GENA: Generic Extensible Network Approach

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GENA is a robust non-linear least-squares generic network adjustment engine. With GENA, geodetic networks, photogrammetric and remote sensing blocks and any other type of network can be adjusted. Observations of different types can be arbitrarily combined into single large adjustments.

GENA is, as well, a simulation tool. It can be used to help design geomatic measurement instruments; in particular, remote sensing sensors and multi-sensor systems. It can be used to help design measurement campaigns.

Design principles. GENA has been designed to be extensible.

GENA, is a software platform and system built on GeoNumerics' ITAVERA framework. The main component of GENA is the GENA runtime platform, a directly executable (.exe) or callable (.dll) programme that, given the appropriate toolboxes, does the actual robust non-linear least-squares adjustment. The GENA runtime integrates all necessary input/output, organizational and mathematical machinery. The GENA runtime itself knows nothing about models. Mathematical models for measurements (observation equations), for unknowns to be calculated (parameters) and for instrument constants (instruments) are provided to GENA in toolboxes. The toolboxes, on the contrary, know nothing about network adjustment; they provide modeling information for a number of measurement types (observables). Typically, a toolbox bundles together a number of models, observation types, parameter types and instrument types that are domain-related. The GENA runtime comes with the BASIC toolbox for the fundamental geomatic modeling entities.

GENA is generic and extensible: with GENA's Software Development Kit (GENA SDK) toolboxes with new models can be designed and programmed.

A manifold of applications. Indeed, non-linear least-squares network adjustment is a fundamental method in geomatics. We illustrate this hereunder with a number of geomatic applications, from geodesy to mapping, aerial and terrestrial, static and kinematic, where network adjustment is instrumental and where GENA –with the appropriate model toolboxes– has been the instrument:

  • geodetic network adjustment,
  • aerial photogrammetry,
  • aerial-drone photogrammetry,
  • close-range photogrammetry,
  • multi-sensor system orientation and calibration,
  • camera and sensor calibration,
  • spatiotemporal sensor calibration,
  • radiometric block adjustment,
  • terrestrial mobile mapping,
  • kinematic gravimetry,
  • GNSS positioning.

Application to geodetic network adjustment. Adjustment of geodetic networks is the oldest application of the least-squares method to the solution of a geodetic problem. Carl Friedrich Gauss (1777-1855) used the method in 1810, in his famous survey of the state of Hannover, where he made the measurements during the day and the computations at night. (Gauss claimed to have been using the method since 1795. It also used it, in 1801, in his celebrated prediction of the orbit of the Ceres asteroid.) Today, network adjustment is a basic, fundamental computational tool in geodesy and surveying.

A classical geodetic network is a set of points, materialized as landmarks, whose coordinates are computed from geodetic and astronomical measurements. A geodetic network is usually depicted in two dimensions, in the horizontal plane. Two points are joined by a line if they are related by a measurement. This graphical representation looks like a network and hence the name which has been adopted by other optimisation problems in surveying, like photogrammetric network.

The GENA platform and its model toolbox BASIC have been used to adjust 3D geodetic networks using coordinate difference measurements –typically obtained in GNSS relative positioning campaigns– and distance measurements.

Application to aerial photogrammetry: GENA and the airVISION toolbox. A photogrammetric network or a photogrammetric block is a set of ground points and of images. Typically a ground point is seen in various images and an image contains various points. The goal of a photogrammetric network adjustment is the optimal estimation of the point coordinates and of the images- orientation parameters. Photogrammetric network adjustment is also referred to as block adjustment and bundle adjustment.

In a photogrammetric network adjustment, measurements of some ground points, the ground control points (GCPs) –the rest of the ground points are called tie points (TPs)– and of the image coordinates of the ground points, the photogrammetric measurements, are used. Position, velocity and attitude (PVA) measurements derived from of an on-board GNSS receiver or a combined IMU/GNSS receiver system,  may be also available. With these measurements, the ground coordinates of all TPs, the orientation and calibration parameters of the images, and even some systematic errors of the on-board IMU/GNSS receiver system are computed with GENA and the airVISION model toolbox.

GENA and airVISION are flexible and powerful. Classical aerial triangulation blocks (dominated by photogrammetric measurements and GCPs), modern integrated sensor orientation blocks (classical aerial triangulation with GNSS or INS/GNSS aerial control) or the new fast aerial triangulation (Fast-AT) where the use of INS/GNSS aerial control makes TPs redundant and therefore only a few photogrammetric measurements –for the GCPs– are required. GENA and airVISION, are the orientation and calibration internal engine of ORIENTA, a GeoNumerics application for image orientation with the Fast-AT method.

