Estimation and Tracking of Excavated Material inMining

Christopher InnesAustralian Center for Field Robotics

University of SydneySydney, Australia

Email: c.innes@acfr.usyd.edu.au

Eric NettletonAustralian Center for Field Robotics

University of SydneySydney, Australia

Email: e.nettleton@acfr.usyd.edu.au

Arman MelkumyanAustralian Center for Field Robotics

University of SydneySydney, Australia

Email: a.melkumyan@acfr.usyd.edu.au

Abstract—This paper provides a method for representing,tracking and fusing information on excavated material as it movesthrough a mining process chain. A constrained augmented stateKalman filter (based on simultaneous localization and mappingprinciples) is used as the basis for this process. A methodfor representing the material properties stochastically based onthe unique location of the lumped material is also developed.Through the application of this method, correlations betweenmaterial at different locations can be maintained. This methodis validated through real world experiments simulating an openpit mine excavation.Keywords: Tracking, Data association, Kalman filtering,Estimation.

I. INTRODUCTION

The ability to accurately track bulk material propertiesthrough a production chain in industries such as mining,agriculture, civil engineering and many more is highly valu-able. In the mining industry, having incorrect estimates ofore grade and quantity in shipping stockpiles can lead tofinancial penalties for the mine [1]. Improving the qualityof information by tracking material through the productionprocess would enable mine engineers to have a more accurateinventory of their product, and provide information enablinggreater planning to avoid these penalties.

The motivating application for this research is to trackexcavated material in an open pit iron ore mine. A typicalexample of the process in this application would begin with aparticular block of material being tasked for excavation. Thereis likely to be some prior information about the material (ore)quality at the level of the block. The ore tracking systemwould maintain an estimate of the material until its destinationpoint. For the work in this paper, the destination is consideredto be a stockpile. One of the primary aims of this researchis to facilitate operation of a fully autonomous mine, wherematerial estimates will be an input into planning and controlof equipment.

Currently, most mine sites have large decentralized sensornetworks deployed that can be used for tracking excavatedmaterial (Figure 1). Common sensors include load cells on ex-cavator buckets, bucket volume fill level estimators, haul trucksuspension strut pressures, plant assay sensors, truck volumescanners and GPS vehicle tracking to name a few. However,there is currently no method for fusing information from these

sensors into a common system to track the excavated material.Existing methods (discussed in Section II) typically use eachpiece of data in isolation.

This paper develops a probabilistic end-to-end method fortracking excavated material in a mine site using a heteroge-neous network of distributed sensors. The system developsthe concept of a discrete set of ‘lumped masses’ of materialat different stages through the mining production process. Forexample, material in an excavator bucket is considered as a‘lumped mass’ as it is excavated. Multiple ‘lumped masses’from an excavator are then fused into a new ‘lumped mass’ ina haul truck as it is loaded. This process continues throughoutthe production chain, and provides an estimate of the locationand amount of material at all times post excavation.

The ore tracking system is formulated with a dynamic statevector to enable new ‘lumped masses’ to be created and re-moved. An augmented state Kalman filter [2] is used to achievethis. This representation supports probabilistic information ina consistent, compact and scalable manner. It also ensures theinformation is represented in a common form at all stages ofthe process.

The augmented state filter explicitly maintains the correla-tions between the ‘lumped masses’ at different stages in theprocess. These then provide a mechanism to reconcile theexcavated material back to the original in-ground estimates.Reconciliation in the mining industry is the process of com-paring the actual quality and amount of material mined from adesignated area with the expected output of that area from theprior model. It is useful as a tool to validate geological modelsand mine plans. Reconciliation is typically performed onmonthly (or longer) schedules which reduces the usefulness ofthe data for planning. A real-time reconciliation of quantitativeproperties is possible using the framework discussed in thispaper.

