Moving Object Modelling Approach for Lowering Uncertainty in Location Tracking Systems
ABSTRACT This paper introduces the concept of Moving Object (MO) modelling as a means of managing the uncertainty in the location tracking of human moving objects travelling on a network.
For previous movements of the MOs, the uncertainty stems from the discrete nature of location tracking systems, where gaps
are created among the location reports. Future locations of MOs are, by definition, uncertain. The objective is to maximize
the estimation accuracy while minimizing the operating costs.
KeywordsMoving object modelling–Managing uncertainty–Location tracking Systems
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ABSTRACT: Publisher’s description: A thorough introduction to the formal foundations and practical applications of Bayesian networks is given, and an extensive discussion of techniques for building Bayesian networks that model real-world situations, including techniques for synthesizing models from design, learning models from data, and debugging models using sensitivity analysis, is provided. Exact and approximate inference algorithms at both theoretical and practical levels are treated. The treatment of the exact algorithms covers the main inference paradigms based on elimination and conditioning and includes advanced methods for compiling Bayesian networks, time-space tradeoffs and exploiting local structure of massively connected networks. The treatment of the approximate algorithms covers the main inference paradigms based on sampling and optimization and includes influential algorithms such as importance sampling, MCMC and belief propagation. The author assumes very little background on the covered subjects, supplying in-depth discussions for theoretically inclined readers and enough practical details to provide an algorithmic cookbook for system developers.01/2009; Cambridge University Press., ISBN: 978-0-521-88438-9
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ABSTRACT: Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns into a computational architecture if the links are used not merely for storing factual knowledge but also for directing and activating the data flow in the computations which manipulate this knowledge.The first part of the paper deals with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. tree-structured), then probabilities can be updated by local propagation in an isomorphic network of parallel and autonomous processors and that the impact of new information can be imparted to all propositions in time proportional to the longest path in the network.The second part of the paper deals with the problem of finding a tree-structured representation for a collection of probabilistically coupled propositions using auxiliary (dummy) variables, colloquially called “hidden causes.” It is shown that if such a tree-structured representation exists, then it is possible to uniquely uncover the topology of the tree by observing pairwise dependencies among the available propositions (i.e., the leaves of the tree). The entire tree structure, including the strengths of all internal relationships, can be reconstructed in time proportional to n log n, where n is the number of leaves.Artificial Intelligence 09/1986; · 2.19 Impact Factor
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ABSTRACT: In this paper we propose a data model for representing moving objects with uncertain positions in database systems. It is called the Moving Objects Spatio-Temporal (MOST) data model. We also propose Future Temporal Logic (FTL) as the query language for the MOST model, and devise an algorithm for processing FTL queries in MOST. 1 Introduction Existing database management systems (DBMS's) are not well equipped to handle continuously changing data, such as the position of moving objects. The reason for this is that in databases, data is assumed to be constant unless it is explicitly modified. For example, if the salary field is 30K, then this salary is assumed to hold (i.e. 30K is returned in response to queries) until explicitly updated. Thus, in order to represent moving objects (e.g. cars) in a database, and answer queries about their position (e.g., How far is the car with license plate RWW860 from the nearest hospital?) the car's position has to be continuously updated. This is unsa...11/1997;
Moving Object Modelling Approach
for Lowering Uncertainty
in Location Tracking Systems
Wegdan Abdelsalam1, David Chiu1, Siu-Cheung Chau2,
Yasser Ebrahim2, and Maher Ahmed2
1School of Computer Science, University of Guelph
2Physics & Computer Science Department, Wilfrid Laurier University
Abstract. This paper introduces the concept of Moving Object (MO)
modelling as a means of managing the uncertainty in the location track-
ing of human moving objects travelling on a network. For previous move-
ments of the MOs, the uncertainty stems from the discrete nature of
location tracking systems, where gaps are created among the location
reports. Future locations of MOs are, by definition, uncertain. The ob-
jective is to maximize the estimation accuracy while minimizing the op-
Keywords: Moving object modelling, Managing uncertainty, Location
Location Tracking Systems (LTSs) are built to answer queries about the where-
abouts of moving objects in the past, present, or future. To answer such queries,
each moving object, monitored by the system, must report its location peri-
odically using a sensing device such as Global Positioning System(GPS) . The
location reports are then saved to a database where they are indexed to facilitate
answering user queries.