More about modern photogrammetric network adjustment with GENA and the toolbox airVISION can be read in (Blázquez 2008; Colomina et al., 2012; Blázquez and Colomina, 2012a; Blázquez and Colomina, 2012d; Molina et al. 2013).

Application to close-range photogrametry: GENA and the closeVISION toolbox.

Close-range photogrammetry is photogrammetry where the imaged objects of interest and the imaging sensors are close. In this case, close means less than about 300 m. Close-range photogrammetry is an overarching field with applications to architecture, civil engineering, industrial metrology, biomedicine and bioengineering (biostereometrics), forensics, robotics, terrestrial mobile mapping and, recently, aerial drone mapping. Close-range photogrammetry usually deals with convergent images, small and not always well calibrated cameras.

GeoNumerics recently launched, in 2017, the model toolbox closeVISION to enable GENA for close-range applications.

Application to drone photogrammetry: GENA and the airVISION toolbox. Drone photogrammetry and remote sensing is a particular case of aerial photogrammetry and remote sensing. Drone photogrammetry can also be seen as aerial close-range photogrammetry. A comprehensive survey thereof can be found in (Colomina and Molina, 2014). The difference between classical –i.e., with manned aircraft– aerial photogrammetry and drone photogrammetry is that aerial images acquired from lightweight drone platforms use to cover a smaller footprint; to be acquired from lower altitudes (less than 150 m above ground); to exhibit larger tilts and scale variations; and to be affected by larger distortions. Also their flight geometry is less regular. While the mentioned differences make the photogrammetric measurement of GCPs and TPs on drones images more difficult, the underlying mathematical models (like those included in the airVISION toolbox) and estimation methods (like those of the GENA platform) are alike.

GENA and the airVISION toolbox have been used to adjust photogrammetric networks of images acquired with drones (Molina et al. 2017).

Application to multi-sensor system orientation and calibration. Many current Earth observation systems are multi-sensor ones. Not only because they include a manifold of motion sensors –for later orientation and georeferencing purposes– but also because their dedicated Earth observation payloads combine sensors of different nature: active and passive; in various bands of the electromagnetic spectrum; and in different geometric configurations (2D arrays or frames, 1D single or multiple arrays, single-plane or multi-plane oscillating scanners, circularly rotating scanners and some others). The complementary nature of the sensors is later on exploited for a wide variety of applications ranging from environmental, to agricultural, to law enforcement, to traditional mapping. However, their synergistic exploitation is not possible –or at least suboptimal– if the sensed data are not correctly and consistently referred to common spatial, temporal and spectral reference frames. Correctness and consistency can be achieved by identifying common measurable features and parameters shared by the different sensors and, subsequently, adjusting the measurements and estimating the parameters in a common, combined grand adjustment. Examples of common features to be measured are the same straight line on a camera’s image and on a laser scanner’s image, or the time of a synchronisation pulse measured by two different sensors or a ground patch visible from two different images of a same or different sensor). Examples of common parameters across the sensors of a multi-sensor payload are the orientation parameters of the common mechanical platform where the sensors are held.

The GENA platform and the model toolbox airVISION have been used for the orientation and calibration of homogeneous (multi-head optical systems, Blázquez and Colomina, 2012b) and heterogeneous  (laser scanners/cameras, Angelats et al. 2012; radar/optical systems, Molina et al. 2013) multi-sensor systems.

Application to camera and sensor calibration. In geomatics, sensor calibration can happen before of after the sensor is used in a real mission, in the field or in the lab. This is known as lab- or field-calibration. It is also known as lab or field pre-calibration as the calibration always takes place before the use of the calibration results in the exploitation of the sensor data. Sensor calibration can also happen at the same time that the sensor measurements are processed –usually for positioning or orientation purposes. This is known as self-calibration. Thus, for instance, in the adjustment of a geodetic network, instrumental offsets or scale factor errors can be estimated for the distance measurement sensors. Or, in the adjustment of a photogrammetric network, the cameras are self-calibrated.

GENA, with either the model toolbox closeVISION or airVISION, is the calibration internal engine of CALIBRA, a GeoNumerics application for the automatic lab-calibration of frame cameras using targeted calibration fields. Similarly GENA and calibration models or airVISION were used for the lab-calibration of the optical payload of the radar/optical multi-sensor BRADAR’s SARVANT system (Molina et al. 2013).