This paper is organized as follows. Section II will outline thecurrent approaches to material tracking on mine sites. It willalso cover possible methods for tracking, representation andperception of material. The ore tracking problem is then devel-oped in Section III. Section IV presents results of the systemdescribed in this paper on representative mining scenarios withreal-world data at two different scales. Section V discusses theresults and conclusions are presented in Section VI.

14th International Conference on Information FusionChicago, Illinois, USA, July 5-8, 2011

978-0-9824438-3-5 ©2011 ISIF 1631

Figure 1. Sensor network at an iron ore mine in the Pilbara region, Western Australia.

II. RELATED WORK

Research in the field of integrated real-time material track-ing in mining is very limited. The state of the art is representedby commercial products from companies such as QMASTOR[3] and Snowden [4]–[6] which provide basic deterministicestimates at different locations in the system. The Dispatchsystem from Modular Mining [7] also provides a limited de-gree of ore tracking during the haul cycle. It has database fieldsfor a material type, which is recorded with the vehicle GPSposition. However, the material properties are not estimatedonline. The current practice in mining is assume all truckscarry a common constant percentage of their maximum load.This value, termed a ‘load factor’, is essentially the averagemass of material moved by trucks calculated over a long timeline. The method, although accurate over large time frames,does not represent the actual material movements in a haultruck on a haul by haul basis. At this shorter time frame, loadsare prone to fluctuations based on operator skill through over/ under filling of trucks and excavation of material outside ofthe designated mining area. It also relies upon the quality ofinitial in ground estimates of the material being excavated.

Substantially more work has been carried out on methodsfor modeling specific stages in the mining process. Robinson[8], for example, looks at the variance on different blendedstockpile configurations. Giacaman et al. [9] describe a fore-cast modeling system for the loading and transportation ofmaterial to a stockpile, this is used to predict the effect ofchanged equipment carrying capacity. Sensogut and Ozdeniz[10] describe a statistical study of a stockpile, using finite

element analysis to predict the behavior of a stockpile.

The techniques for ore tracking used in this work are moreclosely related to target tracking and autonomous vehiclelocalization. In particular, the augmented state estimationmethod developed here can be likened to the SimultaneousLocalization and Mapping (SLAM) problem widely usedin robotics [11]. However, instead of dynamically changingthe state vector to add features to a map, we dynamicallychange the state vector to add or remove lumped massesof excavated material. The augmented state representation isalso used to constrain estimates to preserve mass through thesystem. Constrained Kalman filters have been developed toensure that physical real world constraints are incorporatedinto a Kalman filter framework. An example of this in Simonand Chia’s paper [12], which describes a method for stateequality constraints. Rao et al. [13] show a method for horizonconstrained filtering which can be used to solve nonlinearconstraints.

Utilizing visual sensors to estimate properties, such asvolume, in a mining environment is particularly challengingdue to the large amounts of dust present on site (Figure 2).Sensors such as a millimeter wave radar [14] would be usefulin this domain due to its ability to penetrate through dust.Being able to define a surface using a 3d point cloud is avital component when estimating volume. Some other systemscurrently used in observation of material at various stages inthe mining processes include autonomous estimation of haultruck contents (Mass, Volume) online. This has been testedlive in research by the CSIRO [15] and commercialized by

1632

Figure 2. Dust generated during an excavation process.

Transcale [16]. The use of hyper-spectral camera’s [17] hasalso been used to determine intrinsic material properties atdifferent stages of the mining process. Appropriate sensorobservation models for estimating material properties alsohas many similarities with the observation models used inclimate and weather prediction systems [18]. This type ofresearch will be essential in realizing a complete autonomoussystematic estimation system of excavated material which canbe implemented at a open pit mine site.

