Ranging Techniques

Global Positioning System (GPS) provides world-wide positioning capacity with an accuracy of several meters when the device is equipped with GPS receiver. However, satellite system cannot be used for fine-grained needs of indoor location due to the attenuation of the satellite signals. Angle-of-Arrival (AoA) measurement is a method for determining the direction of propagation of a radio-frequency wave incident on an antenna array. But this method requires special antenna array design which the DA14681 BLE chip does not have and support. Due to mentioned reasons, only RSSI and ToF ranging methods are considered and discussed in this section.

2.1.1 Received Signal Strength Indicator

RSSI is an indication of the signal strength experienced by the receiver for each reception of BLE packet.

For the practical chip used in this project, it is an unsigned 8-bit integer value indicating signal strength varying between -112dBm to -19dBm with a step of 0.47dB/unit, where an increasing value indicates a stronger signal. The value can be easily retrieved in the RX descriptor field of the BLE stack.

The RF power decays as the electromagnetic waves travel through the air. In open space, the relationship between signal strength and distance can be represented by the log-distance path loss model. The model is given in Eq. (2.1) [3], where 𝜌𝜌𝑑𝑑 is the RSSI value at distance d; 𝜌𝜌0 is the RSSI value at a reference distance d0 = 1m, and includes the aggregated effects of transmission power, antenna gains, and frequency attenuation; and α is the path loss exponent that represents the propagation medium properties.

𝜌𝜌_𝑑𝑑 = 𝜌𝜌₀− 10𝛼𝛼𝛼𝛼𝛼𝛼𝛼𝛼_𝑑𝑑^𝑑𝑑

0⇔ 𝑑𝑑 = 𝑑𝑑₀× 10^{(𝜌𝜌0−𝜌𝜌𝑑𝑑)/(10𝛼𝛼)} (2.1) [3]

However, in the presence of interference, multipath, changing of indoor environment and none LOS condition, there will be a variation on 𝛼𝛼 depending on the local statistics that typically ranges from 2 to 5.

Some sample values for 𝛼𝛼 in the model are shown in Table 2.1 [4].

Environment Path Loss Exponent

Free space 2

Flat rural 3

Rolling rural 3.5

Suburban, low rise 4

Dense urban, skyscrapers 4.5

Table 2.1 Sample values for path loss exponent [4]

9 This results in the inaccuracy of this method especially for indoor environment. The iBeacon [5] technology developed by Apple Inc. is a proximity service based on RSSI and BLE. But the distance between transmitting iBeacon and receiving device is categorized into 3 distinct ranges instead of accurate meters.

To improve the stability of the RSSI measurements, the online channel estimation can be applied to update the path-loss model parameters to accommodate the dynamic environment. In [6], the stability of RSSI for BLE devices in real scenarios is empirically studied and the data smoothing performance of different filters is evaluated. After data pre-processing, the online channel estimation are done with particle filtering or simply least squares fitting. In an indoor environment with people movements and other BLE devices enabled, the distance error obtained by particle filtering is around 1m while the result by least squares fitting is 2.885m. Although indoor measurement with particle filtering achieves good accuracy, considerable number of samples, time and computation complexity are needed to accommodate the intrinsic instability of RSSI method.

Another way to improve the distance accuracy is to design a calibration scheme to determine the a-priori knowledge about the environment conditions before measurement. In [7], the a-priori knowledge about the environment is gathered offline by fingerprint. It determines between the received power measurements and the corresponding grid of locations. The practical experiment shows the localization accuracy of around 5cm and good tracking ability for moving object, which is very precise compared to online estimation way. However, a-priori data are usually unavailable for unknown environment, which greatly limits the application of this method.

2.1.2 Time-of-Flight

Once we can measure the signal ToF from one device to another, we can calculate the distance according to the speed of light (1m = 3.3ns). Measuring the RF signal ToF between nodes avoids stability problem of RSSI method, but it is challenging on its own.

2.1.2.1 Clock Synchronization

In the simplest ToF ranging system with two wireless devices A and B, B need to measure the time of arrival of a signal sent by A. To achieve accuracy of 1m, GHz (ns) clock synchronization is required which is not feasible for a low-cost wireless system. Two-way Ranging (TWR) is a good method that mitigates the effect of clock synchronization error [8]. It allows the time offset between transceiver 1 and 2 to be cancelled as is shown in Figure 2.1 [8].

With 100MS/s sampling rate and 50MHz signal in the 2.4GHz ISM band, they achieve 3m range accuracy although no communication standard is compliant. In TWR method, the measurement takes place over a relatively long time. We need to make sure that the clock offset during measurement causes only ns bias on the RF signal.

10 Figure 2.1 Illustration of TWR concept [8]

Time-Difference-of-Arrival (TDoA) uses a set of wire-synchronized reference nodes at known locations to determine the time difference of arriving ranging signals to or from a blind node for localization. Its ability to operate well in high multipath environments and provide sub-meter ranging accuracy has been demonstrated using Ultra-Wideband (UWB) technology [9]. However, GHz clock is needed and the base station infrastructures are expensive.

2.1.2.2 Noise

A ToF ranging measurement influenced only by white noise has been studied in the context of radar applications. The Cramer-Rao Bound (CRB) [10] provides a lower bound for the variance of the range estimation in white noise . For a one-way ranging system using IEEE 802.15.4 modulation, the CRB is given by Eq. (2.2) [11].

𝜎𝜎𝑟𝑟2 ≥ _{4𝜋𝜋2∗𝐵𝐵}^𝑐𝑐2_{2∗𝑆𝑆𝑆𝑆𝑆𝑆} (2.2) [11]

The range variance limit is related to speed of light c, signal bandwidth 𝐵𝐵 and signal to noise ratio SNR.