Application to spatiotemporal sensor calibration. Spatiotemporal sensor calibration is the simultaneous estimations of a sensor’s geometric and synchronisation systematic errors. An example of synchronisation error is a delay t2 – t1 between a sensor’s actual data acquisition instant t1 and the sensor’s output synchronisation pulse time t2, nominally equal to t1. Up to relatively late after the introduction of INS/GNSS kinematic control systems in geomatics, the concept of sensor orientation with spatiotemporal self-calibration was not considered, probably because only few orientation experts were aware of the velocity output of an INS/GNSS system. (Blázquez and Colomina, 2012b) used GENA to perform the first ever spatiotemporal self-calibrating network adjustment for sensor orientation.

Application to radiometric block adjustment. Radiometric block adjustment is the estimation of an imaging sensor radiometric calibration parameters together with other atmospheric radiative transfer parameters. Benefits and applications of radiometric block adjustment are: the reduction of the radiometric differences between overlapping images captured at different times or from different points; the production of time series of consistent radiometric ground scenes for correct evolution analysis; or the generation of Digital Radiometric Models (DRMs) of the terrain. (A DRM is a function that for each ground point returns a reflectance value and a Bidirectional Reflectance Distribution Function (BRDF)). If a Digital Terrain Model (DTM) and/or Digital Elevation Model (DEM) together with a DRM are available, not only the traditional cartographic representations of the terrain can be produced, but also realistic simulations of an area can be produced by freely setting parameters like the time (date and time within the day) and the atmospheric conditions.

In (Pros et al., 2013) GENA was used to perform a radiometric pre-calibration –correction of the vignetting effect–  first step. In a second step it was used to perform a self-calibrating radiometric block adjustment with BRDF and atmospheric radiative transfer (ART) models. In the adjustment, the measurements were the image digital numbers (DN) and the ground control reflectances (r). The unknown parameters were the sensor calibration parameters, the ground reflectances of the radiometric tie points and additional BRDF and ART parameters. From these parameters, both the DRM and the radiometrically corrected images could be derived.

Application to terrestrial mobile mapping. Terrestrial mobile mapping systems (TMMS) date back to the mid 1990s when the first so-called GPS vans were developed, at the Ohio State University [N95] and at the University of Calgary [S96]. At that time, the technology enablers of TMMS were inertial/GPS navigation and digital cameras. Later on, laser scanning units –the lidars– were added. Ever since, the configuration of TMMS has not essentially changed in the last 15 years: the navigation/orientation subsystem typically includes one or two GNSS receivers, one inertial measurement unit (IMU) and one odometer; the mapping payload includes several cameras and one or two laser scanners.

The Achilles’ heel of TMMSs is their sensitivity to the poor reception of GNSS navigation signals in canyons, vegetation covered areas and urban canyons. In these scenarios the GNSS signal is mitigated, obstructed or diverted (multipath). The result: shifted or just wrong trajectories caused by weak, wrong or missing GNSS signals.

Moreover, the mapping sensors of TMMS are affected by systematic errors that cannot be fully compensated for with independently estimated laboratory/field calibration parameters. Last not least, the TMMS’ IMUs are also affected by systematic errors that result in trajectory drifts when quality GNSS signals are not available.

(Note that by a trajectory we mean here a time series of position, velocity and attitude (PVA) 3D vectors. Also note, that the time dependent PVA vectors can be transferred to each TMMS mapping sensor –camera, laser scanner, video or any other– using TMMS geometric internal relative orientation parameters. Thus, the TMMS trajectory essentially contains each TMMS sensor orientation parameters.)

The common practice in terrestrial mobile mapping is to take advantage of the complementary nature of the GNSS receivers, IMUs, odometers, cameras and laser scanners in a way that the strengths of one sensor compensate for the weaknesses of the others. GNSS ranges, inertial measurements, traveled distances, image measurements and range-angle measurements respectively of the aforementioned sensors are processed, in a couple or few steps, that end up in a final adjustment to estimate a correct trajectory and sensor calibration parameters.

More about GENA for TMMS sensor orientation and calibration can be found in (Angelats and Colomina, 2012).

Application to kinematic inertial strapdown gravimetry. Gravimetry is the measurement of the strength –or the strength and direction– of a gravity field. In practice, to be usable, a gravimetric measurement shall be spatially referenced.

