- 1. INTRODUCTION
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- 2. LOCALIZING GROUND PENETRATING RADAR SYSTEM
- Localizing Ground Penetrating RADAR: A Step Toward Robust Autonomous Ground Vehicle Localization
- 2.1. Localizing GPR Sensor
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- 2.2. Real‐Time Localization
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Self‐driving vehicles and driver‐assist systems have been pursued on a worldwide basis. One main objective is to reduce the yearly vehicle accident fatalities (32 K US [National Highway Traffic Safety Administration, 2011] and an estimated 1.24 M worldwide [World Health Organization, 2013]). Effective GPS/INS (internal navigation system), LIDAR, and camera‐based autonomous navigation techniques were developed and honed in the DARPA Grand and Urban Challenges, though operation was in a carefully staged and mapped environment (Buehler, Iagnemma, & Singh, 2009).
However, GPS/INS approaches, even aided by wheel odometry, typically have real‐time 2σ values well over 1 m (Kennedy & Rossi, 2008) which is insufficient to maintain a vehicle in a travel lane on most roads. Failure modes for GPS‐dependent solutions include blockage and multipath, such as arise in urban and heavily forested or mountainous environments.
LIDAR‐based algorithms fused with GPS/INS, wheel odometry, and cameras offer a very successful approach to localization. One of the most successful approaches was the modification of LIDAR mapping algorithms to use surface intensity probabilistic maps (Levinson, Montemerlo, & Thrun, 2007; Levinson & Thrun, 2010).
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Notably, using this method, the GPS/INS solution was improved to approximately 9 cm in urban environments and demonstrated in traffic and during rainfall. The surface intensity probabilistic map approach breaks down when the LIDAR beam is significantly attenuated or blocked, such as occurs in snow, fog (Yamauchi, 2010), dust, or with dirt on the lens.
In addition, changes to the road surface, such as would be expected on dirt roads or after repainting, may require updating of the map. Camera‐based approaches continue to be refined, with active vehicle localization approaches such as topometric localization (Badino, Huber, & Kanade, 2012), FAB‐MAP (Cummins & Newman, 2011), and linear mosaicing (Unnikrishnan & Kelly, 2002).
These approaches also have similar limitations to the LIDAR systems because of their use of optics and their operation in dynamic environments.
Self‐driving vehicles must be robust to environmental conditions and related failures in order to be broadly useful and live up to their potential.
Milford and Wyeth (Milford & Wyeth, 2012) sought robustness in camera‐based localization by identifying sequences of matches rather than single feature matches. Nuske et al.
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(Nuske, Roberts, & Wyeth, 2009) used a multihypothesis particle filter to select among matches to three‐dimensional (3D) edges in the environment.
Brunner, Peynot, Vidal‐Calleja, and Underwood (2013) augmented visual sensing with thermal sensing to do localization in the face of obscuration and darkness.
In this paper, we detail localizing ground penetrating radar (LGPR), a form of ground penetrating radar specifically designed to enable a priori map‐based localization. LGPR offers complementary capabilities to traditional optics‐based approaches to map‐based localization, including the ability to transmit through air‐based obscurants, such as fog and dust, and common surface obscurants, such as dirt and snow (Abe, Yamaguchi, & Sengoku, 1990; Hoekstra & Delaney, 1974).
Hence, LGPR offers increased resistance to common failure modes of existing localization techniques, which potentially allows for significant improvements in robustness when fusing it with those existing approaches. In addition, LGPR senses a generally stable environment, discussed in Section 4.1., which complements the dynamics of surface environments.
Many research challenges and risks, discussed in Section 4., remain to be addressed, including all‐weather operation, data storage requirements, and array size reduction.
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We developed an early stage version of the LGPR system, shown in Figure 2, which has been used to automate the steering of multiple armored vehicles and was tested in three US states prior to several months of operation in Afghanistan in 2013. This large‐scale system, which operated at 7.5–15 km/h, was tested on several soil types, on and off road, and demonstrated over thousands of kilometers of operation.
While the rough concept of localizing GPR has been introduced in limited detail (Stanley, Cornick, & Koechling, 2013), here we present in sufficient detail as to allow peer verification, the first practical (small size, low power) design for an LGPR system on a commercial passenger vehicle, with the capability of achieving high‐speed operation (at least 100 km/hr).
In addition, we, for the first time, characterize the real‐time localization accuracy, long‐distance highway operation, and high‐speed performance of an LGPR system.