III. PROBLEM FORMULATION

A. Lumped Mass Model

The lumped mass model is a representation for discretizingthe excavated material into manageable components based ontheir physical location. This is done to reduce the complexityof the estimation problem into smaller manageable parts. Thelumped mass model implies that material is estimated basedon its physical separation from other lumps of material. Alumped mass representation can be written as:

P (Xn) (1)

Where:

Xn = [M,V, Fe, SiO2, Al2O3, Origin]T (2)

Xn is a vector of material properties to be estimated. Wheren = A represents the location identifier for each lump (e.g.Excavator Bucket, Haul Truck, Stockpile), M = Mass,V =Volume, Fe = Iron%, SiO2 = Silicon Dioxide%, Al2O3 =Aluminium Oxide%, Fragmentation = Ore FragmentationLevel, Origin = Co-ordinates of where original material waslocated in-situ. Although the intrinsic properties are includedhere for completeness, the work in this paper will focusspecifically on forming the problem with mass and volume.

A probabilistic estimate will exist for each of the listedmaterial properties defined in the vector Xn.

Mass is used as the measure in estimating other intrinsicmaterial properties when combining lumps of material. Thealternate selection would be to use the volume of materialpresent in lumps. Mass and volume represent the two qualities

of lumped material which can measure the quantity of thematerial present at any location. Typically however, massis a more readily measurable quantity compared to volume.The majority of volume estimation techniques on this scalemeasure bulk volume. Bulk volume is the volume of area thematerial occupies including the gap spaces between lumpedmaterial. Volume can be extrapolated from this by determina-tion of the bulk factor.

Bf =VbVt

(3)

Where Bf = Bulk Factor, Vb = Bulk Volume, Vt =Volume. Depending on the consistency of the material andthe configuration in the space which it is occupying, this canlead to variations on the bulk factor.

B. Data Fusion Engine

1) Representation: There exists many possible approachesto probabilistically maintaining the estimates of material atdifferent locations. For the purposes of this work, a Kalmanfilter framework was used due to its simplicity and compactrepresentation.

The standard linear Kalman filter equations are as follows:

Prediction Step:

xk+1 = Fxk +Buk +Gqk (4)

Pk+1 = FPkF′ +GQkG

′ (5)

Where, uk (linear control input) and qk (system noise) willbe assumed to be 0. F is known as the state-transition matrix,and describes how the states in vector xk will change aftera given process. Pk is the covariance matrix describing howthe different states relate to each other. Qk and G denoterespectively system noise and a projection matrix of that noiseonto estimated states.

Update Step:

vk+1 = zk+1 −Hxk+1 (6)

Sk+1 = HPH ′ +R (7)

Wk+1 = Pk+1H(Sk+1)−1 (8)

x+k+1 = x−k+1 +Wk+1v (9)

P+k+1 = P−k+1 −Wk+1Sk+1W

′k+1 (10)

Where, z is the State Observation Vector, H describes howobservation vector applies to state vector. R is the SensorNoise, v = Innovation (Error between observed states andcorresponding predicted states) S = Innovation Covariance andW = Kalman Weighting which describes how much weight

1633

to apply to the sensor observation compared to the originalestimate on affected states.

When choosing to model the amount of material at eachlocation a simple solution is to dedicate a Kalman filter foreach location. This choice would be beneficial in that all thefilters would have state vectors with a fixed size. However,the multiple instances of separate Kalman filters have a majordrawback in practice. The lumped material estimates arecorrelated to each other when they originate from the samegrade block. This correlation will be shown to be crucialin ensuring system mass consistency and reconciliation. Thiscorrelation is not inherently maintained in a multiple instanceKalman filter approach.

To maintain the correlations in the system, an AugmentedState Kalman Filter is used. The key difference from standardKalman filtering is that the system has a state vector whichis dynamic. The state vector expands and decreases as theamount of physically unique lumps of material in the systemevolves over time. Mathematically, this can be seen in Equa-tion 11.

