AUTOMATIC FINE-GRAINED RADIO MAP CONSTRUCTION AND ADAPTION

Abstract

An automatic wireless fine-grained ratio map construction and adaptation system may include a Gaussian process regression (GPR) model constructed with real wireless received signal strength (RSS) measurements collected in a free space to provide coarse RSS estimation in a constrained space, and a generative adversarial network (GAN) to provide fine-grained RSS estimation in the constrained space by using an output of GPR as an input for a generator of GAN, modeling the irregular RSS distributions in complex indoor environments. The system may generate realistic RSS data in the constrained space that has not been manually site-surveyed.

Claims

1. An automatic wireless fine-grained ratio map construction and adaptation system, comprising: a sensor configured to collect real wireless received signal strength (RSS) measurements in a free space; a processor configured to construct a Gaussian process regression (GPR) model based at least in part on the real wireless RSS measurements collected by the sensor in the free space to provide coarse RSS estimation in a constrained space; and a generator of a generative adversarial network (GAN) configured to provide fine-grained RSS estimation in the constrained space by using an output of the GPR as an input for the generator of the GAN.

2. The system of claim 1, wherein the system is further configured to model the irregular RSS distributions in complex indoor environments.

3. The system of claim 2, wherein the system is further configured to generate realistic RSS data in the constrained space that has not been manually site surveyed.

4. The system of claim 1, wherein the environment can be classified as the free space where the sensor can access freely.

5. The system of claim 1, wherein the environment can be classified as the constrained space where the sensor cannot access easily or where the noise of its measurement is high.

6. The system of claim 1, wherein the processor is configured to construct the GPR model by using the RSS measurements at calibration points as well as their two-dimensional coordinates collected by the sensor in the free space to capture anomalous RSS variations on a rough level.

7. The system of claim 6, wherein the processor is further configured to construct the GPR model by providing a coarse RSS estimation at the calibration points and adopting them as the input for the generator of the GAN instead of random noise.

8. The system of claim 7, wherein the nonlinear relations between the spatial and radio space captured by the GPR can be inherited by the GAN.

9. The system of claim 1, wherein the generative adversarial network (GAN) is configured to reveal the irregular RSS distribution in an environment that is not explored by the GPR.

10. The system of claim 1, wherein the generative adversarial network (GAN) is configured to synthesize realistic RSS data to fool a discriminator of the GAN while the discriminator of the GAN tries to distinguish whether the data is real or fake.

11. The system of claim 1, wherein providing the fine-grained RSS estimation comprises leveraging the GPR model to generate coarse estimations and use them as the input for the generator of the GAN.

12. The system of claim 11, wherein the output of the generator of the GAN is the fine-grained RSS estimation.

13. A method, comprising: a sensor of an automatic wireless fine-grained ratio map construction and adaptation system collecting real wireless received signal strength (RSS) measurements in a free space; a processor of the automatic wireless fine-grained ratio map construction and adaptation system constructing a Gaussian process regression (GPR) model based at least in part on the real wireless RSS measurements collected by the sensor in the free space to provide coarse RSS estimation in a constrained space; and a generator of a generative adversarial network (GAN) of the automatic wireless fine-grained ratio map construction and adaptation system providing fine-grained RSS estimation in the constrained space by using an output of the GPR as an input for the generator of the GAN.

14. The method of claim 13, further comprising modeling the irregular RSS distributions in complex indoor environments.

15. The method of claim 14, further comprising generating realistic RSS data in the constrained space that has not been manually site surveyed.

16. The method of claim 13, wherein the processor constructing the GPR model includes the processor using the RSS measurements at calibration points as well as their two-dimensional coordinates collected by the sensor in the free space to capture anomalous RSS variations on a rough level.

17. The method of claim 16, further comprising the processor constructing the GPR model by providing a coarse RSS estimation at the calibration points and adopting them as the input for the generator of the GAN instead of random noise.

18. The method of claim 13, further comprising the GAN revealing the irregular RSS distribution in an environment that is not explored by the GPR.

