to further recticfiation of the path information. The corrected data, endowed with enhanced directional accuracy, signicfiantly mitigates the cumulative error issue inherent in PDR. This process culminates in the creation of foundational data for the real-time positioning system, thereby enabling the provision of highly precise, real-time location services. 4.2.1 HAR in map
The training set for the self-attention model mentioned in the previous chapter was self-collected, with a sampling frequency identical to that of the current experiment. The crux lies in the fact that the input length of the training dataset is 200*3, encompassing only a single activity type. To augment the model's adaptability, the positioning of the activity within the sample is randomized. However, in real indoor settings, data is temporally continuous, necessitating a more precise demarcation of the boundaries between behavioral nodes to avert signicfiant recognition errors. We have e mployed a sliding window technique to delineate these boundaries. The window's width is set to 30, with padding of zeros at both ends to fullfil the model's input requirements. It is pivotal to note that the width of the sliding window is contingent upon the sampling rate, and the specicfi range for this setting can be referenced from the following formula:
≈ /max ( ) (9) Where denotes the width of the sliding window, represents the sampling frequency, and is the frequency of the movement, typically ranging from 0.6Hz to 1.5Hz. Utilizing the maximum value of the frequency ensures that the data within the sliding window is minimized, as an inuflx of additional data into the window could precipitate severe recognition inaccuracies. when the window length is increased to 50 ( 50) the accuracy rates plummet to 6.66%, 7.30%, and 9.24%, with an average of 7.69%. The rationale behind this steep decline is fairly evident: a longer window encompasses a more extensive range of movements, leading the model to misinterpret simple actions as complex ones. 4.2.2 Path in map
Utilizing conventional PDR, we initially generate a path, within which substantial cumulative errors are inherent. To rectify these errors to the greatest extent possible, we adopt the approach of aligning the serialized behavioral information, unearthed using the method mentioned in the previous subsection, with the original path on a time series basis. The ensuing Figure 9. serves as a case illustration. The top-left corner of the image represents a path gener ated by traditional PDR, with the top-right legend depicting an enlarged view of a turning point, which is the landmark, within the path. The lower sequence illustrates the behavioral detection results based on accelerometer data. We designate these specifi c points in the temporal domain as breakpoints and then eefctively correct the heading direction from the previous breakpoint or origin to the current one. This strategy aims to minimize the CE caused by sudden directional changes during sustained activities. Moreover, the post-correction data provide a high-quality foundational basis for the heading estimation model. will serve as inputs for training the Multilayer Perceptron (MLP) model. These samples encapsulate the dynamics of movement within indoor environments, encompassing various positions and directions. The sample data is bifurcated into training and testing sets, utilized both for the training and the evaluation of the model's performance.
In the validation phase, the test paths involve data collection over extended durations, with the experimental setting situated within the intricate connfies of an ocfie building. This environment encompasses ocfies, corridors, conference rooms, and stairwells. The methodology for collecting validation data is consistent with the approach detailed in Section 4.1. For ground truth, we rely on GPS and laser rangenfiders to obtain high -precision indoor location information, which is crucial for subsequent error assessments.
Initially, we conducted an error analysis of the results, as depicted in the Cumulative Distribution Function (CDF) graph in Figure 11. which reveals that the method proposed here has improved the maximum error by approximately 8 meters, equating to a nearly 26.8% enhancement. Notably, in the initial phase, the steeper slope of the green line indicates that the overall errors are more densely clustered around smaller magnitudes. In contrast, the steeper sections of the orange and blue lines are observed in the latter half, suggesting that their errors are more prevalent in larger ranges. Within the CDF graph, the most signicfiant discrepancy is at the median position, where the error corresponding to the green line is around 7 meters, compared to approximately 17 meters for the other two lines.
Subsequently, we visualized the results, as shown in Figure 12. The red path represents the data collection route, while the top-right orange path signiefis the positioning results of the PDR algorithm. The bottom-left blue path indicates the PDR positioning outcomes augmented by the Kalman lfiter. The top-left green path represents the positioning results obtained using the proposed algorithm. From a visual standpoint, it is evident that both the traditional PDR and the Kalman lfiter enhanced PDR algorithm exhibit signicfiant deviations in heading calculations.
To pinpoint the sources of error more accurately, we conducted separate assessments for heading and step length errors. As presented in Table 5., the total path length in the experimental data was 214.43 meters. The lengths computed by the three methods were 221.18m, 221.18m, and 215.01m, respectively. Both the PDR + Wi-Fi and XMU_PDR methods employed the same step length detection technique, resulting in identical total lengths for these two approaches. Their respective errors were 6.75m, 6.75m, and 0.68m, averaging out to an error of 0.01m, 0.01m, and 0.001m per step. Concurrently, we quantiefid the errors in heading estimation with each position update. The Table 5. displays the total errors in heading determination across 677 position updates in this experiment, tallying to 30901.67, 17859.26, and 12693.75, respectively. The average error per update was 45.65, 25.38, and 18.75. The positional deviations caused by heading judgment errors with each position update were 0.26m, 0.15m, and 0.10m, respectively. Compared to the errors induced by step length estimation, the impact of heading determination errors on the results was more than 100 times greater. These statistics indicate that the primary source of CE is the misjudgment in the heading. Addressing this issue has been a focal point of our work.
In this study, we leverage the nuanced pedestrian behavior data and intrinsic path information within buildings to augment PDR positioning. This initiative heralds the advent of a few landmarks assisted, real-time PDR positioning system, adept at surmounting the traditional PDR's dependency on extraneous data for CE correcting. Former methodologies, which sought to rectify PDR's cumulative inaccuracies by amalgamating additional data sources, have signicfiantly impeded PDR's evolution, predominantly due to the prohibitive costs and logistical complexities involved in data acquisition. Conversely, our approach of exploiting IMU data to substantially attenuate these cumulative errors represents a minimal investment with maximal yield, poised to catalyze the broader implementation of PDR. The proposed self-assisted PDR system is instrumental in enabling devices to ascertain real-time locations, thereby facilitating location-based services for users, given that IMU data invariably mirrors the motion state of its carriers. To enhance the precision of indoor path reconstruction, we employ multiple reference coordinate points as aids. While this method markedly elevates accuracy, it concurrently diminishes the system's autonomy. The rich tapestry of motion-related information encapsulated within IMU data is a boon to PDR's real-time positioning capabilities, necessitating advanced processing and extraction techniques. Moreover, the exploration of latent information within IMU data remains a paramount focus of our future endeavors. Our application scenario, predominantly within ocfie buildings, presents unique challenges. The diverse architectural layouts of diefrent bu ilding types necessitate a broader spectrum of behaviors to adapt to varying contexts. Thus, validating and enhancing the algorithm's adaptability in such multifaceted environments is a primary objective we aim to pursue moving forward. [9] C. Tan, X. Zhu, Y. Su, Y. Wang, Z. Wu, and D. Gu, "A new analytic alignment method for a SINS," Sensors, vol. 15, no. 11, pp. 27930-27953, 2015. [10] Y. Zhang, L. Luo, T. Fang, N. Li, and G. Wang, "An improved coarse alignment algorithm for odometeraided SINS based on the optimization design method," Sensors, vol. 18, no. 1, p. 195, 2018. [11] X. Xia et al., "Estimation on IMU yaw misalignment by fusing information of automotive onboard sensors,"
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