Xs = [X1, X2, ..., Xj−1, Xj ]T (11)

Xs is a vector space with j vectors. The vector Xi ∈ Xs,where i = [1, 2, ..., j − 1, j], represents a physically uniquelumped mass. Xi can contain states such as those showed inEquation 2. Xs effectively therefore contains all states to bemeasured in the system. Given this information Xs can beseen as the equivalent to the state vector xk commonly givenin Kalman filtering literature.

Through specific constraints on the applied system models,a system is developed which consistently maintains the corre-lations between parent and child lumps (and their children) asmaterial moves through the process chain.

2) Initializing and Removing Lumped Mass States: Initial-izing and removing new lumped mass vectors (Xn) into thesystem is a straightforward task and follows very closely theequations for initializing a new landmark into a SLAM system.Equations 12 - 13 below explain the process of initializing anew state.

xk,Xn =

[xkXn

], Pk,Xn =

[Pk 00 σ2

Xn

](12)

x#k = Axk,Xn, P#

k = APk,XnAT +BQk,Xn

BT (13)

Where A and B are design matrices used to initialize thenew states correlations to previous states in the state vector andcovariance matrix. X#

k = the state vector post initializationof the new lumped mass. P#

k = the covariance matrix postinitialization.

Take a very simple example of a filter with one existinglumped mass. For this example the existing lumped mass is astockpile which an excavator will remove material from. Theonly property to estimate is mass (Xn = [ m ]). Assuming thatthe prediction model noise is incorporated during initialization,

the equations below describe the loading process and thedevelopment of the correlations between the two lumped massstates. Variables:

xk,Xn=

[mstockpile

mexcavator

](14)

A =

[1 −10 1

], B =

[1 −10 1

](15)

Qk,Xn=

[0 00 σ2

excavator

](16)

Result:

x#k =

[mstockpile −mexcavator

mexcavator

](17)

P#k =

[σ2stockpile + σ2

excavator −σ2excavator

−σ2excavator σ2

excavator

](18)

As seen from the results above the system behaves intu-itively. The mass in the stockpile is reduced by the mass inthe excavator. The significant result from this process is theoff-diagonal terms being equal in magnitude but opposite insign to the excavator mass state. This fact will be pivotal whenfusing new information about the excavator mass state at alater time.

Removing lumped mass states and their correlations whenthe lumped mass is removed from the system or combined withanother lumped mass is important to ensure the conservationof mass in the system is upheld. Practically it also reducesthe complexity in the system (reduced covariance matrixsize) enabling faster operation. Removing a lumped massis performed when a system process removes all lumpedmaterial from a unique location and it is combined withanother lump (or initialized into a new lump at a new location).Mathematically, this process involves removing the rows andcolumns associated with the lumped mass in the covariancematrix (Pk) and state matrix (xk).

3) Modeling Quantitative Lump Properties: Quantitativelump properties are those which define the amount of materialpresent at each lumped mass location. These are the propertiesof mass and volume. Previously an example initialization wasshown which involved modeling a quantitative lump propertyfrom a stockpile to an excavator. The modeling in that examplecan be generalized for any process with quantitative lumpproperties as, using the Kalman filter Equations 4 and 5.

Variables:

xk =

[ω1

ω2

], F =

[i jk l

](19)

Qk =

[σ21 00 σ2

2

](20)

Assume that Qk = 0.Result:

1634

Figure 3. Mass loss example during excavation.

xk+1 =

[iω1 + jω2

kω1 + lω2

](21)

Pk+1 =

[i2σ2

ω1+ j2σ2

ω2ljσ2

ω2+ ikσ2

ω1

ljσ2ω2

+ ikσ2ω1

l2σ2ω2

+ k2σ2ω1

](22)

In order to constrain the problem to ensure linearity incorrelations i and l must equal one. With this informationthe equation becomes:

xk+1 =

[ω1 + jω2

kω1 + ω2

](23)

Pk+1 =

[σ2ω1

+ j2σ2ω2

jσ2ω2

+ kσ2ω1

jσ2ω2

+ kσ2ω1

σ2ω2

+ k2σ2ω1

](24)

This results shows that in material transfer process cases(j, k = +1, 0,−1) the variance will linearly add to eachstate dependent on the process occurring. This is an importantresult when considering how to implement a mass loss modelconsistently.

