Optimal parameter values for mode detection in GPS post-processing: An experiment D. Upadhyay N. Schüssler K.W. Axhausen M. Flamm V. Kaufmann
Arbeitsbericht Verkehrs- und Raumplanung 507
July 2008
Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Working paper
Optimal parameter values for GPS post-processing: An experiment Devendra Upadhyay IIT Guwahati IN - 781039 Guwahati
Telephone: +91 9954249403
[email protected]
Nadine Schüssler Kay W. Axhausen IVT ETH Zürich CH - 8093 Zürich
Michael Flamm Vincent Kaufmann INTER EPF Lausanne CH - 1015 Lausanne
Telephone: +41 44 633 30 85 Telephone: +41 21 6937302 Fax: +41 44 633 39 43 Fax: +41 21 6933840
[email protected] [email protected]
Summary Mode detection stage is a crucial step of post-processing of GPS raw data. In the procedure developed by Schüsssler and Axhausen (2008), a fuzzy logic based algorithm is used for mode detection of each stage of a trip. This fuzzy logic uses fuzzy variables with three or four membership functions. Each membership function has four key points or parameters. This paper deals with optimization of these parameters to give best possible match of the results from GPS data post processing. Calibration of these parameters was carried out with the help of SPSS and Microsoft-Excel. A program was developed which was able to measure the stage by stage modal mismatch between the results from GPS data post processing and a sample of well-coded GPS data. Final optimized parameter profile produces considerably less modal mismatch than the original profile that was used before. Keywords GPS data processing, mode detection, fuzzy logic, parameter optimization Preferred Citation Style Upadhyay, D., N. Schüssler, K.W. Axhausen, M. Flamm and V. Kaufman (2008) Optimal parameter values for GPS post-processing: An experiment, Working Paper, 507, IVT, ETH Zurich, Zurich.
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
1. Introduction Person based GPS data comprising of three dimensional position and time stamp can be used for determining individual trips and activities, including further characteristics, such as modes and routes. The very large amount of GPS raw data acquired from the individual participants requires appropriate post-processing to deduce the information about the trips and activities. An important step for the large scale and affordable use of GPS data for the analysis of the travel behaviour was taken with the post processing procedure formulated by Schüssler and Axhausen (2008). It was applied to GPS records collected in the Swiss cities Zurich, Winterthur and Geneva. The post-processing procedure described in the next section consists of filtering and smoothing of the data, detection of trips and activities within the continuous stream of GPS points, segmentation of trips in (single mode) stages and detection of their modes. Mode detection is based on speed and acceleration characteristics of each mode in the study area and it uses an open source fuzzy logic engine (Sazonove et al., 2002). The membership functions used in the original post processing work were based on visual inspection of the speed and acceleration patterns of the data and making reasonable assumptions about the individual modal characteristics. However, the values of these parameters could not calibrated for the optimum results as there were no GPS tracks with a correct coding of the stages and activities present at that time. This paper deals with the calibration of the membership functions to give better results by using the data collected in the comprehensive investigation of travel behaviour adaptation process during life course transitions (Flamm and Kaufmann, 2007). The 6-weeks of GPS tracks collected in this study were coded by hand into stages and activities and the codes verified by extensive personal interviews with the respondents. These data can be assumed to be as close to a true record as its currently possible. Each trapezoidal membership function representing different levels of the fuzzy variables is described by four key points, the starting point, the left top corner, the right top corner and the end point. There were three variables employed for each mode in the algorithm each having three or four membership functions. The parameters which have to be optimised are the key
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
points of each membership function. All in all there were 40 key points or parameters, 4 for each membership function of the fuzzy variables. The fine-tuning of these parameters is performed between the upper and lower bounds of each parameter, which respect the necessary overlap between the membership functions. This range was characterised by three levels (values) each. The experiments were based on orthogonal designs of the parameters. The orthogonal design was created with the statistical analysis program SPSS. The quality of the mode detection of the post processing procedure was determined by stage by stage comparison of the modes. The weighted modal error score of each stage is added for a total modal error for that particular parameter profile, i.e. set of parameter values. A linear regression analysis of the total modal error was performed with the parameters as the independent variables. The regression model identified the parameters which have a high impact on the modal error. This provided the basis for the generation of a second experiment with a focus specifically on these high-impact parameters. This process was repeated until a true understanding of the effect of the parameters was achieved. The final regression model was used to find the optimum profile with the help of optimization solver in MS-Excel. The quality the post processing can also be measured in a more refined way by comparing the mode-chains of the output of the post processing and the interview data. This can be accomplished by sequentially aligning the mode-chain or sequence obtained from the post processing with the mode sequence reported in the interview. An available one-dimensional sequential alignment algorithm was tested for this purpose, but this work could not be completed as the one-dimensional sequential logarithm could not handle large number of sequences to be processed here (see Joh, Arentze and Timmermans, 2001 for appropriate multi-dimensional sequence alignment approaches or Clarke, Harvey and Thompson, 2005 for an uni-dimensional approach).