Previous work has combined robotics with GPR. Herman (1997), Williams (2012), and Lever et al.
(2013) all used autonomous systems to move GPR systems, enabling them to create subsurface maps. They did not, however, attempt to localize the robots using those maps.
We have integrated the LGPR sensor onto a 2000 Chevrolet Silverado truck (see Figure 3), which we also equipped with two Oxford Technical Solutions (OxTS) RT3003 GPS/INS systems: one is a real‐time kinematic (RTK) system solely used for truth reference while the other receives WAAS differential corrections and is loosely coupled with the LGPR system to provide the LGPR position estimates for both mapping and localization.
The RTK truth reference unit is coupled with a local base station that allows local 2‐cm accuracy location measurements. The RT3003 uses a MEMS‐based IMU and dual GPS antennas to produce a 6‐DOF (degrees of freedom) Kalman filter–based pose output with 1σ heading error of approximately 0.1 degrees. The LGPR array is mounted underneath the vehicle behind the front wheels.
We use spacers underneath the chassis to fix the array height at 15 cm (6 in) above the ground, the initial design point. In general, the performance of GPR systems improves monotonically as the array is lowered to the ground surface, but this must be balanced with the need for ground clearance.
We first discuss designing an under‐vehicle‐mounted LGPR system, including key design parameters. We then move on to the algorithms supporting mapping and real‐time localization before discussing the experimental results from high‐speed highway testing.
We conclude by discussing remaining concept risks that should be addressed in future research.
2. LOCALIZING GROUND PENETRATING RADAR SYSTEM
The localizing ground penetrating radar (LGPR) system, designed and developed by MIT Lincoln Laboratory, consists of both hardware and processing components. The hardware component is a uniquely designed type of ground penetrating radar that allows high cross‐track resolution to accurately detect subsurface features and has specially designed uniform elements to allow comparison of measurements even if the array element overlaps a different portion of the map than during its original pass.
The key parameters of the LGPR system are shown in Table I.
|Radar type||Stepped frequency continuous wave|
|Frequency range||100–400 MHz|
|Frequency spacing||51 tones spaced by 6 MHz|
|Array dimensions||152 cm × 61 cm × 7.6 cm (5.0 ft × 2.0 ft × 3.0 in)|
|Array offset from ground||15.24 cm (6 in.)|
|Number of antenna elements in array||12|
|Number of channels (number of pairs of elements)||11|
|Total radiated power||40 µW continuous (one element at a time)|
|Leakage power (radiated above‐ground)||4 µW|
|Radar sweep rate (all 11 channels)||126 Hz|
|Depth of penetration||2 m–3 m (New England soil)|
|Radar range resolution||20 cm–30 cm|
The LGPR operates at low frequencies to allow deep ground penetration and to reduce the amount of small clutter in the image.
Localizing Ground Penetrating RADAR: A Step Toward Robust Autonomous Ground Vehicle Localization
Details, including the unusually low‐radiated power, are covered in Section 2.1..
The processing component is made up of the mapping and registration components. The unique aspect of the mapping and registration components is that they are streamlined so that they are all accomplished automatically in real‐time at 126 Hz on a consumer‐grade dual core processor.
The key components of the current LGPR processing subsystem are shown in Table II.
|Real‐time localization rate||126 Hz|
|Type of RADAR Data Filter||High pass|
|Type of registration algorithm||Heuristic search, maximizing correlation over 5 DOF|
|Correlation threshold (integrated velocities used below this value rather than GPR solution)||0.9 (out of range −1 to 1)|
|Overlap threshold (integrated velocities used below this value rather than GPR solution)||2 elements (out of 11)|
The mapping and registration components are detailed in Section 2.2..
2.1. Localizing GPR Sensor
In the area of subsurface sensing, ground penetrating radar (GPR) is one of the most versatile and prolific sensing modalities today.
All soil and most road materials are semitransparent to radio waves. GPR systems work by sending a pulse of electromagnetic radiation into the ground and measuring reflections that originate from scattering below the surface. Reflections occur at the interface between objects of different electromagnetic properties; for example, the interface between soil and pipes, roots, or rocks. However, it is not these discrete objects but rather the inherent inhomogeneity in subterranean geology that often dominate GPR reflection profiles.
This can be seen in Figure 4, in which soil layers and variations in moisture content cause extended reflections in the data. GPR data paints a fairly complete picture of the subsurface environment.