4) Mass Loss Modeling: Modeling and observing the massloss in each process (e.g. Figure 3) of lumped mass system isof vital importance. It is required to ensure that the estimatesdo not become positively or negatively biased. Figure 3 is anexample of how in a mining system, the amount of materialestimated and observed in a bucket does not neatly transitionfully into the waiting haul truck. These system losses can bemodeled in the same way as initializing a new lump of materialinto the system shown in Equations 12 - 13.

In Figure 3 the mass loss lump would be initialized as a sub-traction from the estimate of material in the excavator bucket.This lump would then be transferred back to the original blockto where the material was mined and removed from. In mining,generally a dozer will push any loose material back into thearea of excavation. This following is the equivalent matrixoperation:

xk =

mstockpile

mexcavator

mexv.loss

, F =

1 0 10 1 −10 0 1

The loss state would then be removed from the system. Ide-

ally, the lost material would be observable, modeled accuratelyor a combination of the two. This would help prevent inaccu-rate loss models from inflating the variance on estimates.

5) Reconciliation and Conservation of Mass: In bulk ma-terial tracking it is important to ensure that material is not‘invented’. Take again the simple example case of modeling anexcavator loading material from a stockpile using two separateKalman filters. One filter for the stockpile and the other forthe excavator bucket. When fusing new information about thematerial in the excavator bucket, there is no automatic methodto update the material in the stockpile to reflect the correlationbetween the two lumped materials. The excavator bucket canbe carrying more or less material then what is estimated to beremoved from the original stockpile. Thus after fusing in newinformation there is a discrepancy of total mass in the systemfrom what is originally estimated.

This problem can be overcome using the augmented statefilter and general equations for mass transfer shown in Equa-tions 19 - 22. The correlations developed in the systemmodeling act as natural constraint of mass in the system,preventing the ‘invention’ or unexplained disappearance ofmaterial. This can be proved by looking at the co-variancedeveloped between a state and other states.

Take as an Example: Observing ω2 (From Equation 23).PkH

T is used in calculating the Kalman Gain, it is a columnvector containing the variance on the observed state and its co-variance to other states.

PkHT =

[jσ2

ω2+ kσ2

ω1

σ2ω2

+ k2σ2ω1

](25)

Given j and k is controlled to take one of the discrete values[−1, 0, 1], the relationships developed through the systemmodels will remain linear since k2 will always equate to 0 or1. It is under these circumstances that the conservation of massprinciple can be maintained. By extrapolating this to multiplestates which develop over time, it is possible to harness thisproperty for other uses such as probabilistic reconciliation.

One example implementation can be achieved by instead ofin the example shown in Equation 14 - 16 where material issubtracted from the original stockpile; the stockpile estimateis left unaltered. By adding a new special reconciliation stateinitialized with 0 mean and variance. Material removed canbe added to this state and conversely material added can besubtracted. This example process can be shown in Equation26.

xk+1 =

[mreconcile

mexcavator

], F =

[1 10 1

](26)

This will result in a state which in this example will trackthe net movement into and out of that designated stockpile.This could be applied to a mining grade block, and candetermine the amount of material removed. By taking a mockobservation of this state with estimated mean and 0 variance,the location and mean amount of material removed from theoriginal stockpile can be viewed in the vector PkH

T postobservation.

1635

Figure 4. Small scale experiment process overview.

IV. EXPERIMENTS

A. Small Scale

The small scale data set, or ‘toy scale’ data set was gener-ated by using equipment on a very small scale to simulate theout of ground mining processes. The small scale experimentsdata sets are performed with approximately 3L(0.003m3) ofmaterial in total. The advantage of using this small scale isthat measuring the properties of the material (volume, mass)at the different stages is significantly easier than when theexperiment is scaled up in size. The planning, personnel andtime required to run each experiment is also significantlyreduced in comparison. Small scale experiments also allowprecise measurements and control over processes, giving aground truth upon which to compare results with to ensurethe system is consistent.

