Handling Location Imprecision in Moving Object Database

Xinfa Hu

March 2007

Moving Objects nd Database

Database Server

Moving Object

Location Update

Location Update

Is Exact Location Recording Possible?

1. Exact location requires that the location information is updated with high frequency.

Heavy load of index maintenance.

Large communication bandwidth requirement.

Lot of energy is consumed.

Is Exact Location Recording Possible (Cont.)?

2. Inaccuracy due to the limitation of measurement technology

Inaccuracy of measurement of the position

Inaccuracy of measurement of speed and direction.

Is Exact Location Recording Possible (Cont.)?

3. Linear function (of time) characterize movements.

x(t) = x(tref) + vx (t- tref) (along the X dimension)

Lead to inaccuracy if the movement is non-linear.

tref t1 t2 t

v x

?

How to Handle the Imprecision Problem?

Approach-1: Approximation technique.

Approach-2: Incoporating uncertainty into index or query.

Approximation Technique

Consider the movement ( in a n-dimensional space) of a moving object O

At time ti : its location is at Pi =‹ pi,1, pi,2, …, pi,n›

At time ti+1 : its location is at Pi+1 =‹ pi+1,1, pi+1,2, …, pi+1,n›

The progress made by O between time ti and ti+1 is:

δi = ‹ δi, 1, δi, 2, …, δi, n › = Pi+1 – Pi

How to get δi at time ti (without knowing Pi+1 )?

Approximation techniques are used to estimate δi

Approximation Technique (cont.)

1. Mean scheme:

The mean scheme attempts to estimate the δi, k (the kth dimension of δi) by averaging the previous i-1 steps. According to this idea, the estimated value of δi, k can be obtained as follows.

δ'i, k = ( ∑δj,k ) ×

i-1

j=1

1—i-1

Approximation Technique (cont.)

2. Window scheme:

Similar to the mean scheme, but only the most recent W previous steps are used to estimate the δi, k . According to this idea, the estimated value of δi, k can be obtained as follows.

δ'i, k = ( ∑δj,k ) × i-1

j=i-W

1—W

Approximation Technique (cont.)

3. EWMA( Exponentially weighted moving average) scheme:

similar to the mean scheme, but assign every previous step

with a weight so as to adapt quickly to the movement changes.

steps: δ1 , k , …, δi-2 , k , δi-1 , k

weights:αi-1 , …, α , 1(α0)

the estimated value of δ i, k can be obtained as follows.

δ'i, k =∑(α(i-1-j) × δj,k ) ×

i-1

j=1

1——∑ (αi-1-j)i-1 j=1

Approximation Technique (cont.) Safe Region:

A safe-region S is defined as a (Minimum Bounding Box) MBB covering both the current and the POSSIBLE next location.

How to compute safe-region?With the estimated

δ'i =‹ δ'i, 1, δ'i, 2, …, δ'i, n ›The kth dimension of safe region S is computed as follows:

[ min(pi,k +δ'i,k , pi,k), max(pi,k + δ'i,k , pi,k )]

Approximation Technique (cont.)1.The safe-region rather than the exact location is recorded in the database.

2. A moving object needs to update its location ONLY when it moves out its safe-region.

3. With the safe-regions in hand, the index can be implemented by a Modified R-Tree structure.

Approximation Technique (cont.)

Modified R-Tree Structure

…

Object record #1

Root

Node

Node

…

Leaf

Leaf

Object record #2

…

Object record #k

…

Object record #i

Object record #i+1

…

Object record #N-1

Object record #N

Leaf

Leaf

…

Object Records R-Tree Index

Approximation Technique (cont.)Location Update:

step-1. Find the object record.step-2. Locate the corresponding leaf node.step-3. Update the location: 2 cases may happen.

case-1: if the new safe-region is still covered by the leaf MBB, then update the safe-region entry in the leaf node, and finish.

case-2: otherwise, delete/insert operation areconducted at the closest ancestor whose MBB

can entirely cover the new safe-region, and the new safe-region is accommodated at a appropriate leaf node.

Approximation Technique (cont.)

Query:

►Traversal starts from the root of the Modified R-Tree index tree.

►If the query boundary intersects with the MBB of a node, then the child nodes are traversed .

►This process is repeated until the leaf node is reached and the required object record (s) is located.

Incorporating Uncertainty into Index or Query

Uncertainties:

1. Inaccuracy of measurement of position

2. Inaccuracy of measurement of speed and direction

3. Inaccuracy incurred by linear function

x

tupd t

∆v

Incorporating Uncertainty into Index or Query(cont.)

Total uncertainty and uncertainty region

Upper bound

Lower bound

x

tupd t

Incorporating Uncertainty into Index or Query (cont.)

TPR-tree (Time Parameterized R-tree). (Consider one-spatial dimension)

In leaf node: a tuple (id, x(tref),vx) identify a moving object . id is the identifier of the object; x(tref) is the position at tref ; vx is the velocity.

The position of a moving object is modeled as a linear function of time: x(t) = x(tref) + vx (t- tref)

In non-leaf node: An entry contains a bounding rectangle (interval) and a pointer that points to child node. All entries in the child node is bounded by the bounding rectangle.

A bounding rectangle/interval is described by: (x├, x ┤, vx├, vx

┤), where x├ and x ┤ are the lower and the upper bounds of the interval at tref, and vx

├ and vx┤ are

the lower and the upper bounds of the velocities at that time.

Incorporating Uncertainty into Index or Query (cont.)

Incorporate uncertainty into index

To incorporate uncertainty information into the index, we use the Modified TPR-tree, where the uncertainty regions rather than the linear trajectories is contained in the leaf node. The uncertainty region is computed as follows:

x├ (t) = x(tupd) + (vx - ∆u) (t- tupd) - ∆s

x ┤(t) = x(tupd) + (vx + ∆u) (t- tupd) + ∆s

x(tupd), vx, ∆s, ∆u = ∆v+ ∆v, and tupd need to be recorded in the modified TPR-tree.

Incorporating Uncertainty into Index or Query (cont.)

Incorporate uncertainty into query by expanding query region

compute the expansion:expan(t) = max {∆si} + max {∆ui} × (t- told)

max {∆si}: is the max ∆s among all objects.max {∆ui} : is the max ∆u among all objects.told is the update time of the object that has not been updated for th

e longest time.

Expand bounds of the query region along each dimension by an equal distance: expan(t) .

Summary

• Exact location recording is impossible in real world.

• 2 approaches are introduced to handle the imprecision problem in moving object database.

• Approximation technique predict the movement of moving object. Can greatly reduce the overload of index maintenance. The precision of prediction depends on the precision of the safe-region (depends on approximation technique).

• Uncertainties can be incorporated into index structure or query.

References

1. Ken C.K. Lee, Hong Va Leong and Antonio Si, “Approximating Object Location for Moving Object Database,” Proc. Of the 23th International Conference on Distributed Computing Systems Workshops, 2003.

2. Jens Henrik Hosbond, Simonas Šaltenis and Rasmus Ørtoft, “Indexing Uncertainty of Continuously Moving Objects,” Proc. Of the 14th International Workshop on Database and Expert Systems Applications, 2003

3. A Guttman, “R-trees a dynamic mdex structure for spatial searching,” Proc. Of the ACM International Conference on Management of Data (SIGMOD), 1984.

Thank You!