In spite of the continuous nature of the MO’s movement data, location data
can only be acquired in a discrete time. This leaves the location of the MO
unknown for the periods of time between the location reports. It is economically
infeasible to capture and store a continuous stream of the location data for
each MO. Rcording location reports discretly introduces uncertainty about the
location of MOs between reports.
Lowering uncertainty has been addressed by a number of researchers over the
past few years [1–4]. These approaches try to find a link between the amount of
uncertainty and the frequency of location reporting. By increasing the reporting
frequency, the uncertainty can be kept within acceptable bounds. We believe
that there is a need for a new approach for lowering the uncertainty without
increasing the reporting frequency. This new approach must be integrated with
the system database in a way that facilitates the efficient execution of the user
C. Butz and P. Lingras (Eds.): Canadian AI 2011, LNAI 6657, pp. 26–31, 2011.
c ? Springer-Verlag Berlin Heidelberg 2011
MO Modelling Approach for Lowering Uncertainty in LTSs 27
We propose a MO modelling approach for lowering the uncertainty about
MO locations in a LTS. MO modelling includes collecting information about the
environment (i.e., the context) under which MOs operate. The MO model is used
to reach a more accurate estimate of the MO location. This is done by estimating
the location calculation parameters (e.g., speed and route) in terms of the MO’s
historical data, collected for these parameters under similar circumstances.
2 Moving Object Modelling
The goal is to equip location-tracking systems with an MO model for each of
the MOs being tracked. The model encompasses the MO’s characteristics, pref-
erences, and habits. The location-tracking application utilizes the information
about the MO to more accurately estimate his/her position.
Because the location of an MO is determined primarily by the chosen route
and the travelling speed, the MO is modelled in respect to these two variables.
2.1 MO Speed Model
Our proposed approach adopts a Bayesian Network (BN) to build the MO speed
model. Figure 1 depicts a BN for the suggested MO speed model. As shown in
the figure the BN structure is a single contacted DAG, most often refereed as
The child-node Speed is influenced by three parent nodes: the driving condi-
tion (DC), level of service (LoS), and road speed limit (SL). In turn, the driving
condition is affected by two parent nodes weather condition (WC) and road type
(RT). The LoS is affected by three parent node: day-of-week (DW), time-of-day
(TD), and area of city (A).
To build the model, the first step is to determine the possible states for each
variable (i.e., node) in the Bayesian Network. It is possible to either intuitively
Fig.1. Example BN for the MO speed model
28W. Abdelsalam et al.
choose the values or elicit them from the domain expert. For example, the speed
variable can have the finite discrete values 0,1,2,3,...,199,200k/hr representing
all the possible MO speeds (assuming no decimals values). For the road type, a
Geographic Information System (GIS) is consulted for the possible road types
in the city.
The next step is to initialize the CPT with the probability of each state of the
node, given the possible states of its parents. In a polytree the size of the CPT
of each variable is determined by the possible states of its parent(s). Each entry
(i.e. probability value) in the CPT corresponds to a combination of the parent
node’s states, combined with one of the evidence.
The state of the Speed variable is inferred according to the evidence of the
root variables. The evidence is propagated (using Pear’s BP algorithm) down the
network. The resulting probablity table is then queried for the most probable
speed (i.e., the highest probability).
2.2 MO Trip Route Model
In principle, a trip route is determined by the trip source and destination. Dif-
ferent MOs can take different routes, based on their preferences. For example,
some MOs prefer to take the shortest route, while others may prefer the fastest
For each trip (i.e., source/destination duo) for each MO, a directed graph is
built to represent the route such that a node represents a road segment, and an
edge represents a connection between two road segments. Each edge is given a
weight representing the probability the MO to achieve the transition from the
parent node to the child node. The edge weight is based on the frequency the
transition is made in relation to the total transitions from the parent node. Each
edge is associated with a counter that is incremented each time the transition is
The graph is built, based on the received location reports. If the reported
road segment is on the graph, the transition frequency counter is incremented.