19. The method of claim 13, further comprising the GAN synthesizing realistic RSS data to fool a discriminator of the GAN while the discriminator of the GAN tries to distinguish whether the data is real or fake.

20. The method of claim 13, wherein the generator providing the fine-grained RSS estimation comprises the generator leveraging the GPR model to generate coarse estimations and use them as the input for the generator of the GAN.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIG. 1 illustrates an example methodology of a system including a Gaussian process regression (GPR) initialized Wasserstein generative adversarial network (GAN) in accordance with certain implementations of the disclosed technology.

[0012] FIG. 2 illustrates an example of a layout of calibration points in free space and virtual/testing points in constrained space in accordance with certain implementations of the disclosed technology.

[0013] FIG. 3 illustrates an example of a boxplot of receiving signal strength (RSS) estimation errors of nine access points (APs) by way of the WiGAN and GPR in accordance with certain implementations of the disclosed technology.

[0014] FIG. 4 illustrates an example of a distribution of the RSS estimation errors of FIG. 3.

DETAILED DESCRIPTION

[0015] Implementations of the disclosed technology, referred to herein as WiGAN, are generally directed to an automatic fine-grained ratio map construction scheme that is empowered by a Gaussian process regression (GPR) initialized Wasserstein generative adversarial network (GAN). Any environment can be divided into two categories: free space where a signal measurement sensor can access freely, and constrained space where the sensor cannot access or the noise level of its measurement is high. The WiGAN may firstly establish a GPR model using the real RSS readings collected by the sensor in the free space. Then, the outputs of the GPR may be adopted as the input of GAN's generator.

[0016] A training objective of the GAN may be to model the irregular RSS distributions in the environment, and generate realistic RSS data in the constrained space that have not been manually site surveyed. The trained GPR model may be used to generate coarse RSS estimations at those virtual points within the constrained space. Then, by using them as the input for the GAN's generator, the fine-grained RSS values at points inside the area of interest may be estimated from the generator. The WiGAN can be leveraged to generate radio map for any suitable RF signals, e.g., GPS, LTE, BLE, and WiFi.

[0017] In certain implementations, WiGAN can be leveraged to generate a radio map for any RF signals (e.g., GPS, LTE, BLE). WiGAN may be used to construct a fine-grained WiFi radio map automatically in a complex indoor environment. The RSS distribution can be modeled with Gaussian Process Regression (GPR) and fundamentals of Generative Adversarial Network (GAN). After that, WiGAN can construct the fine-grained radio map by way of the GPR initialized Wasserstein generative adversarial network.

[0018] Gaussian Process Regression for Coarse RSS Estimation

[0019] GPR has been used in many applications, e.g., spatial smoothing, geostatistics, and robotics. Since its nonlinear regression capacity is more suitable to capture the anomalous RSS variations in complex indoor environments than linear signal delay function, researchers have leveraged it to interpolate RSS values and, consequently, reduce the cost for offline calibration.

[0020] Consider a mobile robot that collects RSS values from p access points (APs) at n calibration points in the free space. The spatial map and radio map dataset includes n pairs of (l.sub.i.sup.ƒ, S.sub.i.sup.ƒ).sub.i=1.sup.n where l.sub.i.sup.ƒ=(x.sub.i, y.sub.i) is the two-dimensional coordinates of a calibration points, and S.sub.i.sup.ƒ is the RSS values from p APs at location l.sub.i.sup.ƒ. The relationship between the spatial space L and the signal space S can be modeled as:

S=ƒ(l)+{grave over (σ)}

[0021] where {grave over (σ)} is independent and identically distributed (i.i.d.) additive zero-mean Gaussian noise with variance σ.sub.{grave over (σ)}.sup.2. The latent function ƒ(l) can be modeled as a Gaussian Process (GP):

S˜GP(m(l),k(l,l′))