2. A review of the Schüssler-Axhausen algorithm The fundamental questions for the GPS post processing are:
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
1. How to detect trips and activities? 2. How to derive the modes used by the participants? 3. How to extract the routes chosen on the network? The post-processing-procedure of GPS raw data developed by Schüssler and Axhausen (2008) addresses all these questions. The approach followed is not only able to handle the huge amount of data efficiently but it is independent of the quality of the network and spatial information available.
2.1
GPS records used
The input data used for the post-processing procedure is merely the raw data obtained from the GPS receivers carried by the participants. The records were collected in the Swiss cities of Zurich, Winterthur and Geneva. The original study was conducted by a private sector company with an aim to explore whether or not participants pass certain billboards. Hence, here not only all modes have been included in the study but also trip chains covering the whole day have been obtained. Each of the 4882 participants carried the GPS logger for several days resulting in about 32,000 recorded person-days.
2.2
A brief description of the post-processing technique
First part of the post processing of GPS raw data concerns with filtering and smoothing of data. Systematic and random errors present in GPS data due to various inevitable reasons had to be minimized. To get rid of erroneous points filtering and smoothing techniques were applied. Filtered and smoothed points had to be subdivided into trips and activities. Number of criteria were used which determine whether the GPS point in question belongs to a trip or an activity. Mode determination was the major part of the post processing of the GPS data. Each trip was segmented into single-mode-stages. The mode of each stage was then determined by employing speed characteristics and the proximity to the public transport stops and routes. It was assumed that walking is required for any mode change. The trip was segmented into several mode stages by finding the points where the mode changes from walk to another
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
mode or vice versa. Walk stage was determined with the help of its unique attribute of consequently low speeds and accelerations. The modes in the study area were distinguished as walk, cycle, car, urban public transportation (i.e. bus and tram) and rail. The modes of the remaining stages were determined by applying an open source fuzzy logic (Sazonov, Klinkhachorn, Gangarao and Halabe, 2002) the crucial elements of this logic were: 1. Fuzzy Variables 2. Fuzzy Rules: describing the relationship between the modes and the fuzzy variables. 3. Membership Functions: Representing different levels of the fuzzy variables. The three fuzzy variables chosen, were: 1. The Median of Speed 2. 95th percentile of the Speed 3. 95th percentile of the Acceleration These statistical location parameters were explicitly chosen over the average speed or the maximum speed and acceleration to make the algorithm more robust against outliers. Each variable was then divided into three or four membership functions. Each trapezoidal membership function had four key points: the starting point, the left top corner, the right top corner and the end point. All in all there were 40 key points or parameters. The figures depicting these fuzzy variables and corresponding membership functions are as shown in the figures 1, 2 and 3.
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
Figure 1
Fuzzy Variable: Median of the speed
Figure 2
Fuzzy Variable: 95 percentile of the acceleration
th
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Figure 3
th
Fuzzy Variable: 95 percentile of the speed
The values of the parameters were assigned after an analysis of the available modes and the speed and acceleration characteristics in the GPS data. After establishing the values of the parameters the fuzzy rules were derived. These fuzzy rules established the relationship between the modes and the fuzzy variables. Each mode was described by at least one rule. It can be seen that the membership functions overlap for each fuzzy variable. This overlap ensures that more than one fuzzy rule may apply to a stage and the same stage can be linked to different modes. Further, the defuzzify method combines the membership values for each individual mode using the AND operator. Thus the final score for each mode equals the minimum membership value amongst all its rules. Subsequently, the likelihood for each mode was calculated based on all modal scores of a stage.
