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its physical sensor model to have parameters and metadata
which are particular to the sensor. Third, the metadata re-
quired to feed many of these models is not passed through the
current lidar processing chains. Finally, the tools and meth-
ods required to exploit such data do not exist. So, while the
theory and literature show the benefits of the sensor modeling
concepts, the detailed implementation of such concepts has
not been addressed.
The goal of the Universal Lidar Error Model ( ULEM), devel-
oped by the National Geospatial-Intelligence Agency (NGA)
Sensor Geopositioning Center (SGC ), is to address many of
these current shortcomings and provide the utility of sensor
modeling to the users of lidar. Through the ULEM Specifica-
tion (NGA, 2013), the sensor-specific metadata aspects are
mitigated by mapping these metadata to a few standardized
parameters. Likewise, modeling is provided that allows for
the storage and calculation of correlations among these pa-
rameters. This ULEM metadata is stored in existing file formats
such as LAS (ASPRS, 2011) that are used by the community,
and maintains compliance with those format specifications.
Additionally, the exploitation methods are standardized
based on existing sensor modeling efforts of the community.
While the literature has shown the benefits of the sensor
modeling and error propagation, ULEM makes those concepts
accessible to the lidar users.
Concept
ULEM was developed to provide support for rigorous error
propagation and adjustability in the essential lidar point
cloud scenarios while efficiently storing the requisite meta-
data. It employs two implementation modes, Sensor-Space
ULEM and Ground-Space ULEM. Sensor-Space ULEM offers an
effectual generic physical sensor model, consolidating the
parameters from the full physical model into a few standard-
ized parameters. In certain cases where this storage of sensor
parameters becomes impractical and/or unwieldy, ULEM offers
a ground-space implementation. Ground-Space ULEM repre-
sents an efficient strategy for the storage and exploitation of
error covariances in point space that maintains the ability to
generate full covariance matrices among multiple points. Fur-
thermore, the Ground-Space ULEM formulation is sufficiently
general to apply to point clouds, dense digital surface models
(DSMs), or general 3 D data derived from any source, e.g., from
overlapping passive electro-optical or SAR images.
Many applications, such as precise geopositioning from re-
motely-sensed data, need sensor metadata to generate ground-
point uncertainties using error propagation. Also needed are
rigorous methods to fuse and adjust datasets, even among
differing modalities, which require accurate representations
of correlations and cross-correlations among adjustable pa-
rameters (values which define how a dataset may be adjusted,
e.g., translations in geodetic X, Y, and Z). In response to these
needs, the US Air Force Aeronautical Systems Center and
NGA formed the Community Sensor Model Working Group
(CSMWG), which maintains a strict set of rules that define an
application programming interface (API) to which many sen-
sor model builders design their sensor models (Rodarmel et
al., 2011). As a result, sensor exploitation tool builders can
write photogrammetric processing programs in a sensor-ag-
nostic manner. ULEM was designed to be compatible with CSM
guidelines. The CSMWG is working towards expanding the CSM
3.0.1 API, which is currently used to exploit imagery (raster, or
2D datasets), to handle 3D product (e.g., point cloud) datasets
by incorporating ULEM into its current suite of sensor models.
CSM also provides rigorous modeling for correlations using
the Strictly Positive Definite Correlation Function (SPDCF) as
discussed by Dolloff (2013). Using a common CSM interface
ensures that during exploitation the differences in ULEM
implementation modes, and the source of the point cloud
data, are imperceptible to the user.
Data storage is a key aspect to implementing the concepts
of sensor modeling and error propagation into existing work-
flows and making the metadata available and exploitable by
the mass of users. The data must be stored in data formats
that users are willing to use, the formats must be transparent
so that anyone can parse the data, and the impact on the total
required storage should be minimized. ULEM has addressed
these issues by using the ASPRS-developed LAS format as a
storage mechanism (although ULEM could be applied to other
formats). The ULEM metadata, for Sensor-Space or Ground-
Space, is stored in a format compliant with the LAS specifica-
tion by encoding the added metadata into Variable Length
Records (VLR s) that are included in the LAS file with the point
data. The data has been stored using methods that minimize
the storage burden. For example, for Sensor-Space ULEM , the
size of a typical LAS file grows by less than 0.1 percent when
the ULEM metadata is added. Finally, the metadata can be eas-
ily parsed from the VLR by exploitation tools and models.
ULEM supports the storage of adjustable parameters as-
sociated with the dataset as well as the full covariance for
adjustable parameters. The covariance storage is implemented
using the direct and indirect methods. The direct method
captures the entire covariance matrix by storing all the upper-
diagonal entries (since symmetric), including zeros. For large
numbers of adjustable parameters, this method may prove a
bit unwieldy, take up much space, and be wasteful for sparse
matrices. The indirect method stores only the block-diagonal
covariance entries (e.g., Σ11, … Σnn in Equation 2) of the full
covariance matrix. Cross-covariance values are calculated us-
ing correlation coefficients obtained from a correlation model
(i.e., SPDCF (Doucette et al., 2013)), the parameters for which
(A, α, β , τ) are stored in the ULEM metadata. For example, the
correlation coefficient ρ of a parameter (r) over a time range
(Δt) is computed from SPDCF parameters as follows:
( )
1 1
ρ α α β
β Δ τ = + − +( )
+
A
e r r
r r
r
t r
[ ]
/ (5)
In Equation 5, parameter Ar controls the maximum cor-
relation that can be obtained, Ar αr determines the minimum
correlation value that can be obtained, βr primarily controls
the shape of the correlation curve, and τr controls the rate of
the decay. It is important to note that while this example used
temporal differences between points, spatial differences are
also used in some of the ULEM correlation modeling. Similar-
ly, τ may relate to time or distance, depending on the imple-
mentation. Additional detail regarding full-covariance storage
is provided in the Implementations Section.
The intent of this paper is to provide a high-level introduc-
tion to the ULEM concept; therefore many of the details are
absent. The reader is encouraged to obtain the ULEM Imple-
mentation and Exploitation Document (NGA, 2013) for further
information.
Implementations
Sensor-Space ULEM
Sensor-Space ULEM approximates the physics of the sensor
during the original data collection. It requires the ability to in-
terpolate the sensor position at which any lidar point was col-
lected. This interpolation is enabled by access to timestamps
for every lidar-point record and time-indexed collection tra-
jectory data. Sensor-Space ULEM permits sensor-space param-
eter uncertainties (pointing, ranging, etc.) to be propagated
546 July 2015 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING