ParkGauge: Gauging the Occupancy of ParkingGarages with Crowdsensed Parking Characteristics

Jim Cherian? Jun Luo? Hongliang Guo? Shen-Shyang Ho? Richard Wisbrun†?School of Computer Engineering, Nanyang Technological University, Singapore

†Traffic Management, Traffic Assistance, BMW Group, GermanyEmail: ?{jcherian, junluo, guohl, ssho}@ntu.edu.sg †richard.wisbrun@bmw.de

Abstract—Finding available parking spaces in dense urbanareas is a globally recognized issue in urban mobility. Whereasprior studies have focused on outdoor/street parking due to acommon belief that parking garages are capable of deliveringreal-time occupancy information, we specifically target at (in-door) parking garages as this belief is far from true. This problemis very challenging as all the infrastructure supports (e.g., GPSand Wi-Fi) assumed by existing proposals are not available toparking garages, so counting how many vehicles are using aparking garage by crowdsensing can be extremely difficult.

To this end, we present ParkGauge, a method to gauge theoccupancy of parking garages, along with a reference system pro-totype for performance evaluation; it infers parking occupancyfrom crowdsensed parking characteristics instead of countingthe parked vehicles. ParkGauge adopts low-power sensors (e.g.,accelerometer and barometer) in the driver’s smartphone todetermine the driving states (e.g., turning and braking). Asequence of such states further allows the inference of drivingcontexts (e.g., driving, queuing and parked) that in turnyield temporal parking characteristics of a parking garage,including time-to-park and time-in-cruising/queuing. Miningsuch mobile data opportunistically collected from a crowd ofdrivers arriving at various garages yields a good measure oftheir occupancies and hence useful recommendations can begenerated (in real-time) to inform drivers coming toward thesevenues. Through extensive experiments, we demonstrate that ourmethod fully explores these parking characteristics to efficientlyinfer occupancies of parking garages with high accuracy.

I. INTRODUCTION

With a rapid economic growth, the vehicle population indense urban areas has been witnessing a drastic rise aroundthe world; this has led to a higher demand on parking in-frastructure especially in mega-cities. While on-street parkinghas led to serious traffic congestion due to vehicles cruisingin searching for parking places [1], multi-storey car parks(aka, parking garages), which are the major urban parkingfacilities for mega-cities, can also produce serious on-roadcongestion because of long queues of vehicles waiting to enterthem, even though their total capacity may be sufficient tomeet the parking demands. A reason for this paradox is thatthe occupancy information measured at the garages (if any)is mostly displayed only locally, rather than published onlineand available to drivers in advance. As illustrated in Figure 1,our study on the central business district (CBD) of Singaporeduring the year 2014 shows that, out of 360 garages, 28%have no occupancy monitoring system installed and 93% do

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Fig. 1: Parking garages in the CBD area of Singapore, withpercentages of the types of occupancy monitoring shown onthe left. Garages with online occupancy information and on-street parking are marked in green and purple, respectively.

not publish the real-time occupancy information online, whichcan cause waiting queues as shown in Figure 2.

Vehicles waiting to get parked also cause environmentalissues, as their emissions produced during cruising/brakingresult in serious air pollution [2], [3]. Many cities try tocontrol the problem by establishing road-side parking guidancesystems, adding occupancy sensor infrastructure, and evenenforcing special policies (e.g., a dynamic parking pricingscheme) to discourage people from driving into a CBD, butthey all need heavy investments to get fully deployed and someof them actually increase the overall carbon footprint. In fact,the majority part of the parking problem can be tackled ifthe occupancy information is available to drivers in advance,enabling them to drive towards less congested venues or re-plan their trips. Our studies reveal that some popular parkinggarages may remain full for several hours with acute queuingduring peak hours, while close-by ones possess surplus, asshown by the two garages A and B shown in Figure 3.

Fig. 2: Queuing in front of parking garages: examples fromSingapore on the left and Dortmund, Germany on the right.

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Fig. 3: Parking availabilities for two close-by parking garagesA and B during a day.

Existing infrastructure-based systems deployed to collectparking occupancy data often require occupancy sensors andwireless beacons at parking lots (e.g., SFpark [4]) or extrasensors on vehicles (e.g., ParkNet [3]), making them expensiveand not very scalable. Consequently, it would be very helpful,from both economic and environmental points of view, if thecrowdsensing ability [5], [6] of the driving population can beexploited to tackle the parking problem in an infrastructure-free manner. Inertial sensing has been widely used for humangesture and transportation mode detection (e.g., [7], [8], [9],[10], [11], [12]) without depending on any infrastructure sup-port, but it is extremely hard to infer occupancy informationfrom direct inertial sensor readings: inertial sensing may wellsuggest driving states such as braking and turning, but suchevents are seemingly unrelated to parking occupancy unlesscertain inference mechanisms are in place to establish thenecessary connections.

In this paper, we propose ParkGauge, a method to gaugethe occupancies of parking garages in urban areas. In order toapply inertial sensing for this purpose, ParkGauge innovates inusing (temporal sequences of) driving states (e.g., braking andturning) to infer parking characteristics (e.g., time-to-park,time-in-queuing) that are in turn exploited to deduce garageoccupancies. To the best of our knowledge, ParkGauge is thefirst crowdsensing method 1 that uses temporal informationto efficiently and effectively indicate parking occupancy forindoor parking garages. The primary contributions of this workare summarized as follows:• We propose a fundamentally new idea to measure the

occupancy of parking garages, exploiting seemingly ir-relevant but readily available mobile sensing data.

• We develop a full sensing framework in order to completethe transformation from (mostly) inertial sensor readingsto temporal parking characteristics.

• We identify, combine and re-engineer machine learningalgorithms in a hierarchical manner, aiming to guarantee ahighly effective inference process on the diverse datasetstypically obtained through a crowdsensing system.

• We demonstrate the efficiency and effectiveness of Park-Gauge with extensive experiments in several parkinggarages, using a prototype implemented on Android.

It is worth noting that, unlike existing crowdsensing-basedparking systems that directly count the available parking lots,

1A poster abstract of this work [13] explores the potential of using SimpleLinear Regression to infer discrete occupancy levels from time-to-park.

ParkGauge does not require a “crowd” (hence high penetrationof the application) for sensing individual parking garages.Instead, a minimal amount of sensing data acquired from asmall number of users for each parking garage would besufficient for ParkGauge to deliver useful information, whereasthe “crowd” is needed only for covering many parking garagesacross a large urban area.

The rest of our paper is organized as follows. We firstdiscuss the related proposals that lead us to the design ofParkGauge in Section II, followed by an overview of thearchitecture and key concepts in Section III. We further presentthe technical details of ParkGauge methodology in Section IVand our extensive experiment results in Section V. Finally, wediscuss potential extensions and conclude the paper.

II. RELATED WORKS

In this section, we motivate ParkGauge by showing themismatches between existing literature on parking occupancyinference/activity recognition and the actual challenges of theindoor parking problem.

A. Parking Occupancy Inference

ParkNet [3] initiates the idea of crowdsensing-assisted park-ing availability detection, but its reliance on extra sensors(i.e., ultrasonic range finders) installed on ParkNet vehicleshas tagged it with a more infrastructure-dependence nature.Instead, a few of the recent parking systems, PhonePark [14],ParkSense [15] and PocketParker [16], have taken more advan-tage of the driver-vehicle crowdsensing ability: they combinesmartphone sensors and localization techniques to detect park-ing and unparking events and to infer the availability of park-ing spaces. ParkSense [15] relies on the ubiquitous presenceof Wi-Fi beacons in urban areas to detect unparking events,while the detection procedure is initiated by a phone-basedparking payment system and keeps working until an unparkingevent is detected. Focusing on outdoor parking areas (surfacelot), PocketParker [16] requires GPS or Wi-Fi to roughlylocate a parking vehicle and further applies a probabilisticinference mechanism to account for non-participating vehicles.It utilizes accelerometer to deduce transitions between drivingand walking and thus to detect parking and unparking events.PhonePark [14] proposes a similar approach to build up ahistorical parking availability profile, while additionally ex-ploiting the pay-by-phone parking system and bluetooth sensorto detect parking and unparking events.

Though relying on GPS, Wi-Fi, or a payment system isplausible for outdoor parking, it is often not feasible forindoor parking: while both GPS and Wi-Fi are often notaccessible, a payment in garage typically happens at thedeparture time. Also, ParkSense [15] requires the system tokeep Wi-Fi sensing between a pair of parking and unparkingevents, potentially increasing the overall energy consumptionof the smartphone. Moreover, inferring occupancy from asubset of parked vehicles (as suggested by PocketParker [16])may not work well in a garage, simply due to its much

larger capacity than an outdoor parking area. Crowdsourcingapplications are available for drivers to report the occupancyinformation (e.g., Google OpenSpot). Such approaches oftenlack proper incentives to stimulate driver participations [15],because a driver would deem it too troublesome to input datamanually. In addition, we note that existing vehicle navigationsystems provide a useful feature called estimated time ofarrival (ETA) at destination. However, if a parking systemonly delivers the number of available parking lots, a driverhas insufficient information at his disposal to plan the arrivalat the final destination.

B. Activity recognition

Existing literature on human activity and transportationmode detection is bountiful [7], [8], [17], [9], [10], [11],[18]. These proposals often have a low-power profile dueto the use of inertial sensing techniques. However, it isalmost impossible to directly apply inertial sensing to de-rive occupancy information. Fortunately, recent advances inmachine learning and data mining techniques allow indirectinference to be performed when proper logical correlationscan be identified [19]. Previous studies [20] have also exploredthe feasibility of using hierarchical Bayesian non-parametricmethods for mobile context discovery from raw sensor data.Therefore, it is potentially feasible to avoid the sensing-prohibitive parking lot counting and still gauge the occupancyinformation with seemingly irrelevant sensor readings.

III. BACKGROUND / OVERVIEW

This section explains the design rationale of ParkGauge,followed by an overview of the architecture.

A. Design Rationale

Whereas counting the available parking lots is not feasiblefor indoor parking garages, it is not effective either because thecrowdsensing application has to be adopted by most (if not all)drivers. Therefore, ParkGauge aims to gauge the occupancyevaluation from a different perspective. In particular, if wedeem a parking garage as a queueing system, the occupancydetermines its service rate, which is functionally related to thewaiting time in the queue. In the parking context, we termthis waiting time time-to-park and consider it as a temporalparking characteristic; it is composed of other parking charac-teristics such as time-in-cruising and time-in-queuing. While

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Fig. 4: Parking occupancy and time-to-park at a popularshopping mall: a negative correlation is obvious.

Context Layer

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SVR withPUK kernel

Gauging objectivesCongestion levelETA adjustmentDetailed parking guidance

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Fig. 5: Architecture of ParkGauge.

time-to-park is defined as the time span from a vehicle’sarrival at a parking garage till it gets parked, time-in-cruisingand time-in-queuing measure the time spent in looking fora free parking lot and that for waiting in a stationary state,respectively. From the data that we have collected shown inFigure 4, there exist strong correlations between occupancyand time-to-park.

Using parking characteristics such as time-to-park to inferoccupancy can also satisfy our other design objectives. Firstof all, these characteristics can be detected mostly by inertialsensing techniques (if properly used), making the systemboth autonomous and energy-efficient. Secondly, it is scalableto very large metropolitan areas: since only a few tens ofsamples (so as to reach certain statistic significance) need tobe obtained for each parking garage, a small number of Park-Gauge equipped drivers/vehicles would be able to cover a verylarge area. Thirdly, the data used for inferring occupancy canextend to serve other purposes, including a more accurate ETAindication. Finally, the system is self-incentivizing: if driverswish to get the occupancy information for their respectivedestinations, they would enable the ParkGauge application toshare their data in the first place.

B. System Architecture

ParkGauge runs as an application in a driver’s smartphonethat is assumed to be taken along with the driver uponcompleting a parking. The architecture of ParkGauge has a3-layer presentation shown in Figure 5, so that connectionsbetween the seemingly unrelated sensing data and our gaugingobjectives can be made through a multi-stage inference. Sens-ing functions are performed at the lowest layer (the SensingLayer), where ParkGauge collects data using several sensorsembedded in the smartphone, including mainly gyroscope,

accelerometer, and barometer for continuous sensing in aparking garage, as well as 3G, GPS, and Wi-Fi only fordetermining the starting context of a parking process. Featuresextracted from the sensor data collected within a slidingwindow are fed into a Random Forest-based classifier thatestimates the driving state. The outputs of this layer are thedriving state, such as accelerating, braking and turning.

The Context Layer applies a Hidden Markov Model (HMM)to represent the relation between the input (driving state) andthe output (driving context), where driving states are treatedas observable states and the parking-relevant driving contextsare the hidden ones to be inferred. As the HMM factors in thetemporal correlations between consecutive driving contexts, itmay potentially counteract the errors in classifying the drivingstates. Note that a few driving contexts require direct sensorinputs, resulting in direct connections that bypass the HMM.

At the Presentation Layer, parking characteristics are de-rived from driving contexts. For example, the time spanbetween start-parking and parked is counted as time-to-park, whereas a brake count counts the number of brakings.Some of these characteristics can be used directly (e.g., toimprove ETA estimations), but inferring the occupancy of aparking garage requires an independent learning module basedon regression. Using the historical data, we build a regressionmodel to represent the relation between occupancy and thederived parking characteristics, so that ParkGauge can infer theoccupancy in real-time. To perform regression on our diversecrowdsensed data, we employ Support Vector Regression(SVR) with a universal kernel function based on Pearson VIIfunction (PUK) [21]. As all the learning models are trainedoffline, the online inferring process run by ParkGauge clientinvolves only low complexity arithmetic operations, making itboth time and energy efficient to be hosted in commercially-available smartphones.

IV. METHODOLOGY

We explain the key aspects of our methods in this section.We first present two direct-sensing components of ParkGauge,namely parking-arrival and floor-change detectors. Subse-quently, we focus on the driving context detection and explainhow we learn the HMM model from observed sensor dataand infer the driving contexts. We finally discuss the novelaspects on utilizing the various parking characteristics to inferoccupancy of a parking garage.

A. Parking-Arrival Detector (PAD)

As the contexts to set and reset a gauging process, start-parking and give-up-parking need to be captured in order forParkGauge to decide whether to start or to end. ParkGaugerelies on a low-energy 3G-based location detector to roughlyindicate if the geo-fence (e.g., a 500m circle around a parkinggarage near the destination is entered. If true, ParkGauge startsthe GPS-based localization to capture either start-parking orgive-up-parking context. If the vehicle further approaches thegarage within a small circle (e.g. 50-75m, empirically very

close to the entry point), the start-parking context is signaledand ParkGauge starts its gauging process. The current timeis recorded as the candidate Parking Arrival Time, and theDriving Context Detector (DCD) is invoked. Note that thethresholds (50-75m, 500m, 60s) are configurable for individuallocations or garages.