Nearly every discrete object and soil feature is captured, provided that it is not significantly smaller than a wavelength and that it has sufficient dielectric contrast with the surrounding soil. The premise of GPR localization is that these subsurface features, as represented in GPR data, are sufficiently unique and static to permit their use as identifiers of the precise location where they were collected.
2.1.1. Introduction to GPR
A general guideline is that the maximum detection depth of a GPR will often be three to four skin depths, where skin depth is a measure of the depth to which the pulse can propagate before losing most of its energy (specifically 1/e lower in field values thus ∼8 dB lower in power). Skin depth is determined by soil losses caused by Joule heating and dipole losses. High‐conductivity soils, such as those with high moisture and salinity, have smaller skin depths (Jol, 2008).
The range resolution of a GPR specifies the resolving power in depth and is approximately
The lateral (along‐track and across‐track) resolution achieved by a GPR system is dependent on the physical beam width of the antenna (in units of area), which increases with depth but in general is not better than the range resolution. Further information on GPR theory can be found in (Daniels, 2004).
Traditional GPR systems for road inspection are often centered in the 1 GHz to 3 GHz band (Saarenketo & Scullion, 2000), with nearly 100% bandwidth (BW = 1 – 3 GHz), which provides excellent resolution (2 cm – 5 cm) at the expense of penetration depth.
One of our key findings is that such high resolutions can actually be detrimental to the task of localization, as it increases the fragility of the map correlation process, for several reasons.
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First, high‐resolution features in GPR data become increasingly difficult to correlate when pass‐to‐pass offsets are present. For example, at 1 GHz, radar data decorrelates at distances around 2–3 cm, resulting in a very fine requirement for antenna element spacing. In addition, the phase differences resulting from vehicle motion (pitch and roll) are significant and can lead to difficulties in correlating coherent GPR data to the map, as each vehicle pass will have slightly different suspension trajectories.
High frequencies also suffer from being too sensitive to small changes, such as trash on the road surface, and are more susceptible to phase errors due to thermal drifts in the transmitter/receiver. For all of these reasons, the GPR data correlation process becomes easier at lower frequencies, which has the benefit of improving penetration depths as well. The only factor preventing one from lowering the frequency indefinitely is that the radar cross section of the most important subsurface geology tends to drop off steeply below 100 MHz as well, and the required antenna sizes grow rapidly below 100 MHz.
For this reason, we have selected the frequency range 100 MHz to 400 MHz as best suited to the task of localization. This frequency range is capable of resolving large subsurface geology on the scale of 20 cm to 30 cm, while remaining robust to the sensitivities of high‐frequency systems mentioned above. We note that the variation in range resolution is due to variation in εr, primarily driven by moisture content (dry soil will typically be in the range εr = 4 to 6, whereas fully saturated soils are closer to εr = 25 to 36).
In the frequency range where our system operates (100 MHz to 400 MHz), soils have skin depths that range from D = 10 cm to 100 cm, depending on soil composition and moisture content (in New England soils, for example, D ∼ 100 cm skin depths are common, leading to 2–3 m penetration depths).
2.1.2. System Components
It is important to note that our GPR design differs from traditional GPR systems to allow localization to be achieved. The LGPR consists of four basic functional components: a unique antenna array, a 2 × 12 switch matrix, a custom VHF stepped frequency continuous wave (SFCW) GPR, and one single‐board computer (SBC).
These components are shown in Figure 5 (the radar electronics and SBC are within the chassis shown). The switch matrix switches the individual transmit and receive channels of the radar to each of the array elements (Figure 6). Data sent to the SBC are processed using standard SFCW radar techniques to generate data as seen in Figure 4.
One key difference between the LGPR array and traditional GPR array designs is the spacing between the elements (12.7 cm), which is approximately one tenth of a center frequency wavelength. This resolution is finer than typically seen in GPR arrays and is driven by a desire to allow for high‐fidelity matching to baseline data.
In addition, the elements and array cavity are designed so that every element has identical near‐field (and thus far‐field) patterns. This is required to allow path retraversal in which pass‐to‐pass offset or misalignment is present. This element similarity requirement is especially difficult to meet for our close element spacing (relative to wavelength), which, in traditional GPR arrays, ordinarily results in significant mutual coupling and array end effects.
An array with these characteristics, shown in Figure 2, has been developed previously at MIT Lincoln Laboratory (Fenn, Hurst, Pacheco, Cornick, & Parad, 2013) having favorable radiation characteristics for localization.