The principle of inertial strapdown gravimetry is that, if you are static and know your position, you can use an IMU to measure gravity. The principle of kinematic strapdown gravimetry is that, if you know your position and velocity, you can use an IMU to measure gravity even if you move. Let us put it in more technical words. An object in motion is affected by the acceleration of the Earth gravity field and by that of the motion itself. We will refer to the latter as geometric acceleration, to the former as gravity acceleration and to the first one as total acceleration. If you can measure the object’s total acceleration and its geometric acceleration, you can measure the gravity field. (In fact, if you know your position as a function of time, you know your velocity and geometric acceleration by simply differentiating once and twice respectively.)

Inertial strapdown gravimetry is a special case of kinematic gravimetry; while kinematic gravimetry is conducted with tailored kinematic gravimeters, inertial strapdown gravimetry is conducted with off-the-shelve IMUs. In both cases, a GNSS receiver is required. Inertial strapdown gravimetry was invented by K.-P. Schwarz (University of Calgary) more than thirty years ago. The traditional approach to inertial strapdown gravimetry is to process the inertial and GNSS measurements in a sequence of steps using Kalman filter-like algorithms. Instead, with GENA, a one-step network adjustment approach can be applied where gravity disturbance vectors, with respect to a reference gravity field, are obtained. GENA and this approach was used in the Spanish DINA and international GAL project.

Details about GAL and the use of GENA for airborne inertial strapdown gravimetry can be found in (Skaloud et al., 2016).

Application to GNSS static and kinematic point determination.

Since 2015, GENA has been used at GeoNumerics, internally and for the EU research projects mapKITE  and COREGAL to validate static and kinematic GNSS positioning with the US GPS and EU Galileo satellite navigation systems. More specifically GENA and the dynamicSURVEY toolbox were used for positioning with code and phase measurements, with GPS L1, L2 and Galileo E1 and E5 AltBOC signals and in the relative and Precise Point Positioning (PPP) modes.


  • robust non-linear least-squares parameter estimation (network adjustment)
  • stochastic (static) and stochastic differential (dynamic) models
  • generic outlier detection-&-removal with regression diagnostics (data snooping) and robust iterative re-weighting
  • computation of parameter and residual co-variances, correlations, internal-external reliability and variance components
  • virtually unlimited number of measurements
  • simulation and actual estimation modes
  • separation between estimation (GENA platform) & modelling (model toolboxes)


  • linear and non-linear, implicit and explicit observation equations (Gauß-Helmert model formulation)
  • iterative Gauss-Newton solution
  • block-sparse organisation of design (A) and normal equations matrices (N)
  • virtually unlimited number of measurements
  • block-sparse Cholesky factorisation of normal equations matrix
  • unknowns' sorting for fill-in reduction and faster linear system of equations solution
  • control of numerical singularity condition
  • generic control of solution convergence
  • partial inversion of the normal equations matrix for Cxx estimation
  • selective inversion of normal equations matrix for off-diagonal Cxx estimation (parameter correlation)
  • partial computation of the Cvv matrix for residual analysis, outlier detection and reliability (internal and external) analysis including redundancy numbers, controllability and sensitivity factors
  • internal and external residual studentization
  • outlier detection and removal based on regression diagnostics (data snooping) and robust estimators (re-weighted least-squares)
  • variance component estimation
  • generic text (XML) and binary file formats
  • standardized (SI) selectable physical units
  • standardized coordinate system and reference frame notation
  • comprehensive generic (model toolbox independent) adjustment reporting
  • Interface Control Document (ICD) available for third party developers

History. GENA is the current embodiment of the experience accumulated in the past more than thirty years; it has been developed at GeoNumerics since 2004, partly supported by EU and Spanish research and innovation programmes (FP7, H2020) with projects like ATENEA (grant 247975, FP7), GAL (grant 287193, FP7), COREGAL (grant 641585, H2020) and mapKITE (grant 641518 , H2020) and DINA (grant PTQ-12-05688, Programa Torres y Quevedo). In other words, GENA is the result of the long experience of GeoNumerics’ researchers and developers, dating back to the early 1980s at the former Institute of Cartography of Catalonia (ICC) and, more recently in the period 2000-2010, at the former Institute of Geomatics (IG). Since its inception, GENA has been based on the classical methods of mathematics, numerical analysis, geodesy and photogrammetry. Along years, GENA has been also the recipient of considerable research originating in PhD dissertations, in academic research and in internal GeoNumerics activities. Last, and above all, GENA has been shaped by user requirements and needs: GENA and some of its toolboxes are the core of many geomatic computational systems installed in mapping organisations worldwide.

Product data sheet: download the GENA PDS.

Product description and applications: download the GENA brochure.