The process and scale of the experiment can be seen inFigure 4. The mass was measured by digital kitchen scales(+−1g accuracy) and a measuring cylinder with 5ml gradients.Each excavator bucket and haul truck load were measured bythese two sensors. In order to simulate losses for the excavatorbucket, the assumption was made to return material which wasdid not arrive in the haul truck from the excavator bucket backto the grade block. Before doing this, the losses are measuredusing the aforementioned sensors. Losses generated over thehaul truck to final stockpile stage are measured for each truckand then stored in a separate container to simulate generallyunrecovered material over those states.

B. Large Scale

A larger scale experiment was designed to represent thesame processes which occur on a real mine site. The aim ofthis is to create a more realistic data set in regards to both theprocesses of moving the material in the given scenario as wellas the available information and its format. The process scopeis still limited to moving material from an original Stockpileto a ROM Stockpile (See Figure 4). The material used in thisexperiment is a uniform density beach sand blend to allow theassumption of constant density.

Figure 5. Larger scale experiment equipment and size example.

The equipment used to move the material included a frontend loader of approximately civil construction scale as wellas a 3T dump truck. These can be seen in Figure 5.

At each location (Grade Block, Excavator, Haul Truck,ROM Stockpile) a survey scan was performed. Volume wascalculated using the survey data to make observations on theexcavator bucket as well as to initialize the original stockpile.Mass data was gathered for the haul truck loads only. Thesurface scan data was acquired by using a ’Riegl SurveyingLaser’. The mass of the haul truck load was collected by usinga set of CAS RW-10P (10T Capacity) [19] truck scales.

V. DISCUSSION

A. Small Scale

The residual plots seen in Figures 7 and 8, show the con-sistency of the mass at the excavator and haul truck locations.Volume observations are used as inputs to the system atthese locations. Mass observations are used as the measure ofground truth given the accuracy of this sensor. The horizontalaxis on each graph represents the load number, the verticalaxis represents the residual value. Two standard deviationconfidence intervals are included. Table I gives a comparisonbetween the material estimated as haul truck losses and thematerial located in the destination ROM stockpile state withthe ground truth of those respective states. The result of addingthe mass estimated in the system at the end of the experimentcompared to the initial stockpile estimated mass shows howthe conservation of mass in the system holds (The values areequivalent). Figure 6 gives an example of how the reconcilingprinciple works in practice. It begins with a 2 state systemshowing one lump location of the initial stockpile. A predictionof material in the excavator bucket from this stockpile is thenmade. A sensor update showing more material in the bucket isthen performed. This update process on the excavator bucketcan be shown to reconcile the discrepancy from increased massin the bucket with the previous prediction of material removedfrom the initial stockpile.

Using this framework, a consistent probabilistic real-timeinventory of material at any location is possible. Material canalso be reconciled in real-time. In contrast, current systemsprovide deterministic estimates of material at limited locations

1636

Figure 6. Reconciliation using correlations system example from initialstockpile to excavator bucket.

Figure 7. Excavator bucket residual plot with 2SD boundaries for small scalemass / volume experiment.

(e.g. averaged haul loads). Reconciliation is done with a delayof possibly months.

B. Large Scale

Preliminary results from the large scale system experimentare positive. One of the main obstacles in verifying the systemis obtaining an accurate measure of ‘Ground Truth’ at certain

Figure 8. Haul truck residual plot with 2SD boundaries for small scale mass/ volume experiment.

Table ICOMPARISON OF SYSTEM ESTIMATES AND GROUND TRUTH IN SMALL

SCALE EXPERIMENT.