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
3. Identification of optimum set of parameter values The values assigned to the parameters in the post processing were merely by inspection of the observed speed and acceleration characteristics of the modes for the study area. The optimum set could not be found due to the unavailability of the true GPS records. The data obtained Flamm and Kaufmann (2007) allow the search for an optimal set, as the post-processing results can be compared with the coding performed by Flamm and Kaufmann.
3.1
The GPS data used
The work of Flamm and Kaufmann (2007) combines the GPS based person tracking and qualitative interviews. GPS tracking units were handed out to the participants and extensive data was collected about their travel behaviour. This data collection was followed by prompted recall interviews of the participants consisting questions about their travel behaviour, location choices, their underlying activity space and their mobility experiences. The GPS observation period encompassed 6 weeks. This intensive contact allowed the correct coding of the GPS traces into stages, trips and their modes.
3.2
Measurement criteria for the quality of the output
Single mode stages are identified by the post processing of GPS data. The output comprises the modes for these stages, their starting and ending location and time and other speed and acceleration data. The same stage-characteristics were also present in the data collected from the interviews of the individual participants. The modes for each stage from the output are compared with the mode reported in the interview data. If a mismatch is found an error weighted by type of mismatch is added to the total error. The weights used are shown in Table 1. They increase by the inherent size of the mismatch. This total error gives an idea of the quality of the output. This procedure is implemented by a C program which gives the final modal errors for each profile. The errors by type of mismatch are shown in Table 2. The diagonal reports the number of correct matches.
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Table 1
Weights of the mismatches by mode
Reported by the Mode detected in the post- processing of GPS raw data participant (including Activity) Walk
Bike
Car
Not Decided
Urban Rail public transportation
Walk
0
1
2
3
4
1
Bike
1
0
1
2
3
1
Car
2
1
0
1
2
1
Urban public transportation
3
2
1
0
1
1
Rail
4
3
2
1
0
1
Activity
1
1
1
1
1
1
Table 2
Number of the mismatches: Original parameter settings
Reported by the Mode detected in the post- processing of GPS raw data participant (including Activity) Walk
Bike
Car
Not Decided
Urban Rail public transportation
Walk
1795
240
144
127
0
0
Bike
13288
768
40
222
0
5
Car
413
205
732
331
68
19
Urban public transportation
262
297
47
120
0
0
62
1
203
7
0
0
0
2420
4420
2432
315
146
Rail Activity
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
3.3
Generation of the experimental parameter profiles
As a first step only starting and ending points of each membership function were varied. This reduced the number of parameters to be optimised from forty to fourteen. The values or levels to these parameters were assigned such that the membership functions maintain an overlap. All these values are listed in the Table 3. The slopes of the modified membership function were maintained as in the original membership function. This allowed automatic determination of the top left and top right parameters of each function. Since, running all the combination of parameter values would take considerable time, an orthogonal design was chosen to generate the parameter profiles. Orthogonal design is a common tool for selecting the parameter profiles for experiments (Box, Hunter and Hunter, 1978). It was produced with the relevant SPSS module (SPSS, 2008). SPSS produced total 64 parameter profiles (combinations of the 14 parameters) for which the post processing procedure was applied. Table 3
Parameter values
Parameter
Speed in m/sec and Acceleration in m/sec2 Assigned Values
Original value
Low 1
medSpeedVeryLowEnd
2
High
Medium
2
1.88
2
2.13
medSpeedLowStart
1.5
1.38
1.5
1.63
3
medSpeedLowEnd
6
5.75
6
6.25
4
medSpeedMediumStart
5
4.75
5
5.25
5
medSpeedMediumEnd
15
14.25
15
15.75
6
medSpeedHighStart
12
11.25
12
12.75
7
ninetyFiveAccLowEnd
0.6
0.58
0.6
0.63
8
ninetyFiveAccMediumStart
0.5
0.48
0.5
0.53
9
ninetyFiveAccMediumEnd
1.2
1.15
1.2
1.25
1.5
0.95
1.5
1.05
8
7.88
8
8.13
12 ninetyFiveSpeedMediumStart
7.5
7.38
7.5
7.63
13 ninetyFiveSpeedMediumEnd
18
17.25
18
18.75
14 ninetyFiveSpeedHighStart
15
14.25
15
15.75
10 ninetyFiveAccHighStart 11 ninetyFiveSpeedLowEnd
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
4.