Figure 2.2 [11] shows the CRB as a function of bandwidth for SNR of 10dB and 26dB. We can see that the white noise only does not prevent 1m accuracy for 2MHz bandwidth (BLE and IEEE 802.15.4). In TWR systems, round-trip measurements are made and averaged to obtain range estimation resulting in 𝜎𝜎𝑟𝑟2

reduction of 2 [11].

11 Figure 2.2 CRB as a function of bandwidth [11]

2.1.2.3 Sampling Artefacts

It is proved in [12] that the resolution of a ToF measurement suffers from the finite sampling clock-frequency resolution. This occurs when a matched filter is used to estimate the time of arrival with a sampling rate of 𝑓𝑓𝑠𝑠= 2𝐵𝐵. Sampling adds error to ToF result because the estimate space is divided up into range bins of 𝑐𝑐/𝑓𝑓𝑠𝑠 wide. The range uncertainty added by sampling in each bin is given by Eq. (2.3) [11].

𝜎𝜎_𝑠𝑠²=_{12∗𝑓𝑓}^𝑐𝑐2

𝑠𝑠2 (2.3) [11]

To reduce this error, the signal can be oversampled. Figure 2.3 [11] shows the CRB for a 2MHz bandwidth signal with SNR = 26dB, the standard deviation of the sampling error and the combined effect of both error sources. We can see that in this noise condition, when 𝑓𝑓𝑠𝑠> 70𝑀𝑀𝑀𝑀𝑀𝑀, the range error caused by white noise will become dominant. It can also be concluded that with better noise condition, large sampling rate is needed to reduce the error. If the signal is sampled above Nyquist (𝑓𝑓𝑠𝑠> 2𝐵𝐵), the signal’s entire information content is fully captured and better time resolution than 𝜎𝜎𝑠𝑠 is possible. Interpolation between samples can yield significant improvements in resolution [13].

12 Figure 2.3 Comparison of CRB to sampling error as a function of sampling frequency [11]

Code Modulus Synchronization is presented in [11] as one improved TWR method. In this method, a code is transmitted between both ends and proper cross correlation is calculated between the transmitted and received code to determine ToF. Finally, 1m accuracy is achieved for outdoors and 1-3m is achieved for indoors. Besides, the standard deviation of ranging measurements, the CRB for their system as a function of SNR and the previous ranging binning limit are shown in Figure 2.4 [11]. We can see that the practical results approach CRB when the SNR is low and are limited gradually by sampling frequency error.

Figure 2.4 Measured noise performance as function of SNR [11]

2.1.2.4 ToF by Phase Measurement

In GPS, there are code-phase and carrier-phase methods that can achieve different level of range accuracy and have different level of cost. The code-phase method calculates the cross correlation between received pseudo random code and code replica generated at the received to determine the time shift and the ToF.

This method suffers from all the issues mentioned above and can achieve meter level accuracy [14]. The

13 carrier-phase method is a measure of the range between a satellite and receiver expressed in units of cycles of the carrier frequency. The pseudo random code has a bit rate of about 1 MHz but its carrier frequency has a cycle rate of over a GHz which is 1000 times faster. This method achieves precision varies from 1 mm to 10 cm, depending on the processing strategy [14]. Similarly, the phase shift of transmitted and received RF signals can be used to measure distance more accurately in low-cost devices.

In [15], the full available ISM bandwidth of 80 MHz and 16 ZigBee channels are utilized to estimate distance with phase difference method. With a low-cost oscillator and sampling frequency of 250MHz, a positioning bias error of 16cm and standard deviation of 3cm are achieved. In [16], only two measurement frequencies in ISM band are needed to perform the distance estimations. 30cm range accuracy is achieved with frequency hub of 75MHz, measurement in RF anechoic chamber and at least 250 samples. The Atmel ranging toolbox [17] uses proprietary algorithm based on phase difference to calculate distance. The full 2.4 GHz ISM band is suggested for best performance and the ranging procedure is not compliant with IEEE 802.15.4.

Because of design convenience, all the ToF methods mentioned in this section is based on IEEE 802.15.4 standard. But the BLE standard also shares similar problems as it is designed for low-cost consumer devices. For example on the DA14681 BLE chip of Dialog, it only has low accuracy clock (16MHz), inaccurate synchronization (1µs), low online processing power (96MHz) and low sampling frequency (8MHz). These are fundamental limits to walk around for the design of accurate ToF ranging solutions on BLE devices.

2.1.3 Fusion of ToF and RSSI

Both ToF and RSSI methods have their own merits and demerits but we can fuse the data to achieve better resolution and stability. In [3] data fusion of RSSI and two-way ToF are applied to improve ranging accuracy. The general blocks are shown in Figure 2.5 [3] where least squares fitting is used to estimate channel parameters and extended Kalman filter is used for range tracking. Dotted lines apply only when ToF data are available. For the experiment with lab environment, the RSSI method only achieves 2.5m accuracy and the fusion method reaches 1.3m accuracy.

Figure 2.5 ToF and RSSI fusion ranging blocks [3]

In [18], the calculated speed and location information from processed ToF and RSSI are fed into two Kalman filters to track the state change. The final output distance value depends more on term with

14 smaller estimated uncertainty. In their indoor measurement, the RSSI method has accuracy of 0.5m-1.5m and the ToF method has accuracy of 2.5m-3.5m. The fusion algorithm reaches accuracy less than 1m which proves the improvement on individual techniques.

2.2 Bluetooth Low Energy