Init. StockpileEstimate Mean[g] 2σ Ground Truth[g]

Mass 13815 50 13815Material LeftIn Stockpile Mean[g] 2σ Ground Truth[g]

Mass 18.2 88 30Haul Truck

Losses Mean[g] 2σ Ground Truth[g]

Mass 1379.7 204 1351ROM Stockpile Mean[g] 2σ Ground Truth[g]

Mass 12417 222 12442

Figure 9. Haul truck consistency for large scale mass / volume experiment.

locations for different properties. It can be obtained for massat the haul truck location given the accuracy of the truckscales is very precise. Volume estimates for this location canbe obtained under the assumption of a constant known density.

The generally accepted value for density of sandvaries based on the conditions the sand is placed under(dry,wet,combined with other materials etc). These valuesrange from ≈ 1600kg (dry) - 1900kg (wet) [20]. The densityof the material used in the large scale experiment is calculatedto be 1674kg. Appropriate density calculated is critical whenmaking the assumption of constant density given that massand volume will be directly correlated through this value.

Figure 9 shows a residual plot at the haul truck locationfor mass. Each truckload (the horizontal axis) consists of 3buckets loads of material from the initial stockpile. The finaltruckload has only 2 bucket loads of material which is thereason for the reduction in variance on the final haul truckload. Each bucket load is initialized with a general expectedload (and variance) based on the carrying capacity of theexcavator bucket. A bucket volume sensor is used to estimationthe volume of material in each bucket load. This informationis fused with the initialized estimate. By assuming the constantdensity model, it is possible to test to see if the system remainsconsistent comparatively to the ground truth estimate at thehaul truck location. As seen in Figure 9, the residual (verticalaxis) remains within the 2 σ confidence limits. Table II showsthat over the experiment, the reconciled excavated materialencapsulates the higher accuracy initial stockpile estimate.

1637

Table IIINITIAL ESTIMATE COMPARED TO PROBABILISTIC RECONCILED ESTIMATE

IN LARGE SCALE EXPERIMENT.

Init. StockpileEstimate Mean[Kg] 2σ

Mass 21665 63Reconciled Estimate

In Stockpile Mean[Kg] 2σ

Mass 22171 1350

Figure 10. Covariance matrix with non-zero elements marked as shades ofwhite. It can be noted that a high level of sparsity is present.

C. Scalability

Figure 10 shows the sparsity of the covariance matrixin an example experiment. In this example, the lumps arenot removed or zeroed in order to show how the systemcorrelations are developed over time. The important aspect isthe level of sparsity present. The most numerous equipmentand corresponding unique lump locations is present in thehaul trucks. At any point in time this equipment will only becorrelated to the point of excavation and then that correlationtransferred to the stockpile once it is unloaded. Given thatmaterial transfer equipment is the most frequent on a minesite, and most bulk material transfer operations in general, thecovariance matrix will remain highly sparse.

VI. CONCLUSION

This paper develops a probabilistic representation of lumpedbulk material and a framework for tracking this materialthrough a production chain. A method for fusing data from in-formation sources in a distributed mining network is presented.The framework is developed using an augmented state filterwith constrained system models. This provides a method forallowing probabilistic reconciliation of material while ensuringthat the total mass in correlated states remains constant.

Experiments are shown to prove the concept over a smallscale in a highly controlled and fully measurable environment.Preliminary results from large scale testing are also includedto show how the method can be applied in a real worldapplication. The results are promising and show that it islikely that this system will scale up with larger equipment andmaterial. Future experiments aim to provide greater validationfor consistency and scalability of the current approach.

This research is ideally suited for application in the miningindustry, although the fundamentals (such as a augmented statefilter framework) can be applied across a range of other bulkmaterial handling and processing industries.

ACKNOWLEDGMENTS

This work is supported by the ACFR (Australian Centre forField Robotics) and the Rio Tinto Centre for Mine Automa-tion.