That design was impractically large for consumer‐vehicle applications and was demonstrated at speeds below 15 mph. After performing a study and simulating expected performance, we designed a miniature version, which consists of 12 dipole elements linearly aligned within a reflective rectangular metal cavity having dimensions 152.4 cm × 61 cm × 7.6 cm (Figure 5).
Other than this change in cavity size and number of elements, the design is identical to the larger array. This array is capable of mounting rigidly under the vehicle body. Care was taken in the array design to minimize the effects of the large metal vehicle chassis, which has the potential to alter the radiation patterns of the elements. The cavity, as designed, is able to reduce the impact of the vehicle chassis on radiation patterns of every element.
The transmit/receive data collection sequence, called a “sweep” pattern, begins by transmitting a pulse from the first antenna element and receiving on the second.
Once the first pulse is complete we transmit on the second and receive on the third and so on to the last pulse in which we transmit on the 11th and receive on the 12th. Hence, the 12‐element array produces 11 channels of data.
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This sweep takes approximately 7.8 ms, so the vehicle advances several centimeters during the whole sweep (at highway speeds), which is sufficient to limit the effect of blurring the data due to motion. Each element “pulse” is formed by a sequence of 51 tones evenly spaced from 100 MHz to 400 MHz.
The radiated power is extremely weak, with less than 40 microwatts (peak) radiated in total, and less than 4 microwatts (peak) leaked into the surrounding air (the majority is absorbed by the ground).
This radiated peak power is significantly (1000x) less than traditional pulsed GPR designs and is made possible by the power efficiencies of the SFCW design approach (in which the radar transmits and receives continuously). This extremely low‐power design alleviates spectrum conflict issues faced by traditional GPR designs.
A direct digital synthesizer (DDS) generates each tone and simultaneously generates a local oscillator (LO) signal at the sum of the tone frequency and the intermediate frequency (IF). The super heterodyne receiver multiplies the received radar signal with the local oscillator and filters the result to yield a signal at the intermediate frequency with the same amplitude and phase as the received radar signal.
An analog‐to‐digital converter (ADC) samples the intermediate frequency signal four times per intermediate frequency period. Each tone lasts for six intermediate frequency periods. We skip the first and last intermediate frequency periods. For the remaining four intermediate frequency periods, we compute and average the complex Fourier parameter, or S‐parameter, for that tone.
Because the environment's ambient temperature may be significantly different from one pass to the next (i.e., the map is created on a hot summer day and then subsequently used through the winter), we have incorporated an automatic calibration channel.
The purpose of this calibration path is to frequently adjust the signal to compensate for variations caused by component heating, thermal expansion, cable flexing, and so forth. We calibrate the system on every sweep (every 7.8 ms). To apply the automatic calibration, we divide the S‐parameters (frequency domain I,Q) for each of the other element pulses, Sf,ant, by the S‐parameters for the calibration channel pulse, Sf,cal.
Our experiments indicate that this self‐calibration allows the system to operate in an ambient temperature range from −5° C to 50° C with only minor changes to the amplitude and phase response of the system (generally at the −20 dBc level or below). Temperature changes in the subsurface (such as freezing and thawing) may still cause unwanted artifacts over temperature, but these effects have not been explored in this study.
In addition, a onetime “factory” array calibration is performed in a quiet anechoic chamber after the array is fabricated to measure all element direct‐coupling responses.
This measurement is then used to calibrate out, to first order, element differences.
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To apply the “factory” calibration, we first apply the automatic calibration to the factory calibration, Sf,ant,factorycal, using Eq.
3. We next divide the S‐parameters for each element pulse by those from a "factory" calibration, and subtract 1 Eq. 4.
A time delay is next applied to the sequence to prepare the data for conversion to the time domain.
Doing so keeps the negative part of signals, centered on zero, from appearing at the end of the reconstructed time‐domain signal. To apply the time delay, we multiply the S‐parameters of each element pulse by the frequency domain representation of an 8‐ns delay.
The sequence is then windowed to reduce “ringing” in the reconstructed time‐domain signal.
To apply the window, we multiply the S‐parameters of each element pulse by a Chebyshev window with 45‐dB attenuation of the highest and lowest frequencies.
We next construct a time‐domain sequence of 1,024 real, time‐domain values by applying a complex‐to‐real discrete Fourier transform for each element pulse.
Finally, a high‐pass IIR spatial filter is applied to all data to eliminate any residual internal reflections and suppress the ground bounce, which is uniform and not helpful for the matching process.
