RNN-based Distance Estimation using UWB Signaling
Tae-YunJung1, Eui-RimJeong*2
1Department of Mobile Convergence and Engineering, Hanbat National University, Daejeon,34158,Korea
*2Department of Communication and Information Engineering, Hanbat National University, Daejeon, 34158,Korea
1[email protected], *2[email protected]
Abstract
Background/Objectives: The objective of this paper is to develop a new distance estimation method for indoor localization by using ultra-wideband (UWB) signals.The new technique is based on recurrent neural network (RNN), one of the famous deep learning techniques.
Methods/Statistical analysis: RNN is one of the most suitable methods for learning time series data. Hence, it is useful in processing data that change with time. The proposed method estimates the distance based on RNN from the received UWB signals. Specifically, from the received signals via IEEE802.15.4a indoor channels, the proposed RNN regressor estimates the distance. The proposed method is validated by computer simulation.
Findings: In order to estimate the distance using UWB signals, it is necessary to accurately detect the first arrived signal along the shortest path.To find this signal or time instance by using RNN, we convert 1-dimensional received signal into 2-dimensional signal. The converted signal is input to RNN regressor and trained so that the RNN output is the distance between the transmitter and the receiver. The conventional method needs received signal-to-noise ratio (SNR)estimation, and the threshold is determined by the estimated SNR. When the received signal exceeds the threshold, the first arrived signal is detected and the arrived time is called the time of arrival (ToA). However, the proposed method estimates the distance directly from the received signal without SNR estimation.According to the simulation results, the proposed method shows RMSE of less than 2 [m] in low SNR, and less than 0.5 [m] in high SNR.Those performancesare much better than the conventional method.
Improvements/Applications: The performance of the proposed RNN based distance estimator is examinedthrough computer simulation. To compare estimation accuracy, the root mean square error (RMSE) is measured. According to the results, the proposed estimator is superior to the conventional method.
Keywords:distance estimation, indoor localization, ultra-wideband (UWB), recurrent neural network (RNN), regression, root mean square error (RMSE)
1. Introduction
Recently, the development of mobile communication technologies leads to a growing demand for location-based services (LBS) [1].Usually, LBS acquires location information from satellites such as global positioning system (GPS). Although the GPS provides sufficientaccuracy in outdoors, it often fails to estimate a userβs location in indoors[2].
Therefore, new localization techniques for indoors have attracted much attention. Various techniquesfor indoor localization based on communication signals have been researched, mainly focusing on Wi-Fi, Beacon, Bluetooth, ultra-wideband (UWB), and Zigbee[3,4].
In this paper, indoor localization technology using UWB signals is considered. An UWB system, which uses a considerably wider bandwidth over 500MHz, is a short-range
radio communication technology that transmits information at low power spectral density [5]. UWB usesa very short pulse less than a few nanoseconds.It is useful to acquireaccurate location information because of high time resolution. Thus, indoor localization based on UWB signaling has been widely researched [6,7]. Among them, time of arrival (ToA)based methodsestimate the time it takes for a transmitted UWB signal to propagate. The ToA methods can estimate the exact location of the transmitter (Tx) by collecting more than 3 ToAs at different receiver (Rx)positions. Here, the locations of Rx's should be known priorly, and the location of Tx can be estimated by using the trilateration method[8]. Thus, it is important to accurately estimate ToA or the distance between Tx and Rx. Those methods estimate ToA by detecting the time when the power of the received signal exceeds acertain threshold. The threshold is a function of signal to noise ratio (SNR), which results in SNR estimation before ToA detection.
In this paper, we propose a distance estimation method based on recurrent neural network (RNN), one of the famous deep learning techniques. RNN is suitable for correlated time series data because RNN is designed to repeatedly utilize previously calculated results[9,10]. The proposed distance estimator is based on RNN consisted of LSTM cells[11]. For the input of the proposed RNN, squared magnitudes of the received signal are used. Then, the RNN estimates the distance from the Tx and the Rx.
Specifically, the 1 dimensional squared magnitudes are converted into 2 dimensional signals, and inputted to the RNN regressor. The RNN predictsthe distancefrom the 2 dimensional signal. The performance of the proposed method is verified through computer simulation. For the indoor channel model, the CM3 in IEEE 802.15.4a is used[12]. According to the simulation results, the proposed distance estimation method performs much better than the conventional threshold-based method, and the performance is especially outstandingat low SNR region and long the distance.