Results
Linear regression analysis of the 64 runs was used to generate an initial model for the modal error. The 14 parameters were the independent variables. The results obtained are shown in the Table 4. Table 4
Initial regression model
Parameter
Unstandardized Coefficient (B)
(Constant)
Standardized Coefficient (Beta)
t-Value
27.419
24340.939 122.307
.132
2.257
medSpeedLowStart
53.131
.049
.839
3
medSpeedLowEnd
-4.370
.008
-.138
4
medSpeedMediumStart
56.255
.104
1.776
5
medSpeedMediumEnd
-5.873
.033
-.556
6
medSpeedHighStart
-11.748
-.065
-1.113
7
ninetyFiveAccLowEnd
4452.614
-.830
14,200
8
ninetyFiveAccMediumStart
1570.225
.293
5.008
9
ninetyFiveAccMediumEnd
-56.227
-.021
.355
10 ninetyFiveAccHighStart
-19.352
-.007
-.122
11 ninetyFiveSpeedLowEnd
-19.391
-.018
-.306
12 ninetyFiveSpeedMediumStart
1.184
.001
.019
13 ninetyFiveSpeedMediumEnd
26.089
.144
2.471
4.085
.023
.387
1
medSpeedVeryLowEnd
2
14 ninetyFiveSpeedHighStart R2 = 0.833; adj. R2 = 0.785; N = 64
The initial regression model shows high standardized coefficients for certain parameters. This implies that small relative changes have high impact on the modal error. The five parameters with largest standardized coefficients were considered for further analysis: 1. medSpeedVeryLowEnd 2. medSpeedMediumStart
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
3. ninetyFiveAccLowEnd 4. ninetyFiveAccMediumStart 5. ninetyFiveSpeedMediumEnd These are associated with the following modes in particular rail and walk. A second regression model explored, if there are non-linear and interaction effects of these variables. All interactions were calculated and then divided by 100; equally the squared terms. The model (Table 5) has an even higher explanatory power than the linear model involving all parameters. To understand the effects even better, the most important interactions were plotted (Shown in Figure 4 to Figure 6). Modal error by medSpeedWalkEnd and ninetyFiveAccLowEnd
ninetyFiveAccLowEnd
28'700
.58 .6 .63 .58 .6 .63 .58 .6 .63 .58 .6 .63
28'600
Mean ModeError
Figure 4
28'500
28'400
28'300 1.88
2
2.13
medSpeedWalkEnd
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Table 5
Regression model of the high impact parameters Unstandard Standard- t ized ized Coefficient Coefficient (B) (Beta)
Parameter
1
(Constant)
78253
2
medSpeedVeryLowEnd*medSpeedMediumStart
38654
2.516
1.177
3
medSpeedVeryLowEnd*ninetyFiveAccLowEnd
-150E+06
-1.1230
-0.000
4
medSpeedVeryLowEnd*ninetyFiveAccMediumStart
-67607
-4.429
-0.266
5
medSpeedVeryLowEnd*ninetyFiveSpeedMediumEnd
17250
3.843
1.931
6
medSpeedMediumStar*ninetyFiveAccLowEnd
-14100
-0.205
-0.108
7
ninetyFiveAccLowEnd*ninetyFiveAccMediumStart
4.10E+07
6.005
3.156
8
ninetyFiveAccLowEnd*ninetyFiveSpeedMediumEnd
1144
.054
.026
9
ninetyFiveAccLowEnd*ninetyFiveSpeedMediumEnd
59018
2.573
1.143
10 medSpeedVeryLowEnd2
144269
6.224
2.322
11 ninetyFiveAccLowEnd2
6.53E+07
14.753
40.676
12 ninetyFiveAccMediumStart 2
-1.9E+08
-3.590
-1.310
1304
2.601
.851
14 MedSpeedveryLowEnd
-9440
-10.18
-2.386
15 MedSpeedMediumStart
-655
16 NinetyFiveAccLowEnd
-91850
-17.12
-4.314
17 ninetyFiveAccMediumStart
-13124
-2.446
-0.626
-1093
-6.053
-1.601
13 ninetyFiveSpeedMediumEnd2
18 ninetyFiveSpeedMedium R2 = 0.914; adj. R2 = 0.882; N = 64
13
5.524
-1.209 -0.6401
Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
Figure 5
Modal error by ninetyFiveAccMediumStart and medSpeedWalkEnd
ninetyFiveAcc MediumStart
28'700
.48 .5 .53
Mean ModeError
28'600
28'500
28'400
28'300 1.88
2
2.13
medSpeedWalkEnd
Improving the regression model requires the high impact parameter levels to be varied(Table 6). New levels are assigned by observing the graphs, predicting the variation of modal error with change in their values. Table 6 Revised parameter values Parameter
Speed in m/sec and Acceleration in m/sec2 New values Low
High
Medium
1
MedSpeedveryLowEnd
1.76
1.88
2
2