Under a normal situation, the false-positive rate of detectinga start-parking is low, as the chance of a vehicle slowly ap-proaching a parking garage but bearing no intention of entry isvery small. However, we have observed a few vehicles drivingnear a parking garage but hit by a traffic jam, causing a falsealarm. Fortunately, ParkGauge is robust to such anomalies, asthe recorded Parking Arrival Time is only a candidate; itcan be canceled if a give-up-parking is signaled, either dueto the vehicle exiting the geo-fence or as a result of the drivingcontext signaled by DCD (c.f. Sec. IV-C).

B. Floor-Change Detector (FCD)

This detector primarily operates on the barometer sensordata to indicate relative height variations and thereby detectsfloor changes during a vehicle’s parking process. Detectingfloor-change context allows ParkGauge to reinforce its beliefin an ongoing parking process, and it also facilitates derivingparking characteristics for individual floors within a park-ing garage (e.g., time-in-cruising for basement 2), so thatParkGauge can provide fine-grained parking characteristicsdesirable for users who, for example, prefer to park at a floorclose to their favorite shops.2

While the gradual increase in barometer reading is theconsequence of the vehicle’s cruising along a spiral ramp,the overall variations clearly indicates the floor changes:the altitude variation is inversely proportional to that of thepressure with a slope of roughly 0.12mp/m. The patternsare consistent for each parking garage and that helps Park-Gauge offer repeatable floor detection performance even in thepresence of long-term pressure fluctuations [22]. ParkGaugeobtains barometer readings at 1Hz frequency and it appliesa 10s window to check if the readings are sufficiently stable,i.e., variance below a threshold (e.g., 0.1mb). Whenever stablereadings are identified, their average value is then comparedwith that of the previous one. If the resulting altitude differencefalls within a pre-determined height interval applicable forthe parking garage structure (normally around 3.3m) or itsmultiples, a floor-change context is signaled.

C. Driving Context Detector (DCD)

DCD is the core of ParkGauge for inferring the drivingcontexts of a vehicle. We first briefly introduce the basicmodels. Then we explain the feature selection and drivingstate classification at the sensing layer. Finally, we presentthe learning process for the HMM (context layer).

2Such profile information can be of interests to other mobile applicationssuch as advertisement pushing or coupon distribution.

1) Modeling a Parking Process: We use O and C torepresent observation (or driving state3) and driving contextrespectively. The time-granularity of inference is quantifiedusing a window of size W . We use the subscript t to denotethe time index of the state and context for a window. Exceptfor the 3 direct-sensed contexts discussed in Sec. IV-A andIV-B, the relation between observation (driving state) anddriving contexts are modeled as an HMM with standard first-order Markov assumptions made for the temporal sequenceof driving contexts. This can be specified by: (1) stationarycontext distribution, Pr(C1), (2) context transition model,Pr(Ct|Ct−1), and (3) observation model, Pr(Ot|Ct).

When a stream of driving states [O1, O2, · · · ] are estimatedby the sensing layer, ParkGauge takes them for inferring thet-th driving context Ct, where the correlation between con-secutive contexts has been implicitly considered by involvingthe previous context as an input. Table I lists all the drivingcontexts and observations considered by ParkGauge.

TABLE I: List of driving states and contexts.

Driving state Driving context

a. proceeding i. drivingb. accelerating ii. cruisingc. decelerating iii. parkedd. turning iv. queuinge. braking v. start-parkingf. pausing vi. give-up-parkingg. walking vii. floor-change

2) Feature Extraction and Classification of Driving States:As shown in Figure 5, we mainly use the accelerometer andgyroscope for driving context detection. Whereas barometermay be used for this purpose with even lower energy con-sumption [23], our current implementation avoids using itdue to its longer detection latency. Next, we describe howfeatures suitable for ParkGauge are extracted and used to traina classifier that estimates driving states.

ParkGauge uses a sampling frequency of 20Hz to collectsensor readings through Android SensorManager API. Thedriving state is determined by collecting these readings in aninterval of W seconds and feeding it to a classifier. By default,W = 10s and we justify this choice through experimentsin Sec. V-D. Raw acceleration values are pre-processed byapplying a low-pass filter to estimate the gravity componentthat is removed to obtain linear acceleration values. Thesevalues are further smoothed (to mitigate noise) by applying a5-term moving average, and the results are processed to extractthe time-domain and frequency-domain features mentioned inTable II. Similarly, raw gyroscope readings are also smoothedand processed to extract the specific angular time-domainfeatures listed. Figure 6 shows examples of raw sensingreadings corresponding to the driving states considered byParkGauge. Clearly, the aforementioned features characterizethese states sufficiently.

3We shall hereafter use these two terms in an interchangeable manner.

TABLE II: Features used in classifying driving state.

Acceleration-based Gyroscope-based

Time-domain Frequency-Domain Time-domain

Mean Peak Frequency MeanVariance FFT-Peak VarianceRange FFT-0,1,2,3,4Hz RangeGradient Energy Peak Count

Using a dataset obtained from our experiments (c.f.Sec. V-A), we train a Random Forest based classifier [24]offline that enables ParkGauge to efficiently and accuratelyestimate the driving state from sensor data readings at run-time. The training dataset consists of the aforementionedfeatures extracted for a sliding window of size W and 50%overlap. Each data record is labeled with corresponding actualdriving states. The Random Forest algorithm fits randomlyselected samples from the labeled training data to multipledecision trees using the principle of bootstrap-aggregating. Itfurther predicts the class labels for unseen data by taking amajority vote among the trained decision trees and therebyoffers better generalization performance over a single decisiontree. The ParkGauge implementation incorporates a rathermodest set of 10 trees with a maximum depth of 3 each.

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Fig. 6: Visualizing driving states by raw data.

3) Learning and Using the HMM Parameters: Given theobservations made online, the HMM shown in Figure 5allows us to infer the (hidden) driving contexts, if the HMMparameters discussed in Section IV-C1 are fully specified. Webriefly explain how we learn the HMM parameters (offline)based on the driving/sensing data collected in advance, aswell as how to use them for online inference. For learningthe HMM model, we apply the backward-forward recursionsimilar to Baum-Welch EM algorithm [25], but we opt for theGibbs Sampling [19] technique for a more robust estimation:it makes better use of our dataset with driving states manuallylabeled and corresponding observations recorded.

Given the dataset obtained through our intensive tests, weapply common statistics to derive initial values for the modelparameters defined in Sec. IV-C1. For example, the stationaryprobability of Pr(C1 = cruising) is obtained by looking at thefrequency of the cruising context out of all observed drivingcontexts. Now given a sequence {o1, o2, · · · , oT } of observeddriving states, the forward-backward procedure is used tocompute the forward posterior probability and the backwardposterior probability. The model is iteratively updated basedon these probabilities and repeated until convergence to stableestimations of the model. To apply this model for inferringthe driving contexts online, we make use of a modified Viterbialgorithm [26]; it identifies the most likely sequence of hiddendriving contexts from a sequence of observations (drivingstates). At runtime, whenever a change of context is signaled,the timestamp is also recorded. In particular, the Parked Timeis recorded if the context cruising changes to parked.

D. Gauging Occupancy using Parking Characteristics

Given the context changing times recorded, we can computethe parking characteristics. While time-to-park is the dif-ference between Parked Time and Parking Arrival Time,time-in-cruising and time-in-queuing simply accumulate thetime spent in the corresponding contexts. In the following, wepresent how these characteristics can be used to gauge theparking occupancy.

1) Gauging the Occupancy: As explained in Section III-A,there exists an implicit functional relationship between time-to-park and occupancy. Instead of deriving this functionanalytically, we use regression to fit this function based onour labeled datasets (c.f. Section V-F). As a result, wheneverParkGauge obtains an estimated time-to-park, it can infer thecorresponding occupancy. Such occupancy estimations can beaveraged over a sliding time interval (for example, 20 minutesduration in our reference implementation) and reported tousers in real-time. Figure 7 illustrates this relation using real-world data collected from a popular parking garage duringa working day (10:00 to 16:00) with at least 1 observationrecorded every 10 minutes. It can be observed that lowertime-to-park is observed during periods of high parking spaceavailability and vice-versa. When such high-quality data areavailable, a simple linear or quadratic regression fits a modelthat can operate with reasonably low estimation errors.

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Fig. 7: Training the regression model to fit the relation betweenoccupancy and time-to-park.

TABLE III: Features used to infer parking occupancy.

Parking characteristics: input features for regression

time-to-park day of week turn counttime-in-queuing arrival time brake counttime-in-cruising

However, in a practical mobile crowdsensing system, itmay not be feasible to obtain high quality data for everyparking garage and this may limit the quality of the parkingoccupancy inference. To address this issue, we propose touse additional parking characteristics that are obtained fromthe lower layers of ParkGauge and use them to improve theinference accuracy for garages having a lower number ofobservations per day (due to a lower penetration of ParkGaugeusers visiting the garage). Specifically, we propose to exploitthe ability of ParkGauge to extract the features (regressorvariables) in Table III for each parking session and utilizethem offline to train a robust regression model.

In order to choose a robust regression model using thesefeatures, we propose to use the well-known Support VectorRegression (SVR) with an appropriate kernel function selectedthrough experimental evaluation (see Section V-F).

2) Support Vector Regression: There has been extensiveliterature on Support Vector Regression [27] and hence weonly briefly describe the relevant concepts here. Given atraining data set of n observations D = (xi, yi), i = 1, 2, ..., nwith x ∈ Rd representing the d input features obtained fromeach parking session and y ∈ R representing the correspondingoutput parking occupancy to be inferred, SVR tries to findthe function f(x) : Rd → R mapping the input training datafeatures x to output y, that produces estimation of y which isthe closest to the corresponding true values in D.