[0022] where m(⋅) and k(⋅,⋅) represent the mean and covariance function of GP respectively. For RSS radio map construction, the mean function m(⋅) can be modeled as a Log-Distance path loss model and a quadratic polynomial function. The quadratic polynomial function can be utilized as the mean function:

m(l.sub.i)=β.sub.0+β.sub.1x.sub.i+β.sub.2y.sub.i+β.sub.3x.sub.i.sup.2+β.sub.4y.sub.i.sup.2+β.sub.5x.sub.iy.sub.i,

[0023] where (x.sub.i, y.sub.i) are the coordinates of location l.sub.i, and the squared exponential kernel function as the covariance function:

[00001]$k\left(l,l^{\prime }\right)={\sigma }_f^2\exp \left[\frac{-{.Math.l-l^{\prime }.Math.}^2}{2r^2}\right]+{\sigma }_{ò}^2\delta \left(l,l^{\prime }\right),$

[0024] where σ.sub.ƒ.sup.2, r and δ(⋅,⋅) denote the signal variance, the scale parameter, and the Kronecker delta function, respectively.

[0025] The Gaussian process regression model (GP) can be used to provide a coarse estimation of RSS values {Ŝ.sub.j.sup.s}.sub.j=1.sup.m∈Ŝ.sub.GP.sup.s from p APs at m locations {l.sub.j.sup.s}.sub.j=1.sup.m∈L.sup.s locations in constrained space. At each location l.sub.j.sup.s, the RSS value from each AP can be estimated according to the posterior mean of GP:

s.sub.j.sup.s=m(l.sub.j.sup.s)+K(l.sub.j.sup.s,L.sup.ƒ)[K(L.sup.ƒ,L.sup.ƒ)+σ.sub.{grave over (σ)}I].sup.−1(S.sup.ƒ−m(L.sup.ƒ)).

[0026] Generative Adversarial Network (GAN)

[0027] A GAN as described herein generally includes two parts: a generative model G and a discriminative model D. By taking a noisy vector z˜P.sub.n(z) (e.g., Gaussian or uniformly distributed) as the input, the objective of the generator G is to synthesize data ({circumflex over (x)}) resembling real data distribution, x˜P.sub.r(x). The discriminator D can randomly sample a batch of real and synthesized data and distinguish them by maximizing the probabilities that x is real and {circumflex over (x)} is fake. The loss function of GAN can be formulated as:

min.sub.Gmax.sub.DE.sub.x˜P.sub.r.sub.(x)[log D(x)]+E.sub.z˜P.sub.n.sub.(z)[log(1−D(G(z)))]

[0028] where G and D can be trained jointly on the loss function in a minimum-maximum fashion using backpropagation, which updates D to maximize the likelihood of the discriminator being correct while updating G to generate realistic data to fool the discriminator. One potential issue with the GAN is the vanishing gradients for the generator. Thus, WiGAN can be used to minimize the Wasserstein distance between the distributions instead of the original Jensen-Shannon divergence in the settings of GAN.

[0029] The GAN generally obtains groundbreaking results for the generation of realistic images. A few studies apply GAN on RF signal generations, e.g., audio signal and EEG signals. A Tensor Generative Adversarial Network (TGAN) can be used to generate a representation of RSS values with super-resolution for indoor localization.

[0030] WiGAN

[0031] WiGAN may generate realistic and fine-grained RSS values in constrained space (e.g., on a table of cubicles, conference rooms, and personal offices) using its generator G with the output of the GPR model GP learned using the data collected in free space (e.g., corridors, open space). The potential issue is more challenging since RSS values are to be estimated at new coordinates in order to construct a fine-grained radio map in the entire environment, while conventional methods focus on generating more RSS samples at the coordinates where real RSS measurements are already available.

[0032] An example of using WiGAN for radio map construction and adaptation is presented in Algorithm 1 and illustrated by FIG. 1. This example includes four primary steps.

[0033] Step 1: a GPR model GP is constructed using the RSS values of p APs collected at n calibration points (CPs) in the free space as well as their 2D coordinates (S.sup.ƒ,l.sup.ƒ).

