Magnetic sensors are often used in traffic management applications to determine the location of vehicles. Typically, magnetic sensors are used as a proximity sensor: a change in the magnetic field is detected and thus it is known that the vehicle has just passed by the location of the magnetic sensor. In COGSENSE, however, target modeling is used as a priori knowledge as part of a novel algorithm for determining the quadrant in which the vehicle is located relative to the magnetic sensors is developed.
This was accomplished by using Orthogonal Matching Pursuit (OMP), which is an iterative sparse approximation technique that the best linear combination of dictionary elements that fits the measured data in a least squares sense. In the case of magnetic sensing, the magnetic field measured is dependent upon both target type (e.g. size and shape) as well as location. Typically, the dictionary is formed from all possible combinations of parameters given by a model used to describe the measurements. In this work, ferromagnetic modeling is used to define the dictionary entries.
Nevertheless, for now let us mathematically define the dictionary as , where is defined as a vector of unknown parameters and P is the total number of unknowns. If the total number of possible values for each parameter is defined as pi for the ith parameter, then the total number of potential realizations of the target measurement is . Thus, the dictionary may be mathematically expressed as
OMP seeks a coefficient vector C such that
where n is an index into the K dictionary entries comprising the model signal, . The coefficient vector is iteratively found by minimizing the least square error between the measured data and the model signal. In the case when only a single target is present, the OMP algorithm described above reduces to finding the dictionary element yielding the peak projection, i.e. ; or, the minimum distance between the dictionary element and measured signal vectors. If more than one target is present, then at each iteration the peak projection is subtracted from the residual signal until a stopping criterion is met, such as the residual magnitude falling below a threshold. The target parameters of the dictionary entries found to give the best fit to the measurements can then be used for the identification. In the case of magnetic sensing, since each dictionary entry is generated for a different location and magnetic moment, the dictionary entry selected as a result of OMP yields information not just about location, but also about target type.
Most ferromagnetic targets can be modeled as a magnetic dipole,
Here, mu_0 is the permeability of free space, m is the magnetic moment, and r is the distance between the target and sensor. To compute the dictionary, the sensing region about each sensor is discretized into 10 cm × 10 cm squares, as shown below.
At each test point, the magnetic field components Bx and By are measured when a target was present (BxP, ByP) and when a target was not present (BxNP, ByNP). The difference between these values at each test point is then used to form the dictionary:
where and . Because the magnetic field depends not just on the range, r, but also on target properties, magnetic moment, m, the above dictionary is replicated for each different target to form the total, composite dictionary:
Thus, any ferromagnetic target that is desired to be localized should be magnetically characterized, and the expected response stored in the dictionary as defined above.
When a target first enters the sensing region of the magnetometer, the first step of the algorithm is to determine target identity. Because the magnetic field depends on both location and target properties, there is some coupling in the measurements. However, upon initial detection, there may be three possible scenarios: 1) the point of entry is known (as may be the case when a vehicle enters a parking lot); 2) the quadrant of entry is known (if general direction of arrival is known); and 3) no a priori information is available. Generally speaking, when a target first enters the area observed by the entire sensor network, there is no a priori information about target location; however, as the target progresses through the network, the observations from one node can be used to guide and improve the performance of subsequent nodes.
In the case when no a priori information is known, it was found that the ability to discern target identity varied between 46% and 56%; essentially giving no better results than that obtained by simply guessing. However, if the quadrant of entry was known, this rate improved to 75% – 87% for most targets, while knowing the exact point of entry enabled discerning the target correctly 100% of the time.
Once the target type was discerned, the target could then be sequentially localized as it moved through the sensing region of the magnetometer. Two spatial resolutions were tested: ¼ resolution (region divided into four quadrants) and 1/28 (region divided into 28 cells). Results were classified as being either “correct,” “wrong,” or “near”, i.e., target location was estimated as being within one cell (10 cm) of correct location. “Correct” means that the estimated location of the target is the same as the actual location within a 10 cm × 10 cm resolution cell, while “near” shows that the distance between the correct location and the estimated location is not more than 10cm. Estimates that fall beyond the 10 cm limit are classified as “wrong”.
Experimental testing showed that for a positional resolution of 10 cm × 10 cm, yielding 28 different cell locations within the sensing region, correct localization was accomplished 72% of the time, as shown in the pie chart below. However, if the cell resolution is decreased to being that of quadrants, localization performance improved to 100% for 4 targets over 60 observations.
Localization performance for the sensing region discretized into 10 cm × 10 cm cells for 4 targets and 280 observations.
After validating the proposed algorithm in a laboratory environment, the system was then tested on outside for estimating the time-varying positions of a car slowly moving about a parking lot. A network comprised of 8 sensors was set up in the parking lot at the Middle East Technical University, Ankara, Turkey. This parking lot has 8 parking spaces, divided between two groups of four spaces that reside to the left and right of the only entry/exit. Two sensors were applied to detect and localize a vehicle in one of these parking spaces (sensors number 7 and 8).The remaining six sensors were used to estimate the position a car in the roadways of the parking lot. Through experimentation, we found that the maximum distance at which a car could be detected was 3 meters. Thus, the sensor positions were adjusted so that there was at least 6 meters distance between each sensor. The data from each sensor was processed using the proposed algorithm to extract quadrant-level localization information on the vehicle position. Sensors located in the middle of the parking lot (Sensors 4, 7, and 8) had all four quadrants activated, while the algorithm only utilized information from three-quadrants for Sensor 1, and two-quadrants for Sensors 2, 3, 5, and 6. In this way, the system was used to monitor the position of a car in the parking lot and gain information regarding the availability of parking spaces. Results of the developed algorithm are shown in the figure below, which clearly indicates that information beyond just that of proximity are obtained from the magnetic sensors in the network.
Example quadrature localization result of a vehicle within a parking lot equipped with a sparse network of magnetic sensors.
For more details:
- S. Baghaee, S.Z. Gürbüz, E. Uysal-Bıyıkoğlu, “Implementation of an Enhanced Target Localization and Identification Algorithm on a Magnetic WSN,” IEICE Trans. on Communications, 98-B(10): 2022-2032 (2015).
- S. Baghaee, S.Z. Gurbuz, E. Uysal-Biyikoglu , “Application and Modeling of a Magnetic WSN for Target Localization,” UKSIM, England, 2013.
- S. Baghaee, S.Z. Gurbuz, E. Uysal-Biyikoglu , “Orthogonal matching pursuit for ferromagnetic target localization and identification“, IEEE SIU 2012, 20th Signal Processing and Communications Applications Conference, 18-20 April 2012.