Academic literature on the topic 'Horizon tracking'

We have developed a new algorithm for tracking 3D seismic horizons. The algorithm combines an inversion-based, seismic-dip flattening technique with conventional, similarity-based autotracking. The inversion part of the algorithm aims to minimize the error between horizon dips and computed seismic dips. After each cycle in the inversion loop, more seeds are added to the horizon by the similarity-based autotracker. In the example data set, the algorithm is first used to quickly track a set of framework horizons, each guided by a small set of user-picked seed positions. Next, the intervals bounded by the framework horizons are infilled to generate a dense set of horizons, also known as HorizonCube. This is done under the supervision of a human interpreter in a similar manner. The results show that the algorithm behaves better than unconstrained flattening techniques in intervals with trackable events. Inversion-based algorithms generate continuous horizons with no holes to be filled posttracking with a gridding algorithm and no loop skips (jumping to the wrong event) that need to be edited as is standard practice with autotrackers. Because editing is a time-consuming process, creating horizons with inversion-based algorithms tends to be faster than conventional autotracking. Horizons created with the adopted algorithm follow seismic events more closely than horizons generated with the inversion-only algorithm, and the fault crossings are sharper.

Model predictive control is one of the main methods used in path tracking for autonomous vehicles. To improve the path tracking performance of the vehicle, a path tracking method based on model predictive control with variable predictive horizon is proposed in this paper. Based on the designed model predictive controller for path tracking, the response analysis of path tracking control system under the different predictive horizons is carried out to clarify the influence of predictive horizon on path tracking accuracy, driving comfort and real-time of the control algorithm. Then, taking the lateral offset, the steering frequency and the real-time of the control algorithm as comprehensive performance indexes, the particle swarm optimization algorithm is designed to realize the adaptive optimization for the predictive horizon. The effectiveness of the proposed method is evaluated via numerical simulation based on Simulink/CarSim and hardware-in-the-loop experiment on an autonomous driving simulator. The obtained results show that the optimized predictive horizon can adapt to the different driving environment, and the proposed path tracking method has good comprehensive performance in terms of path tracking accuracy of the vehicle, driving comfort and real-time.

Interpreters use horizon autopicking in many seismic interpretations in the modern workstation environment. When properly used and with data quality permitting this technique enables efficient and accurate tracking of horizons but is not without its pitfalls. Four common pitfalls are improper selection of the input control or seed grid, not accounting for the “directional” behavior of tracking algorithms, attempting autopicking in areas with poor reflection continuity and/or low signal-to-noise ratio, and failing to recognize elements of geology that are not suitable for autopicking.

Seismic horizons are the compulsory inputs for seismic stratigraphy analysis and 3D reservoir modeling. Manually interpreting horizons on thousands of vertical seismic slices of 3D seismic survey is a time-consuming task. Automatic horizon interpreting algorithms are usually based on the seismic reflector dip. However, the estimated seismic reflector dip is usually inaccurate near and across geologic features such as unconformities. We are determined to improve the quality of picked horizons using multiple seismic attributes. We assume that seismic horizons follow the reflector dip and that the same horizons should have similar instantaneous phase values. We first generate horizon patches using a reflector dip attribute, which is similar to current methods. We use seismic coherence attribute as the stop criteria for tracking the horizon within each patch. Considering the inaccuracy of reflector dip estimates at and near the discontinuous structures such as fault and unconformities, we use the seismic instantaneous phase attribute to improve the quality of the generated horizon patches. We generate horizons by merging the residual horizon patches and only outputting the best horizon in each iteration. Our method is capable of generating a horizon for each reflection within the 3D seismic survey, and the generated horizons strictly follow the seismic reflections over the whole seismic survey. Finally, each time sample of seismic traces is assigned a chronostratigraphic relative geologic time value according to the tracked horizons.

An adaptive-prediction-horizon model prediction control-based path tracking controller for a four-wheel independent control electric vehicle is designed. Unlike traditional model prediction control with fixed prediction horizon, this paper devotes to satisfy the varied path tracking demand by adjusting online the prediction horizon of model prediction control according to its effect on vehicle dynamic characteristics. Vehicle dynamic stability quantized with the vehicle sideslip-feature phase plane is preferentially considered in the prediction horizon adjustment. For stability during switching prediction horizon and for robustness during path tracking, the numerical problem inherent in the adaptive-prediction-horizon model prediction control is analysed and solved by introducing exponentially decreasing weight. Subsequently, the desired motion for path tracking with the four-wheel independent control electric vehicle is realized with a hierarchical control structure. Simulation results finally illustrate the effectiveness of the proposed method.