MedSpeedMediumStart (not varied)
3
NinetyFiveAccLowEnd
.50
.55
.60
4
ninetyFiveAccMediumStart
.40
.45
.50
5
ninetyFiveSpeedMedium
16.5
17.25
18
5.25
14
Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Figure 6
Modal error by ninetyFiveAccLowEnd and ninetyFiveSpeedMediumEnd.
ninetyFiveAccLow End
28'700
.58 .6 .63
Mean ModeError
28'600
28'500
28'400
28'300 17.25
18
18.75
ninetyFiveSpeedMediumEnd
The revised parameter results were added while keeping the remaining values constant. The experiment for the revised values involved nine experiments. Their results were added to 64 existing one. The regression analysis was repeated. The results are shown in Table 5. The model has even higher explanatory power. The set of values with the minimal modal error can now be determined employing the regression function. Using the Solver (numeric optimiser) available in MS-Excel the parameter set shown in Table 7 predicts the following minimal modal error. Using this set in the post-processing algorithm results in a measured error of 2864. The shape of the fuzzy variables is shown and compared with their previous shape in Figure 7 to Figure 9. As before the slopes of variables were kept constant.
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
Table 7
Regression model of the revised high impact parameters Standard- t ized Coefficie nt (Beta)
Parameter
Unstandardized Coefficient (B)
1
(Constant)
70855
2
medSpeedVeryLowEnd*medSpeedMediumStart
45935
2.699
1.388
3
medSpeedVeryLowEnd*ninetyFiveAccLowEnd
-68368
-.593
-.370
4
medSpeedVeryLowEnd*ninetyFiveAccMediumStart
70284
.553
.256
5
medSpeedVeryLowEnd*ninetyFiveSpeedMediumEnd
-1011
-.229
-.117
6
medSpeedMediumStar*ninetyFiveAccLowEnd
28117
.421
.229
7
medSpeedMediumStar*ninetyFiveAccMediumStart
-1.645E5
-2.347
-2.070
8
medSpeedMediumStar*ninetyFiveSpeedMediumEnd
15502
6.029
2.865
9
ninetyFiveAccLowEnd*ninetyFiveAccMediumStart
1.547E6
3.662
2.152
10 ninetyFiveAccLowEnd*ninetyFiveSpeedMediumEnd
22459
1.456
.736
11 ninetyFiveAccLowEnd*ninetyFiveSpeedMediumEnd
-2205624
-.134
-.079
12 medSpeedVeryLowEnd2
116173
4.743
2.51
13 medSpeedMediumStart 2
19696
3.509
1.23
14 ninetyFiveAccLowEnd2
2.595E6
8.038
5.5
-57200
-.146
-.145
1871
3.816
1.432
18 MedSpeedveryLowEnd
-6645
-6.841
-2.203
19 MedSpeedMediumStart
-4953
-8.803
-2.609
20 NinetyFiveAccLowEnd
-38819
-10.444
-3.630
21 ninetyFiveSpeedMedium
-1532
-8.763
-2.617
15 ninetyFiveAccMediumStart 2 16 ninetyFiveSpeedMediumEnd2
R2 = 0.927; adj. R2 = 0.901; N = 73
16
7.692
Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Figure 7
Median of the Speed: Before and after
Origina
Optimized
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
Figure 8
95th percentile of the Acceleration: Before and after
Original
Optimized
18
Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
Figure 9
95th percentile of the speed: Before and after
Original
Optimized
5. Sequential alignment approach for measuring the quality of the post-processing procedure A more complete approach to the problem of measuring the quality of the output of post-processing of GPS data would be to compare the mode chain with the interview data. This can be done by Sequential Alignment. Method (SAM) (Reference). SAM is one of the various sequence comparison methods, originally introduced in disciplines such as molecular biology, chromatography and speech recognition. The principal idea behind this method is that the smallest number of changes required to equalize the sequential order of letters
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Optimal parameter values for mode detection GPS post-processing: An experiment ________________ July 2008