REFERENCES

[1] O. Mol and A. Gillies, “Cut-off grade determination for mines pro-ducing direct-shipping iron ore.” Australasian Institute of Mining andMetallurgy, no. 289, pp. 283–287, November/December 1984.

[2] R. Smith, M. Self, and P. Cheeseman, Estimating uncertainspatial relationships in robotics. New York, NY, USA: Springer-Verlag New York, Inc., 1990, pp. 167–193. [Online]. Available:http://portal.acm.org/citation.cfm?id=93002.93291

[3] P. Keleher, D. Cameron, and M. Knijnikov, “Improving fundamentalstockpile management procedures,” Coal Operators Conference, pp.422–428, 1998.

[4] M. Thomas and V. Snowden, “Improving reconciliation and gradecontrol by statistical and geostatisical analysis,” Strategies for GradeControl, vol. 10, pp. 49–59, 1990.

[5] C. Morley, “Beyond reconciliation - a proactive approach to usingmining data,” in Fifth Large Open Pit Mining Conference, 2003.

[6] C. Morley and R. Moller, “Iron ore mine reconciliation - a case studyfrom sishen iron ore mine, south africa,” Iron Ore Conference, vol. 1,pp. 311–318, 2005.

[7] J. White and J. Olson, “Computer-based dispatching in mines withconcurrent operating objectives.” Mining Engineering, vol. 38, pp. 1045– 1054, 1986.

[8] G. Robinson, “How much would a blending stockpile reduce variation?”Chemometrics and Intelligent Laboratory Systems, vol. 74, pp. 121–133,2004.

[9] G. J. Giacaman, R. P. Medel, and J. A. Tabilo, “Simulation of thematerial transporting and loading process in pedro de valdivia mine,”Winter Simulation Conference, vol. 1, pp. 1349–1355, 2002.

[10] C. Sensogut and A. Ozdeniz, “Statistical modelling of stockpile be-haviour under different atmospheric conditions- western lignite corpo-ration (wlc) case,” Fuel, vol. 84, pp. 1858–1863, 2005.

[11] G. Dissanayake, P. Newman, and S. Clark, “A solution to the simula-taneous localisation and map building problem,” IEE Transactions OnRobotics and Automation, vol. 17, p. 229, June 2001.

[12] D. Simon and T. L. Chia, “Kalman filtering with state equality con-straints,” IEEE Transactions on Aerospace and Electronic Systems,vol. 38, pp. 128–136, 2001.

[13] C. V. Rao, J. B. Rawlings, and J. H. Lee, “Constrain linear stateestimation - a moving horizon approach,” Automatica, vol. 37, pp. 1619–1628, 2001.

[14] G. Brooker, R. Henessy, and C. Lobsey, “Millimetre wave radar forindustrial applications,” in The 2nd International Conference on WirelessBroadband and Ultra Wideband Communications, 2007.

[15] E. Duff, “Automated volume estimation of haul truck loads.” in Pro-ceedings of the Australian Conference on Robotics and Automation.Melbourne, Australia: CSIRO, 2000, pp. 179–184.

[16] Transcale. (2009, July) Transcale website. www.transcale.com.au.[Online]. Available: www.transcale.com.au

[17] S. Schneider, R. Murphy, and S. Monteiro, “On the development of ahyperspectrali library for autonomous mining systems,” in AustraliasianConference on Robotics and Automation, 2009.

[18] S. E. Cohn, “Introduction to estimation theory,” Journal of the Meteor-logical Society of Japan, vol. 75, pp. 257–288, 1997.

[19] RW-P Road Weigher Platform & Indicator Datasheet, CASScale, 2002. [Online]. Available: http://www.cas-usa.com/supportdocs/brochures/RW-P.pdf

[20] (2010, October) Mass, weight, density or specific gravity ofbulk materials. http://www.simetric.co.uk/si materials.htm. Simetric.[Online]. Available: http://www.simetric.co.uk/si materials.htm

1638