# Multi-Sensor, Multi-Network Positioning

*By Ruizhi Chen, Heidi Kuusniemi, Yuwei Chen, Ling Pei, Wei Chen, Jingbin Liu, Helena Leppäkoski, Jarmo Takala*

Currently, no single technology, system, or sensor can provide a positioning solution any time, anywhere. The key is to utilize multiple technologies. We are now exploring a multi-sensor multi-network (MSMN) approach for a seamless indoor-outdoor solution. Its hardware platform is described in the previous article. The digital signal processor (DSP) is embedded in the GPS module. All sensors are integrated to the DSP that hosts core software for real-time sensor data acquisition and real-time processing to estimate user location. A smartphone handset provides wireless network measurements.

### Positioning Algorithms

The multi-sensor positioning platform enables a positioning solution with a combination of GPS and reduced inertial navigation system (INS), or GPS and pedestrian dead reckoning (PDR). The reduced INS consists of a 3D accelerometer and a 2D digital compass, as a low-cost alternative to augment GNSS positioning. The reduced INS combined with GPS uses a loosely coupled Kalman filter for data integration, while the combination of PDR and GPS uses algorithms for estimating the position change with pedestrian step-length estimation.

**PDR. **The PDR solution uses human physiological characteristics, implemented in a local-level frame, with equations:

where *k* denotes the current epoch, *Y* is the coordinate in East direction, *X* is the coordinate in North direction, *S* is step length, and φ is the heading.

The PDR positioning algorithm includes step detection, step length estimation, determination of heading, and positioning.

To achieve an accurate heading, compass measurements are corrected with an empirical online estimated error model, which requires some training data.

**WLAN and Bluetooth.** Figure 1 describes the basic concept of the WLAN or Bluetooth locating solution using a fingerprint database approach. The circles around the access point (AP) in the figure represent the radio coverage area and the color the signal strength. This radio map is a simplified example representing measurements from just one AP.

For the fingerprinting approach, the received signal strength indicators (RSSIs) are the basic observables. The whole process consists of a training phase and a positioning phase. During the training phase, a radio map of probability distribution of the received signal strength is constructed for the targeted area. The targeted area is divided into a matrix of grids, and the central point of each grid is referred to as a reference point. The probability distribution of the received signal strength at each reference point is represented by a Weibull function, and the parameters of the Weibull function are estimated with the limited number of training observation samples. Based on the constructed radio map, the positioning phase determines the current location using the measured RSSI observations in real time.

Given the observation vector , the problem is to find the most probable location *(l)* with the maximized conditional probability , maximized by Bayesian theorem as:

We applied an assumption of Hidden Markov Models (HMM) to represent the pedestrian movement process. The locating problem is then translated into finding such a state sequence (locations) that is most likely to have generated the output sequence (the measured RSSIs) assuming the given HMM model. The Viterbi algorithm typically solves these kinds of problems efficiently. This study also utilizes the Viterbi algorithm to trace the user trajectory.

**MSMN. **The general integration scheme combining the GPS output, sensor measurements, WLAN, or Bluetooth output, and their variance estimates is depicted in Figure 2. A simplified representation of the central filter combining different input sources can be described with typical Kalman filter equations. The measurement model is z_{k}= H_{k}x_{k}+v_{k} where the state estimate vector is ,

with *X*, *Y*, and φ as previously defined, and *S* the user horizontal velocity (speed). The measurement vector is given as

where* g* refers to GPS, W to WLAN/Bluetooth, *acc* to accelerometer, and *dc* to digital compass. The matrix H_{k} is the design matrix of the system and the vector v_{k} is the measurement error vector.

The recursive sequence includes prediction and update steps. The prediction step includes the typical equations of

and

while the update step includes

### Indoor Test Results

A field test has been carried out on a sports field, described in the accompanying article (see Going 3D). An indoor test was carried out in an office-building corridor, but the test started and ended in an outdoor terrace area. During the test, the indoor corridor was covered with eight WLAN and three BT APs.

Figure 3 shows the positioning results of the GPS-only (red), Bluetooth-only (black), and WLAN-only (magenta) solutions; Figure 4 shows that of the integrated multi-sensor multi-network (MSMN) solution (blue) for an outdoor-indoor-outdoor test. A reference trajectory is in green in both figures and building outlines in grey. The position update rate achievable by the WLAN and Bluetooth fingerprinting approach is only 0.1 Hz whereas the GPS-only and the integrated MSMN solutions are obtained every second and thus have a higher availability.

Figure 5 shows the horizontal errors obtained with the different positioning solutions over time in the indoor test. A mean horizontal error of 2.2 meters was achieved with the WLAN solution. The Bluetooth solution is not as accurate as the WLAN solution, due to the smaller amount of BT APs; it achieved a mean horizontal error of 5.1 meters. When moving inside the corridor, the GPS solutions are used for the MSMN integration only with very low weights due to their poor quality. GPS is mainly used as a source of location outdoors where the test starts and ends. The mean horizontal error of the GPS-only solutions during the whole test is 8.4 meters. WLAN- and Bluetooth-derived locations and the self-contained sensors are the main sources used inside the building for the MSMN positioning solution: the mean horizontal accuracy o

btained with MSMN is 2.7 meters with a solution availability of 1 Hz.

The MSMN solution obviously performs much better than a GPS-only solution indoors. The track of the pedestrian walking inside the corridor can be identified clearly, which is not the case with typical approaches of GPS-only or GPS/low-cost sensors. WLAN fingerprinting provides good position accuracy indoors, but the MSMN solution provides the best result when taking into account positioning accuracy and the solution availabilities in both time and space domains.

### Conclusions

Further development is needed for indoor areas to be able to obtain fully seamless outdoor-to-indoor location, though GPS initialization followed by sensor and WLAN/BT combination already provide very good initial results. Additional sensors and more refined pedestrian-specific algorithms will be added to further improve the positioning accuracy.

### About the Author: GPS World staff

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