We have determined to combine the automatic interpretation of horizons in a seismic cube with a space/time framework to construct a chronostratigraphic model that matched seismic events and could be used later, without having to rework it in reservoir modeling and seismic characterization. A large number of single seismic events were automatically extracted from the cube as horizon patches. Each patch was associated to an individual isogeologic time constraint. An optimization process then proposed a geologically coherent model in the volume, filling the gaps in the area where no patch was extracted, and taking into account additional geologic information, such as unconformities, fault displacement, or well information. Furthermore, this process generated a seismic flattened volume used to check the quality of the model and revealed some geologic features such as unpicked faults, channels, lobes, and splays. We evaluated a use case in which this method was successfully tested on a complex faulted data set.

Autonomous vehicle path tracking accuracy faces challenges in being accomplished due to the assumption that the longitudinal speed is constant in the prediction horizon in a model predictive control (MPC) control frame. A model predictive control path tracking controller with longitudinal speed compensation in the prediction horizon is proposed in this paper, which reduces the lateral deviation, course deviation, and maintains vehicle stability. The vehicle model, tire model, and path tracking model are described and linearized using the small angle approximation method and an equivalent cornering stiffness method. The mechanism of action of longitudinal speed changed with state vector variation, and the stability of the path tracking closed-loop control system in the prediction horizon is analyzed in this paper. Then the longitudinal speed compensation strategy is proposed to reduce tracking error. The controller designed was tested through simulation on the CarSim-Simulink platform, and it showed improved performance in tracking accuracy and satisfied vehicle stability constrains.

In this paper, a synthesized novel strategy of varying predictive horizon-based model predictive control is proposed for the overtaking control of unmanned ground vehicle. The whole control strategy includes path planning and path tracking. First, the preferred path in presence of diverse constraints of states, inputs, and collision avoidance can be calculated using Gauss pseudospectral method where expected position, velocity, and attitude are provided. Correspondingly, the continuous optimal control problem is converted to discrete nonlinear programming. Second, model predictive control is developed for tracking the optimized path. Considering the effect of the predictive horizon and the Gauss points’ distribution on tracking performance, the varying predictive horizon is introduced to improve the tracking accuracy in non-smooth path. By the varying predictive horizon-based model predictive control method, less computation burden and better control performance are achieved. For the difference between the mathematical expressions and the real unmanned ground vehicle dynamics, genetic algorithm is utilized to identify the parameters of tire model. Simulations in MATLAB and CarSim are both implemented to illustrate the effectiveness of the proposed method.

The approximate nonlinear receding-horizon control law is used to treat the trajectory tracking control problem of rigid link robot manipulators. The derived nonlinear predictive law uses a quadratic performance index of the predicted tracking error and the predicted control effort. A key feature of this control law is that, for their implementation, there is no need to perform an online optimization, and asymptotic tracking of smooth reference trajectories is guaranteed. It is shown that this controller achieves the positions tracking objectives via link position measurements. The stability convergence of the output tracking error to the origin is proved. To enhance the robustness of the closed loop system with respect to payload uncertainties and viscous friction, an integral action is introduced in the loop. A nonlinear observer is used to estimate velocity. Simulation results for a two-link rigid robot are performed to validate the performance of the proposed controller.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
PROGRAMA DE EXCELENCIA ACADEMICA
BOLSA NOTA 10
A interpretação manual de um horizonte sísmico é um processo muito custoso em termos de tempo de trabalho do intérprete, o que incentiva a pesquisa de métodos automáticos, ou semi automáticos, de rastreamento. Dentre as propostas existentes baseadas em correlação, uma limitação conhecida é o uso de abordagens locais para definir as amostras pertencentes ao horizonte rastreado. Esse tipo de abordagem possui bom desempenho em dados onde não há a presença de falhas sísmicas, porém, nas regiões de baixa coerência, característica das regiões ruidosas ou de falhas, ao tomar uma decisão local o rastreador fica suscetível à propagação de erro. O objetivo deste trabalho é avaliar o uso de algoritmos de menor caminho em grafos para a solução do problema de rastreamento de horizontes sísmicos, afim de propor um método de caráter global que seja robusto a diferentes feições sísmicas.
The manual interpretation of a seismic horizon is a time consuming process, which drives the research for automatic or semi automatic tracking methods. Among the known propositions that use correlation, there is a common limitation: the usage of local approaches to determine which samples belong to the horizon. This kind of approach performs well in data where there are no seismi faults. However, by using only local information, it is prone to error propagation in low coherency areas, which usualy corresponds to fault regions. The goal of this work is to evaluate the performance of shortest path algorithms as a solution for the horizont tracking problem. It intends to propose a global method that is robust to different seismic features.