The mean removal filter removes constant and very low‐frequency components from the radar data. The filter is a first‐order, linear, infinite impulse response, high‐pass filter. The filter constant is chosen so that information decays with a half‐life of 5 m and has a passband of 0.024 cycles/m. The running mean, Mi, the mean removed value, Ci,mr, and the parameter, β, are calculated as follows.
The IIR filter distance, diir, is set at 5 m, while the current distance, di, is calculated from the difference in current and prior estimated positions.
At the end of this process, a fixed range gain is applied to compensate for soil attenuation and geometric spreading of the electromagnetic wave (Daniels, 2004).
This final data product is one “sweep” of array data containing 11 channels and can be thought of as a scalar image (of signed 1‐byte pixels) that is 369 pixels deep by 11 pixels across the array.
This is the raw data output from the sensor, such as shown in Figure 7, which is sent to both the mapping process and the real‐time localization process. We also maintain a database indexed by the geographic location of each sweep, as indicated by a GPS‐aided inertial navigation system.
The LGPR concept depends on a sufficient density of subsurface features to be present for the registration process. As seen in Figure 7, the signal to noise ratio of the individual sweeps nears 0 dB near the 30‐m‐distance point. In this short region, there are very few subsurface features available for registration.
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We note that this short region has little effect on the localization process, as the system is able to drift through that short segment. Note that this drifting process is possible due to the temporary integration of the RT3003 GPS/INS solution mentioned in Section 1.. It is interesting, however, to investigate the prevalence of these sparse feature regions. To this end, the average density of features was investigated with the LGPR in 3 states as well as in Afghanistan for the purposes of understanding the distribution of suitable subsurface features.
Here we analyze the density of those features by computing the total signal strength (integrated over depth and over all array elements) of the IIR‐filtered GPR data. In this filtered GPR data, low frequency and DC reflections such as vehicle scattering and the surface bounce are filtered out. With some simplifying assumptions (such as stable platform motion), the only remaining energy is from noise and true subsurface features having spatial structure size ranging from ∼50 m (the approximate IIR filter cut‐off) to approximately 0.2 m (the limit of radar resolution).
In general, we find that the radar SNR of these features is sufficient for localization, even in highly attenuating soils (e.g., Arizona). Figure 8 shows the distribution of radar SNR for five test locations. Note that most locations have SNR values over 10 dB. Even in the worst‐case scenario (fewest subsurface features—Afghanistan highway) less than 30% of the data is below our SNR ≥ 8 dB guideline, and the regions where the SNR drops below this value tend to be short (on the order of meters) so that an INS is more than capable of tracking motion between GPR locks.
2.2. Real‐Time Localization
The LGPR system as implemented allows real‐time creation of single‐track maps with no offline processing, as well as real‐time localization of the vehicle to a prior map. The radar operates in the way described above, both for mapping and for localization.
However, when in localization mode, two extra processing steps, gridding and tracking, allow us to determine geographic location and orientation from the radar data. The process is depicted in Figure 9 and described below.
We use a single standard consumer‐grade dual‐core processor running Linux for all processing. All map and localization code was written in C. Low‐level firmware was executed on an FPGA. As this LGPR prototype used a fixed temporal sample rate (126 Hz), the uncompressed raw map data sizes varied from ∼32 MB/km for the 97 km/h collections to ∼192 MB/km for the 16 km/h collections.
Commercial zip packages have shown a factor of 20:1 compression is possible on raw LGPR data. It is likely, based on the results of the testing presented in Section 3., that lower spatial density data would be sufficient for localization at all speeds. Further discussion of data size can be found in Section 4.2..
Similar to Levinson and Thrun (2010), map data were dynamically pulled to RAM in a dual buffer of local 50 m × 50 m grids to keep memory requirements constant.
2.2.1. Grid Map Preparation
At initialization, we prepare a local “grid,” a rectangular 3D data structure of scalar signed values representing the reflected radar signal from the subsurface environment centered on the vehicle.
As the vehicle approaches an edge of the current grid, we replace it with a new grid centered on the vehicle. The gridding process is illustrated by Figure 10. Using a fixed‐size local grid allows us to page in relevant data as needed without keeping huge data sets in memory. Furthermore, it permits fast calculation as data from a newly acquired sweep of the GPR can be quickly matched to the nearest data from the prior passes.
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To create a grid, we query the database for previously collected radar sweeps that fall within the grid area. We interpolate the raw data from each of those sweeps onto grid points spaced 5 cm apart in the horizontal dimensions. This may appear too fine for the stated resolution of the radar (20–30 cm); however, it is often beneficial to overresolve this radar data.