The problem belongs to Reproducing Kernel Hilbert Spaces(RKHS) H and can be formulated as

f∗(x) = argminf∈H

(C

l∑i=1

V (f(xi), yi) + 0.5||f ||2H)

(1)

where C is a parameter controlling the relative weight of theloss function and the regularization penalty ||f ||2H. The lossfunction in our case is V (f(x), y) = |round(f(x))− y|.

3) Choosing Kernel Function: Apart from SVR, kernel-based methods have become highly popular in solving regres-sion and classification problems and several kernel functionshave been proposed. Kernel functions help to transform theinput data space into a Hilbert Space. (i.e. a space whichis spanned by distance-based functions or inner-products ofthe input feature data vectors ∈ Rd) Some of the popularkernel functions are Linear kernel, Polynomial kernel andRadial basis function (RBF). Recently, [21] proposed as a newalternative, the Pearson VII Universal kernel (PUK) functionwhich is basically the Pearson VII function developed in 1895by Karl Pearson [28]. PUK can be regarded as a universalkernel function since it can handle linear, polynomial and RBF

based feature mappings. PUK function possesses the flexibilityto vary between Gaussian and Lorentzian shapes and more,thereby offering more robust mapping capability and enablingit to deal with a broad spectrum of data and problems. SincePUK can help avoid the tedious process of selecting kernelfunctions, the model building process can be made simplerand computationally efficient. The Pearson VII function canbe understood in the general form

H[1 +

(2(x−x0)

√2(1/ω)−1)σ

)2]ω .

(2)

where x is the regressor variable and H represents the maxi-mum height of the peak of x (i.e., the value of y observed atits center x0). The half-width and tailing factor of the peak arecontrolled by the parameters σ and ω. The function is flexibleto vary from Gaussian (ω ≈ ∞) towards a Lorentzian (ω ≈ 1)shape by varying the parameter ω. This property enables PUKto fit peaks of a variety of line widths and shapes, thus helpingto serve as a universal kernel function.

V. EMPIRICAL EVALUATION

In this section, we describe the evaluation procedure, setupfor data collection and parking experiments using our Park-Gauge prototype, as well as evaluation results.

A. Data Collection and Experiment Setup

For an effective evaluation, we have implemented Park-Gauge as an Android-based application along with a back-endserver. While the model learning procedure is done offline inthe server using the collected dataset, all the online detectionsare performed by the ParkGauge client application running (atthe background) in a smartphone, which periodically reportsdata to the server.

Our experiments involved five different phones: SamsungGalaxy S4, HTC One M8, LG Google Nexus 5, SamsungGalaxy S3, and HTC One X. All these phones possess bothaccelerometer and gyroscope, while the first three of them alsohave a barometer. The last two phones were chosen to test howthe ParkGauge system would work without the barometer. Tovalidate the inter-floor height calculated by the barometer, weused a Bosch laser rangefinder DLE40 to obtain the groundtruth. We collected data for two months in two different cities(Singapore and London), during which about 120 traces weregathered, including 62 self-parking sessions. Six drivers ofdifferent nationalities and diverse driving habits contributed tothis dataset and both petrol (Toyota WISH, VW Polo, Mazda3) and electric (BMW i3) cars were used.

The parking garages in our experiments are specificallyselected to be attached to popular shopping malls, so that wedo get significant fluctuations in their occupancies during aday. These garages published their occupancies online, whichwe collect and use as ground truth for our inference. Weperformed two categories of designed experiments: i) parking

among a few close-by garages in a sequence, and ii) parkingin a single garage in a cyclical manner, i.e. enter, park, walk,unpark, exit, and repeat. On one hand, the former helps usto evaluate the robustness of ParkGauge in accommodatingdifferent parking situations: these garages were quite differentin terms of number of floors (ranging from 3 to 12 floors),underground or aboveground, floor area and capacity per flooretc. On the other hand, the latter category enables us toevaluate the consistency of ParkGauge and also to verify thecharacteristics measured by ParkGauge against the groundtruth during the same period of time. Each parking sessiontook roughly 10 to 25 minutes, depending on the occupancyat that time. To capture the fluctuations in the demand forparking, the data collection was performed around the peakhours, i.e., 10:00-16:00 and 18:00-20:00.

B. Data Pre-Processing

We work with 2 kinds of data: (1) sensor data collectedfrom smartphones during parking sessions, (2) parking char-acteristics determined by ParkGauge users.

1) Pre-processing Raw Sensor Data: The sensor data ob-tained from the different phones are cleaned and smoothenedto remove noise and outliers, as already described in SectionIV-C2. The cleaned data is used to extract features and trainthe driving state classifier, and subsequently, the HMM drivingcontexts. 10-fold cross-validation is performed to ensure goodgeneralization performance of these methods.