If not, a new node is added to the graph, and its frequency number is initialized
to 1. The graph nodes represent all the road segments ever visited, while on any
instance of this trip. The most probable route is the shortest maximal weight
path from the source node to the destination node. From the most probable
route and the most probable speed on each road segment along this route, the
system creates the estimated MO trajectory for the trip. Figure 2 signifies the
model for the trip from source 1 to destination 13.
2.3 Estimated Trajectory Updating
Sometimes the estimated trajectory of the MO needs to be updated, based on
the actual location reports received. A certain degree of deviation is detected
between the estimated trajectory (based on the MO model) and the actual lo-
cation reports. This deviation can occur because the MO is either following
the estimated route but at a different speed than expected (called a schedule
MO Modelling Approach for Lowering Uncertainty in LTSs 29
deviation), or because the MO takes a different route from the estimated one,
(called a route deviation). With either type of deviation, with continual use,
the estimated trajectory for answering future queries might produce incorrect
When an MO is detected to be off-schedule, the remainder of the estimated
trajectory can be adjusted in one of two ways: If the MO is behind schedule, the
remaining trajectory is shifted forward one reporting interval to reflect that the
trip can take longer than expected. If the MO is ahead of schedule, the remaining
trajectory is shifted backward one or more reporting interval(s) to reflect that
the trip can finish sooner than expected.
When a route deviation is detected, the trip route model is checked to see
if there are alternate routes that have been taken by the MO in the past. By
comparing the road segments travelled so far (as suggested by the actual location
reports received) to the road segment sequences in the trip model, it may be
possible to find a match that suggests the route the MO is actually taking.
Fig.2. Trip model
3 Experimental Results
To experimentally validate the efficiency of using the MO modelling approach
in the location estimation, query results of three different techniques to esti-
mate the MO’s speed are compared. The three speed estimation methods that
are examined are the last-reported-speed, the average-reported-speed, and the
MO-model-based, most-probable-speed. The estimated speed is applied in the
following formula to estimate the location of the MO (assuming the MO is mov-
ing in a straight line):
Location = last reported location + (estimated speed * time elapsed since
Three route estimation methods are selected. The straight-line method as-
sumes that the MO continues to move along the same line made by the last two
location reports. The trip-route-model method estimates the trip route at the
beginning of the trip, and the trajectory is created, according to the estimated
30W. Abdelsalam et al.
speeds along route. The route-model-with-shifting method employs off-schedule
trajectory updating, as described in Section 2.3. Each MO is randomly assigned
a preference of either taking the shortest or the fastest route.
Reporting intervals, between 0.25 and 3 minutes with 0.25 minute intervals,
are tested. Each experiment is performed five times and the average deviation
per location report (in metres) is obtained.
0.25 0.50.7511.25 1.5 1.7522.25 2.52.753
Average Deviation in m
Reporting Interval in Minutes
Model with Shift
0.25 0.50.7511.251.5 1.75184.108.40.2063
Average Deviation in m
Reporting Interval in Minutes
Model with Shift
Fig.3. (a)Average error at different reporting intervals using straight-line-with-last-
reported-speed, model speed, and model speed with shifting with a 0% probability
of a route deviation. (b)Average error at different reporting intervals using straight-
line-with-last-reported-speed, model speed, and model speed with shifting with a 10%
probability of a 10% route deviation.
From Figure 3, a number of observations can be made. The two model-based
location estimation methods is considerably better than the straight-line-with-
last-reported-speed method for reporting intervals more than 30 seconds. The
straight-line-with-last-reported-speed method deviation grows linearly, as the re-
porting interval grows. On the other hand, both model-based methods deviation
actually improves as the reporting interval grows. This is due to the fact that
higher reporting intervals allow for deviations between the reported and esti-
mated speeds (i.e., estimated speed being above/below the reported speed) to
cancel each other out. The model-with-shifting tends to perform better than
the model alone for shorter reporting intervals. The two converge at a reporting
interval of about 1.5 to 1.75 minutes. This reveals that the proposed shifting
approach does improve accuracy, as the estimated trajectories are adjusted to
reflect received location reports. This effect diminishes as the reporting interval
grows which means that fewer such shifts are performed.
The use of the user movement modelling in location-tracking applications is pre-
sented and the idea of MO modelling is introduced for reducing the uncertainty