[0034] Step 2: this step of WiGAN aims to train its generator G and discriminator D with (S.sup.ƒ,Ŝ.sub.GP.sup.ƒ). In WiGAN, instead of using a noisy vector z˜P.sub.n(z) as the input for G in GAN, the system concatenates the coarse RSS estimation from GP together with the noisy vector as Ŝ.sub.GP.sup.ƒ and uses them as the inputs for G. In this manner, WiGAN inherits the nonlinear relations between the spatial and radio space captured by GP and has better initialization for adversarial training than using the random noisy vector. The inputs for the discriminator D are randomly sampled batches of real RSS data S.sup.ƒ˜P.sub.r(S.sup.ƒ) and synthesized RSS data Ŝ.sub.GP.sup.ƒ˜P.sub.n(Ŝ.sub.GP.sup.ƒ) in the free space. The loss function of WiGAN may be formulated as:

min.sub.Gmax.sub.DE.sub.S.sub.ƒ.sub.˜P.sub.r.sub.(S.sub.ƒ.sub.)[log D(S.sup.ƒ)]+E.sub.Ŝ.sub.GP.sub.ƒ.sub.˜P.sub.n.sub.(Ŝ.sub.GP.sub.ƒ.sub.)[log(1−D(G(Ŝ.sub.GP.sup.ƒ)))].

[0035] Backprogration can be used to optimize the parameters of G and D in the min-max loss function. A primary objective of G may be to generate realistic RSS data to fool D, while D may aim to maximize the likelihood of being correct of the determination of whether the data is real or fake. The Wasserstein distance can be adopted as the metric to measure the discrepancy between the two data distributions to improve the training stability of WiGAN.

[0036] Step 3: to estimate the RSS values at virtual points (VPs) in the constrained space, a coarse estimation ŜG.sub.P.sup.ƒ can be provided via the GP model established in Step 1. Suppose there are m testing point in the constrained space, the coarse RSS value of each AP at each testing point (j=1, . . . , m) may be calculated as:

ŝ.sub.GP.sub.j.sup.s=m(l.sub.j.sup.s)+K(l.sub.j.sup.s,L.sup.ƒ)[K(L.sup.ƒ,L.sup.ƒ)+σ.sub.{grave over (σ)}.sup.2I].sup.−1(S.sup.ƒ−m(L.sup.ƒ)).

[0037] Step 4: the coarse RSS estimations obtained Ŝ.sub.GP.sup.ƒ by Step 3 together with a small random noisy vector may be utilized as the input for the generator G of WiGAN. The fine-grained RSS estimations at VPs in the constrained space may be calculated using the generator G trained in Step 2 as:

Ŝ.sup.s=G(Ŝ.sub.GP.sup.ƒ).

[0038] In this manner, a fine-grained radio map that covers both free and constrained space may be established by WiGAN with higher spatial granularity.

[0039] Algorithm 1 below further describes the radio map construction and adaptation.

TABLE-US-00001 Algorithm 1 WiGAN: radio map construction & adaptation Input: p - Number of APs n - Number of calibration points in free space l.sup.f - 2D coordinates of calibration points in free space S.sup.f - RSS data at calibration points in free space m - Number of virtual points in constrained space l.sup.s - 2D coordinates of virtual points in constrained space Output: Ŝ.sup.s - Estimated RSS at virtual points in constrained space Step 1 Construct Gaussian process regression model ( ) via data collected in free space S.sup.f ~ (m(l.sup.f), k(l.sup.f, l.sup.f ′)) Step 2 Train generator  and discriminator  of WiGAN and use coarse RSS estimation by  as input for [00002]$\hspace{1em}\begin{array}{c}\underset{𝒟}{\max }{𝔼}_{S^f\sim P_n\left(S^f\right)}\left[\log 𝒟\left(S^f\right)\right]+\\ {𝔼}_{)}\left[\log \left(1-𝒟\left(\left(\right)\right)\right)\right]\end{array}$ Step 3 Estimate coarse RSS value of each AP at each virtual point (j = 1, . . . , m) in constrained space via  = m(l.sub.j.sup.s) + K(l.sub.j.sup.s, L.sup.f)[K(L.sup.f, L.sup.f) + σ.sub.s.sup.2I].sup.−1(S.sup.f − m(L.sup.f)) Step 4 Estimate fine-grained RSS value at virtual points in constrained space via the generator  of WiGAN Ŝ.sup.s = ( ) return Ŝ.sup.s