2) Pre-processing the Parking Characteristics Dataset:This dataset included both (a) a feature-rich set of park-ing characteristics computed by the ParkGauge clients andvalidated against corresponding ground truth, as well as (b)(availability, time-to-park) data pairs collected at few garagesthrough manual observation. The former dataset is richer infeatures and very diverse since they are from different days andinvolving different drivers, albeit the number of observationsper driver or vehicle and per garage and per day are small.However, since this is crowdsensed and inferred data, thereare some chances of errors. The latter data is collected fora specific garage for a long duration (e.g. 10:00-16:00) andrecorded at least once in every 10 minutes, and this resulted indata of high quality and reliability, and nearly identically andindependently distributed (i.i.d). This dataset is very importantsince it is used to construct a regression model and inferthe parking occupancy. Therefore, the dataset is first cleanedto remove extreme values or outliers. We first calculate theInter-Quartile Ranges (IQR) on all records and then filter andeliminate the values in 25% and 75% quartiles that exceedthe IQR. Subsequently, we normalize all the numeric featuresin all the data records using min-max normalization processbefore applying the regression process.

a) Feature Selection: After pre-processing, we apply afeature selection algorithm to identify a significant featuresubset i.e., the best features useful for inferring parking occu-pancy. Although this could be performed by a filter or wrappermethod, we employ Correlation Feature Selection (CFS), a

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Fig. 8: Raw data traces corresponding to two parking trials with short and long time-to-park. We only provide full labels tothe long trace for better readability, but the feature-context correspondence can be easily discerned for the other trace also.

correlation-based feature subset selection method for machinelearning [29]. This method evaluates the inference quality ofa subset of attributes by evaluating the individual predictiveability of each feature in addition to the degree of redundancybetween these features. Running the CFS algorithm on ourtraining dataset with 10-fold cross validation helped to arriveat the 7 features listed in Table III. In our original dataset,additional fine-grained feature attributes were available suchas the number of floors traversed, left turns count, and rightturns count. However, these attributes were excluded since theydid not possess significant predictive ability within our dataset.With larger datasets arriving from a large-scale crowdsensingdeployment, such feature selection is useful.

b) Splitting The Dataset for Training and Testing: Afterpre-processing, we evaluate several regression methods. Foreach method, we train the model using our training dataset andperform 10-fold cross validation to understand their general-ization performance. Finally, we test the trained model with atesting dataset and report the performance.

For this paper, we evaluated the methods with data for dif-ferent days from the same driver and different drivers. Finally,we intentionally mixed the ParkGauge-reported data fromactual parking sessions with the manually observed dataset,since this approximates the data inputs with a real-worldcrowdsensing system. This dataset consists of 78 records, ofwhich 37 records are manual observations with a high fidelityand the rest are crowdsensed by ParkGauge during parkingexperiments. The manual observations had empty featureswhich were marked as missing values, but valid features werestill considered. This dataset was further divided into trainingdata and testing data. We performed both 10-fold and leave-one-out cross validation approaches to ensure generalizationperformance. The testing data was obtained by randomlysampling 10 observations without replacement, resulting in a10-record testing dataset and a 68-record training dataset.

C. Inferring Driving States and Contexts from Sensor Data

To provide a rough idea about how ParkGauge operatesin field, we use two sets of raw sensor readings plotted

in Figure 8 to demonstrate the inferred driving states andcontexts. These two parking trials differ in their values oftime-to-park reported by ParkGauge: (1) The left one tookonly 140 seconds as the vehicle arrived at a parking garagewith a rather low occupancy (in the morning), and most ofthe time was spent mainly on cruising and going two-levelsdownwards (indicated clearly by barometer readings). (2) Theright case was a long parking trial. The vehicle arrived at theparking garage with almost full occupancy, so it was first hitby a long queue at the entrance, then it spent quite a longcruising time in finding a parking lot even after getting threelevels down. This trial took place during the peak hour whenpeople drive to the shopping mall to get their lunch.

D. Accuracy of Driving Context Inference

We omit the performance evaluation for driving state infer-ence and directly evaluate the accuracy of estimating drivingcontexts. This is because driving contexts are directly relatedto ParkGauge’s final performance in deriving parking charac-teristics and thus gauging the occupancy. To evaluate the ac-curacy of estimating a certain driving context, we first identifythe time intervals spent in that context according to our groundtruth observation. Then, we check the output of ParkGaugeto see the percentage of these time intervals when ParkGaugehas made a correct estimation. Assuming an ergodic stochasticprocess behind the estimation, this percentage exactly indicatesthe success rate in detecting this driving context. Due to spacelimit, we choose to show evaluation results for three contexts,namely driving, parked, and cruising.

The other goal of this evaluation is to choose the bestwindow size W used for estimating driving state and context.In fact, we initialize W to 5s, as this is the smallest value toaccommodate a certain driving state (e.g., turning). Then, wetry different values of W that are all multiples of 5s. As shownin Figure 9, while it is expected that the latency grows almostlinearly with W , the highest accuracy is achieved at W = 10s.The accuracy first increases with W as ParkGauge gets moreinformation to make a decision, but it starts to decrease lateras the “cost” of making a wrong estimation grows with W .As a result, we fix W = 10s in our final implementation.

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Fig. 9: Detection accuracy and latency for 3 driving contexts(namely driving, parked, and cruising) under various windowsizes W with a stepsize of 5s.