This paper is organized as follows. In section 2, the distance estimation system model using UWB signal is explained. The conventional threshold-based distance estimation method and proposed RNN-based distance estimation method are explained in section 3.
In section 4, the distance estimation performance of the two methods was compared through simulation. Finally, section 5 concludes the paper.
2. System model
Figure 1 shows system model for distance estimation using UWB signals. The Tx transmits a UWB pulse. UWB has short-timepulse width and wide bandwidth over 500MHz. The UWB pulse usually forms a Gaussian shape.The Rx receives the transmitted UWB pulse, and from the received signal, it estimates the distance between the Tx and the Rx.The conventional methods calculate distance after estimating ToA, but the proposed method estimates distance directly. For accurate distance estimation, the Tx and the Rx must be precisely time-synchronized.That is, Tx transmits UWB pulse at the predesignated time, and the Rx also knows the transmit time as well. The Rx estimates the distance by measuring the shortest arrival time and the distance is obtained by the arrival time. Since various reflectors in the indoor environmentsexist, the Rx may observe multiple received pulses rather than a single pulse. Among them, ToA or distance should be estimated from the first arrived UWB pulse.
Figure 1. Overall system model
3. Proposed Distance Estimation Method
This sectionintroduces the proposed distance estimator. First, the conventional threshold-based distance estimatorto be compared is explained, and then the proposed RNN-based distance estimator is introduced.
3.1. Conventional threshold-based distance estimation
The threshold-based distance estimation method offers high performance among the existing distance estimation techniques. If s(t) is a transmitted UWB pulse, the received signal r(t) is as follows:
π π‘ = π π‘ ββ π‘ β π‘0 + π(π‘) (1)
Here, * denotes the convolution operation, β(π‘) is the channel impulse response between the Tx and the Rx, and π(π‘)is the noise. π‘0isthe propagation delay (ToA) by the distance between the Tx and the Rx that we need to estimate. The received pulse is converted into a digital signal by analog to digital converter (ADC). If the sampling period is ππ , the received signal can be written as follows:
r n = π π‘ |π‘=πππ = π πππ ββ πππ β π‘0 + π(ππππ π ) (2) In Eq. (2), β’ represents round. After sampling, the time delay π‘0 to be estimated is changed into the integer value π‘0 . Because the sampling period determines the ππ estimation resolution of the time delay, if accurate ToAis required, the sampling period should be small. For ToA estimation, the threshold-based method needs the received SNR and the threshold is determined based on the SNR. It detected the earliest time where received power exceeds the threshold, and the time is the estimated ToA. Thus, SNR estimation is necessary forToA estimation. TheSNRdenoted by Ξ·is definedasfollows:
π =πππ
π§ (3)
whereππ isthe signal power,andππ§ isthe noisepower.In this paper, to estimate the SNR, instead of signal power, the maximum of the squared magnitudes of the received signal is used instead.The signal powerisestimated as
π = maxπ π π(π) 2 (4)
The noise power is obtained by averaging the received signal in the region (at the end of the received signals) where the UWB signal components does not exist. Assuming that the region is start at n = M, the noise power is obtained by averaging the received signal during L samples:
π =π§ 1
πΏ π+πΏβ1π=π π(π) 2 (5)
As summary, the SNR is estimated as follows:
π =πππ
π§ (6)
The threshold for ToA estimation is determined as follows:
πβ= πΌ π (7)
whereπβis the threshold, and Ξ±is a positive integer. The ToA can be estimated by identifying the sample at which the power of the received signal exceeds πβ. However, the conventional threshold-based distance estimator may not offer accurate ToA estimation if SNR estimationis not accurate.
3.2. Proposed RNN-based distance estimator
Figure 2. Input signal structure of proposed RNN-based distance estimator A new RNN-based distance estimation method is proposed in this section. The squared magnitudes of the received signalsare used for the proposed estimator after some conversion as shown in Figure 2.Total N received signals are used. First, the squared magnitudes of the received signal are normalized to 1. Denote π₯ π bethe normalized signal. π₯ π isobtained as
π₯ π = π(π) 2/πΎ, πΎ = maxπ π(π) 2 for 1β€nβ€ π (8)
The input of RNN is a vector that stacks the received signal π₯(π) into a constant length. Assume that the total signal length is N and the size of the RNN input vector is K.