The extra information obtained by overresolving does diminish rapidly for finer grid spacing, but with a very high SNR (our SNR is typically >20 dB), this additional information is still useful for registration (useful because the small subresolution features are still above noise).
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Note that the accuracy of any correlation‐based registration process is driven largely by the SNR of the data, rather than by the resolution of the GPR or the grid spacing at which we sample that GPR data. Vertically, the samples in depth for each grid point retain their native density and span (369 points sampled over 60 ns).
The data for each grid point are a weighted average of all raw data from prior passes that are within 12 cm. The weight for each raw data point is inversely proportional to its distance to the grid point. For this study, maps were created using single‐pass data sets. Multipass data‐set‐based maps would require additional processing and registration steps to remove “ghosting” effects from relative misalignment of the data sets, an area we have not explored with GPR data.
As each sweep arrives from the radar, we search for the vehicle pose that best fits that sweep to the grid. The search region is five‐dimensional: latitude, longitude, height, heading, and roll. We found that a simple two‐axis (longitude, latitude) search domain produced inferior results, as variations in the vehicle suspension state between passes requires compensating for the subsequent vertical motion (height and roll) of the array, which can cause the individual elements to move as much as 5 cm up or down from their height on the mapping pass.
We used the correlation between the sweep data and the grid data as the heuristic fit criterion. The correlation is calculated as
When correlation is +1, then the match is perfect, while a correlation of −1 indicates the worst‐case correlation (in which one data set is 180 degrees out of phase). Correlation is a simple metric to quantify the matching of subsurface GPR signals and is independent of absolute signal strength. When the vehicle pose for optimal correlation is found, we regard the current sweep as being registered to previous grid data.
Particle swarm optimization (PSO) was chosen as the optimization technique to find the highest correlation 5‐DOF array pose that matches GPR data to the grid. Particle swarm optimization is a well‐known optimization technique (Kennedy & Eberhart, 1995) chosen due to its ability to search a very large space of candidate solutions. Furthermore, this technique makes no assumptions about the correlation space and is robust to local minima. This quality also allowed us to likewise make no assumptions about the GPR data as we expected a wide variation for different areas.
Of the existing heuristic search strategies, the selection of PSO was driven by its relatively lower computational needs, ability to search large solution spaces, and ability be scaled to the computational resources available (Shi & Eberhart, 1999). Moreover, it offers greater robustness in achieving near optimal solutions when compared to simpler techniques such as simplex or hill climbing.
The algorithm begins by creating “particles,” each of which occupies a randomly chosen point in the five‐dimension search space associated with the 5 DOFs. During each iteration of the algorithm, each particle is evaluated for quality of fit (correlation). The algorithm keeps track of the best fit experienced by each particle, and the best fit overall across all particles. Each particle also has a “velocity” value associated with each search dimension. The velocity controls how the position is updated after each iteration of the algorithm.
Each particle then moves through the search space, its position updated from its previous position with the vector velocity :
Next, the velocity of each particle is updated based on a combination of the best position achieved by that particle and the best position of all the particles found thus far:
and are random numbers chosen anew for each iteration. PBestlocal is the best position that a particular particle was able to find in the current or past iterations. PBestglobal is the best position that any of the particles was able to find.
The behavior of the particles can be understood by examining each of the three components of the velocity update equation. A high value steers the particle toward areas where it has found good performance. A high value steers a particle toward the best position found by any particle.
A high will cause particles to stay on their current trajectory, largely unchanged. A low value will allow the particle to be more strongly influenced by the other terms in the equation and thus will tend to veer toward other particles.
In the implemented optimization algorithm, starts high and decreases with subsequent iterations. These values encourage an initially wide level of exploration by the particles, which subsequently converge onto a solution during the latter iterations.
As a further refinement, the size of the search region, the number of particles and the number of iterations evolve, depending on the correlation achieved. When correlation is high, the search region shrinks, allowing it to complete quickly. When correlation is low, the search region expands.
We consider the tracker “locked” onto the grid if the correlation exceeds a threshold (0.9), at least two of the antenna elements overlap the mapped data, and the candidate location is physically possible based on the vehicle speed and previous location (it is within a delta of the velocity‐extrapolated expectation). If the tracker is not locked, then we estimate our location using the velocity integrated position of the vehicle from GPS/INS inputs, and widen the search box for subsequent sweeps.
For an example of how the particles search the space when first initialized with a large 5 m × 5 m region, see Figure 11. The result of this registration process for one sweep is shown in Figure 12.