[0040] Experimental Setup

[0041] To evaluate the radio map construction and adaptation performance of WiGAN, extensive experiments were conducted in a 700 m.sup.2 multi-functional office. As depicted in FIG. 2, the office 200 was composed of 1 lab, 1 pantry area, 2 conference rooms, 4 personal offices, and an open space office with 20 cubicles. Nine TP-LINK N750 routers were deployed to establish the WiFi sensing network of WinIPS. By upgrading the software of these routers, they were able to detect existing WiFi traffic, extract RSS values of MDs with their corresponding MAC addresses from the data packets, and forward this data to the WinIPS back-end server. The back-end server received and parsed the data from routers, and stored the RSS measurements in a MySQL database for WiGAN evaluation.

[0042] An MD (here, an iPhone 7) was placed on a mobile robot (here, Turtlebot 2) to collect the RSS values of the MD automatically in the free space (e.g., corridors, open space) at 62 calibration points (highlighted as blue dots in FIG. 2). RSS values of the MD were manually collected at 80 virtual/testing points (highlighted as red dots in FIG. 2) in the constrained space (e.g., on the table of cubicles, conference rooms, and personal offices), which served as the ground truth to validate the performance of WiGAN.

[0043] Fifty RSS samples were collected in each calibration point. The coordinates of the calibration points and the mean RSS value collected on each point (l.sub.i, S.sub.i).sub.i=1.sup.ƒ were utilized to construct the Gaussian process regression model. Then, the synthesized RSS samples and the real RSS values collected on the calibration points were used to train the generator and discriminator of WiGAN in the min-max manner as illustrated in FIG. 1. After that, the RSS values at the testing points were estimated by feeding their coordinates to the Gaussian process regression model and the generator.

[0044] Evaluation on RSS Estimation Accuracy

[0045] The mean (ē.sub.RSS) and standard deviation (σ.sub.RSS) of RSS estimation errors of WiGAN were calculated with respect to the observed RSS measurements at the 80 testing points in the constrained space. The mean RSS estimation error of WiGAN (80×50 samples) was 3.56 dBm with the standard deviation of 2.7 dBm on average. Its detailed performance at each AP was compared with GPR. As demonstrated in Table 1 (ē.sub.RSS) and Table 2 (σ.sub.RSS), WiGAN reduced the mean error by 54.5% and the standard deviation of RSS error by 49.5% compared to GPR on average, which achieves tremendous performance gain. Statistical measurements of the two methods, including boxplot and histogram of RSS estimation error distribution of the 9 APs are illustrated by FIG. 3 and FIG. 4, respectively. As shown in the visual depiction 300 of FIG. 3, the 75.sup.th percentile of error for WiGAN at each AP was lower than 6 dBm, while those of GPR was much larger. The same conclusion can be drawn from the distribution of error as illustrated by the visual depictions 400 of FIG. 4.

TABLE-US-00002 TABLE 1 Comparison of RSS estimation errors - mean ē.sub.RSS (dBm) Method AP1 AP2 AP3 AP4 AP5 AP6 AP7 AP8 AP9 Average GPR 8.47 11.73 10.03 4.00 6.18 7.48 7.57 3.86 11.12 7.82 WiGAN 3.91 3.77 3.33 3.39 3.26 3.39 3.52 3.73 3.76 3.56

TABLE-US-00003 TABLE 2 Comparison of RSS estimation errors - standard deviation σ.sub.RSS (dBm) Method AP1 AP2 AP3 AP4 AP5 AP6 AP7 AP8 AP9 Average GPR 6.37 7.57 6.21 3.12 4.25 6.24 4.65 3.35 6.40 5.35 WiGAN 2.80 2.42 2.59 2.46 2.29 3.09 2.89 3.07 2.73 2.70