The input of the RNN is N/K vectors with size K.
Figure 3. Proposed RNN-based distance estimator
Figure 3 shows the structure of the proposed RNN-based distance estimator. The
structure on the right side is the same as the sequential unfolding of the left structure in Figure 3. Here π± is the input vector, LSTM cell is the hidden layer, andy is the output.
Total 64 LSTM cells are used. The 64 LSTM outputs are inputted to the fully connected layer and the final output is obtained through the regression layer. The first input of LSTM cell is π1= [π₯ 0 , π₯ 1 , β― , π₯[πΎ β 1]] , the second input is π2= [π₯ πΎ , π₯ πΎ + 1 , β― , π₯ 2πΎ β 1 ] and so on. Once the final vector is entered, the output, π¦π πΎ, is the estimated distance. For the validation of the performance, the RMSE value between the real distance d and the estimateddistanceπ is compared. RMSE is calculated as follows:
π πππΈ = ππ=1(ππβπ π)2
π (9)
4. Simulation Results
4.1. Environments
The transmitting signal is a Gaussian pulse as shown in Figure 4(a). The spectrum of the signal is in Figure 4(b). the bandwidth is approximately 500 MHz at -10 [dB].
Received signals are generated by adding noise after passing through the indoor channel model. Among the IEEE 802.15.4a channel models, the Line-of-sight (LOS) indoor office channel model (CM-3) is used for simulation. The sampling clock is 24 GHz, and the total length of the received signal is 83.33 ns long. Consequently, M is 2,000 (24 GHz x 83.33 ns). The received signal is cut into length K vectors, and by varying K from 10 to 80, the distance estimation performances are compared. As previously explained, 64 LSTM cells are used as the hidden layer. The simulation is conducted by usingTensorflow library with Python 3.6.5.
Figure 4. (a) UWB Gaussian pulse (b) Spectrum of Gaussian pulse 4.2. Results
The performance of the proposed RNN-based distance estimator is verified through RMSE performance. For the training data, 100,000 received signals are generated, and theyhave random distances and SNRs. The distance range is 2to 20 [m], and the SNR range is 10 to 30 [dB]. Each training data is generated randomly within these ranges. The test signal for performance verification consists of 22,000 signals with random distance at each SNR between 10 and 30 [dB].
Figure 5. RMSEswith various K
Figure 5 shows the RMSEsforvarious K. According to the results, at high SNR above 20 [dB], RMSEsare less than 0.5 [m], and negligible performance difference is observed byK. At low SNR, however, there was a difference by K. Smaller Kprovides better performance. ForK = 10, the estimator shows the best performance.
Figure 6. RMSE performances for (a) SNRs (b) distances
Figure 6 compares the proposed method (K=10)with the conventional method. In Figure 6(a), the distance between Tx and Rx is selected randomly from 2 to 20 [m]. As expected,asSNR increases, RMSE decreases. The proposed method offers better performance than the conventional method in all SNRs. In particular, at SNR = 10 [dB], the RMSE difference reaches 10 [m], and at SNR = 30 [dB], the difference decreases to 2 [m]. In figure 6(b) shows the RMSE performance versus distance. SNR is randomly selected from 10 to 30 [dB]. According to the results, the performance of both methods is similar at small distances such as 2 [m], but at the long distances, the proposed method outperforms the conventional methods. Especially, the proposed technique has no RMSE performance degradation at far distance. The simulation result indicates that the proposed method can estimate the distance accurately in all SNRs and distances.
5.Conclusion
In this paper, we proposeda method of RNN-based distance estimation for indoor localization technique in UWB system. The proposed distance estimation method consists of LSTM cells. Learning and performance evaluation was performed using the IEEE 802.15.4a UWB channel model. Compared with the conventional method, the proposed technique showedbetter estimation performance, especially for long distance and low SNR.Therefore, the proposed method is expected to be applied to indoor localization in
the wide space with small UWB transmission power.
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