between two strings is a assumed to be an indicator of the true dissimilarity. The mode chain reported in the interview by the participant is a target sequence and the mode chain generated by the post processing of GPS data is the source sequence. The number of changes required to change the source sequence to the target sequence can be used as a measure of the quality of the output. The sequential alignment approach has been already used in transportation research in the past especially for measuring the activity travel pattern (References) Here it was tried to extend an already existing sequential alignment algorithm to calculate the sequential distance between the source and the target sequences consisting of mode chains from the result of GPS postprocessing output and the interview data respectively. But later it was realized that the existing algorithm is not capable to handle large number of sequences. This stopped the further progress in this direction.
6. Conclusion and further work Inspection of number of mode mismatches at the start of a stage shows incongruity in results of post-processing of GPS raw data. It can be observed that the modes detected as “walk” cause more than half of the modal error. Almost all the stages in which the participants reported their mode of travel as “rail”, are detected as “walk” or “car”. These errors may be in some cases due to the slight time-shift in the results from the post-processing of GPS data and the interview data. The optimized parameter values show a slight reduction in these errors. The approach followed here for measuring the quality of the output of the post-processing of GPS raw data, does not provide a complete picture. A more complete approach would be to analyze the mode chains from both the data in entirety. This can be done by sequence alignment as explained earlier. It was tried to utilize the available one-dimensional sequence alignment algorithm for this purpose but it did not produce any results due to its inability to process large sequences. But recently, an advanced multi-dimensional sequence alignment program called ClustalTXY (Clarke Wilson, Canada Mortgage and Housing Corporation) which could be used for the alignment of the mode chains. This program is a rewrite of Clustal series of sequence alignment packages which provides an integrated environment for reading sequence files, performing pair wise, multiple sequence and profile alignments and analyzing the results.
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Optimal parameter values for mode detection in GPS post-processing: An experiment ______________ July 2008
7. References Box, G.E. P, W.G. Hunter and J.S. Hunter (1978) Statistics for Experimenters, John Wiley and Sons, New York. Flamm, M. and V. Kaufmann (2007) Combining person GPS tracking and prompted recall interviews for a comprehensive investigation of travel behaviour adaptation process during life course transitions, paper presented at the 11th World Conference on Transport Research, Berkeley, June 2007 Joh, C.-H., T.A. Arentze and H.J.P. Timmermans (2001) Pattern recognition in complex activity-travel patterns: A comparison of Euclidean distance, signal processing theoretical, and multidimensional sequence alignment methods, Transportation Research Record, 1752, 16-22. Sazonov, E.S., P. Klinkhachorn, H.V. Gangarao and U.B. Halabe (2002) Fuzzy logic expert system for automated damage detection from changes in strain energy mode shapes, Nondestructive Testing and Evaluation, 18 (1) 1–17. Schüssler, N. and K.W. Axhausen (2008) Identifying trips and activities and their characteristics from GPS raw data without further information, paper presented at the 8th International Conference on Survey Methods in Transport, Annecy, May 2008. Wilson, C., A. Harvey and J. Thompson (2005) ClustalG: Software for analysis of activities and sequential events presented in workshop on sequence alignment methods, Research Development Initiatives Program, Social Science and Humanities Research Council of Canada, Halifax, October 2005.
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