E. Accuracy of time-to-park Estimation

Estimating time-to-park is an important functionality ofParkGauge. As shown in Figure 10, the estimation errors rangefrom 5s to around 30s. While extreme values are rare, most

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errors are around 18s. Given that the normal values of time-to-park are in the order of minutes (or tens of minutes in theworst case), we deem ParkGauge’s performance in estimatingtime-to-park very accurate. In fact, as the error mean is relatedto the window size W (it is systematically biased due to thedetection latency), we could further reduce the estimation errorby subtracting W from each estimated time-to-park. Thiswould bring the error down to the range of (−5, 20)s.

F. Performance in Occupancy Gauging

As explained in Section IV-D1, we use regression to recoverthe functional relationship between occupancy and temporalparking characteristics time-to-park extracted from the data.To perform the evaluation, we use the training and test datasetsdescribed in Section V-B2b. We compare four regressionapproaches, namely: (1) Simple Linear Regression (SLR) withonly time-to-park feature, (2) Multiple Linear Regression(MLR) with all 7 features listed in Table III, (3) ArtificialNeural Network (ANN) using 10 hidden layers, and (4) SVRwith 5 different kernel functions, namely Linear, Polynomial(quadratic, cubic), RBF and PUK.

To compare the different regression methods, we use the

Normalized Root-Mean Squared Error,

NRMSE =

√∑ni=0(pi − ai)2

n, (3)

the square root of the mean of squares of errors between thenormalized actual values {ai} (as discussed in Section V-B2)and the corresponding inferred values {pi}.

Regression method

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Fig. 11: Comparison of different regression methods

From Figure 11, one observes that linear regression ap-proaches (MLR and SLR) performed reasonably well. TheNRMSE is high, but it is still comparable with SVR. ANNdoes not perform very well with this dataset. Using the hiddenlayers, it seems to over-fit the model to the training dataand hence the test data results in higher errors. However,SVR provides good performance with different kernel func-tions. Linear kernel offers slightly worser error performance,whereas Polynomial (both Quadratic and Cubic) and RBFkernel functions offer superior performance. But, it is clearthat SVR with PUK kernel offers the lowest NRMSE (0.0993)and hence, the best generalization performance.

A key observation from this evaluation is that SLR performsdecently (NRMSE 0.2106) even when using time-to-park asthe only input feature. However, the accuracy obtained ismore than doubled (NRMSE 0.0993) when we perform SVRwith PUK kernel on a higher-dimensional training data withadditional features such as time-in-queuing as listed underSection IV-D1. This justifies the multi-layered hierarchicalmethodology adopted by ParkGauge.

G. Tuning The Parameters of SVR(PUK)

Since we have convincing results that help us chooseSVR(PUK) as the preferred approach to infer parking occu-pancy, we now tune the parameters of the PUK kernel function,namely ω and σ, that control its shape and thereby affectsthe inference output of SVR(PUK). We vary each parameteracross a range of 0 to 100 while keeping the other parameterfixed at a value 1. In each iteration, we train a SVR(PUK)model and check its generalization performance using 10-foldcross validation. In Figure 12 (left plot), one observes that thelowest NRMSE is obtained at ω = 2 when σ is fixed at 1. Inthe right plot, one observes that the best performance (0.0993)is obtained at σ = 1 when ω is fixed at 1. Thus, we choose thecommon point σ = 1 and ω = 2 as the Pearson parameters forSVR(PUK) in inferring parking occupancy for ParkGauge.

Pearson parameter, !0 1 2 3 4 5 6 7 8 9 10

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Fig. 12: Determining the values of Pearson parameters ω andσ that yield the best performance for SVR(PUK)

VI. CONCLUSION AND DISCUSSIONS

Based on the observation that indoor parking garages maylack real-time occupancy information, we set out to develop anew mobile parking data collection, processing, and inferencemethod, ParkGauge; it delivers real-time occupancy informa-tion to its users. As indoor parking garages differ in manyaspects from outdoor parking places, the method adopted byexisting proposals for directly counting occupied parking lotsare infeasible. To this end, our design of ParkGauge innovatesin using inertial sensing data to infer parking occupancy withreasonably low errors. Inspired by queueing theory, ParkGaugecomputes parking characteristics such as the time spent to parka vehicle and the time it spends in queuing and cruising, thebrake count and number of turns made during the parkingprocess, and uses SVR to infer parking occupancy.

In future, we plan to make a large-scale deployment ofParkGauge and analyze the crowdsensed parking character-istics inferred by ParkGauge. For a real deployment of mobilecrowdsensing system to be successful, energy managementis also crucial. For this purpose, the application can adopta strategy utilizing operating modes such as a very-low-poweridle mode, a short but energy-hungry prepare mode utilizinghigh-power sensors such as GPS only when necessary to detectstart/give-up-parking, and a low-power active mode utilizingonly low-power sensors to compute the parking characteristics.

VII. ACKNOWLEDGMENTS

This work is supported by the BMW Group, Germany.

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