[0046] Evaluation on Localization Accuracy

[0047] Since an objective of constructing and updating a fine-grained WiFi radio map is to improve the localization performance, the localization accuracy of the IPS was evaluated when WiGAN was utilized. Thirty testing points were randomly selected in the entire office. STI-WKNN was adopted as the localization algorithm together with different radio maps to estimate locations at these testing points and the localization errors (Euclidean distance) were calculated with respect to the physical locations (ground truth). The performance of WiGAN was compared with three radio maps, real RSS data collected by robot at the calibration points in free space (lower baseline), real RSS data collected by robot+generated RSS values via GPR, real RSS data collected by robot+generated RSS values via WiGAN, and real RSS data collected at calibration points in constrained space and free space (manually collected radio map).

TABLE-US-00004 TABLE 3 Comparison of localization errors in terms of mean (ē.sub.LA) and standard deviation (σ.sub.LA) Method ē.sub.LA (m) σ.sub.LA (m) Lower Baseline 3.87 1.64 GPR 3.25 1.53 WiGAN 1.98 0.81 Manual Site Survey 1.79 0.73

[0048] Table 3 above compares the localization errors in terms of mean (ė.sub.LA) and standard deviation (σ.sub.LA) of the four methods. As presented in Table 3, the use of RSS data collected by the robot in free space only is the worst (3.87 m) and cannot meet the localization accuracy requirement for many LBS applications. Both WiGAN and GPR enhance the accuracy over the lower baseline, which validates the necessity of generating RSS data in constrained space. A noteworthy observation from Table 3 is that WiGAN reduces the localization error by 33.5% over GPR, which indicates higher RSS estimation accuracy leading to higher localization accuracy. Another noteworthy point is the mean error of WiGAN reaching 1.98 m, which is only 0.2% lower than the manually collected radio map (upper-baseline).

[0049] The disclosed aspects may be implemented, in some cases, in hardware, firmware, software, or any combination thereof. The disclosed aspects may also be implemented as instructions carried by or stored on one or more or non-transitory computer-readable media, which may be read and executed by one or more processors. Such instructions may be referred to as a computer program product. Computer-readable media, as discussed herein, means any media that can be accessed by a computing device. By way of example, and not limitation, computer-readable media may comprise computer storage media and communication media.

[0050] Additionally, this written description makes reference to particular features. It is to be understood that the disclosure in this specification includes all possible combinations of those particular features. For example, where a particular feature is disclosed in the context of a particular aspect, that feature can also be used, to the extent possible, in the context of other aspects.

[0051] Also, when reference is made in this application to a method having two or more defined steps or operations, the defined steps or operations can be carried out in any order or simultaneously, unless the context excludes those possibilities.

[0052] Furthermore, the term “comprises” and its grammatical equivalents are used in this disclosure to mean that other components, features, steps, processes, operations, etc. are optionally present. For example, an article “comprising” or “which comprises” components A, B, and C can contain only components A, B, and C, or it can contain components A, B, and C along with one or more other components.

[0053] Also, directions such as “right” and “left” are used for convenience and in reference to the diagrams provided in figures. But the disclosed subject matter may have a number of orientations in actual use or in different implementations. Thus, a feature that is vertical, horizontal, to the right, or to the left in the figures may not have that same orientation or direction in all implementations.

[0054] Having described and illustrated the principles of the invention with reference to illustrated embodiments, it will be recognized that the illustrated embodiments may be modified in arrangement and detail without departing from such principles, and may be combined in any desired manner And although the foregoing discussion has focused on particular embodiments, other configurations are contemplated.

[0055] In particular, even though expressions such as “according to an embodiment of the invention” or the like are used herein, these phrases are meant to generally reference embodiment possibilities, and are not intended to limit the invention to particular embodiment configurations. As used herein, these terms may reference the same or different embodiments that are combinable into other embodiments.

[0056] Although specific embodiments of the invention have been illustrated and described for purposes of illustration, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, the invention should not be limited except as by the appended.