The performance of an extended Kalman filter used to track a maneuvering surface target using HFDF lines-of-bearing is substantially improved by implementing a fixed interval smoothing algorithm and a maneuver detection method that uses a noise variance estimator process. This tracking routine is designed and implemented in a computer program developed for this thesis. The Hall noise model is used to accurately evaluate the performance of the tracking algorithm in a noisy environment. Several tracking scenarios are simulated and analyzed. The application of the Kalman tracker to a tropical storm tracking is investigated. Actual storm tracks obtained from the Joint Typhoon Warning Center in Guam, Mariana Islands are used for this research

L’estimation de trajectoires de débris spatiaux pendant la rentrée atmosphérique est un défi majeur pour les prochaines années, renforcé par plusieurs projets liés à l'enlèvement de débris établis par plusieurs agences spatiales. Cependant, ce problème s’avère complexe du fait des erreurs de modèle et des difficultés d’initialisation des algorithmes d’estimation induites par une mauvaise connaissance de la dynamique des débris suite à leur désintégration pendant la phase de rentrée atmosphérique. Tout estimateur choisi doit donc être robuste vis-à-vis de ces facteurs. L’estimateur à horizon glissant (MHE) est reconnu dans la littérature pour être robuste vis-à-vis d’erreurs de modèle et de mauvaise initialisation, et les travaux de thèse ont montré qu’il était adapté en termes de performances à la problématique de l’estimation des débris en phase de rentrée. En revanche, il se fonde sur une stratégie d’optimisation qui requiert de fait un temps de calcul important. Pour pallier ce problème, une nouvelle structure d’estimation à horizon glissant a été développée, impliquant un temps de calcul faible nécessaire à l’application envisagée. Cette stratégie, appelée « estimateur à horizon glissant avec pré-estimation (MHE-PE)», prend en compte les erreurs de modèle via un estimateur auxiliaire, plutôt que de chercher à obtenir les estimées du bruit d’état sur l’horizon d’estimation, comme le fait la structure de l’estimateur MHE standard. Un théorème garantissant la stabilité de la dynamique de l’erreur d’estimation du MHE-PE a par ailleurs été proposé. Enfin, les performances de cette structure dans le cadre de l’estimation en trois dimensions des trajectoires de débris pendant la phase de rentrée se sont avérées meilleures que celles observées avec des estimateurs classiques. En particulier, sans dégrader la précision et la convergence de l’estimation, l’estimateur MHE-PE requiert moins de temps de calcul du fait du nombre réduit de paramètres à optimiser
Space debris tracking during atmospheric re-entries will be a crucial challenge in the coming years, emphasized through many projects on space debris mitigation established by space agencies worldwide. However, this problem appears to be complex, due to model errors and difficulties to properly initialize the estimation algorithms, as a result of unknown dynamics of the debris and their disintegrations during the re-entries. A-to-be used estimator for this problem must be robust against these factors. The Moving Horizon Estimator (MHE) is known in the literature to be robust to model errors and bad initialization, and the PhD work has proved its ability to satisfy performances required by the debris tracking during the re-entries. However, its optimization-based framework induces a large computation time. To overcome this, a new MHE structure which requires smaller computation time than the classical MHE has been developed. This strategy, so-called “Moving Horizon Estimator with Pre-Estimation (MHE-PE)” takes into account model errors by using an auxiliary estimator rather than by searching for estimates of the process noise sequence over the horizon as in the classical strategy. A theorem which guarantees the stability of the dynamics of the estimation errors of the MHE-PE has also been proposed. Finally, performances of this structure in the context of 3D space debris tracking during the re-entries have been shown to be better than those obtained with classical estimators including the MHE. In particular, without degrading accuracy of the estimates and convergence of the estimator, the MHE-PE estimator requires smaller computation time than the MHE thanks to its small number of optimization variables

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California
This paper presents the findings of the Space Tracking Systems/Options Study (STS/OS) and indicates its impact on the telemetering community. The STS/OS was commissioned by Air Force Test & Evaluation (AF/TE) to develop a long range plan (vision and roadmap) for the AF Test & Evaluation (T&E) community to ensure affordable capabilities (telemetry, tracking and commanding) for the future (2003-2008). The study was conducted by the Air Force Materiel Command (AFMC), Space & Missile Systems Center (SMC), Detachment 9, at Vandenberg AFB (VAFB), with support from the primary AFMC T&E centers, the Air Force Operational Test & Evaluation Command (AFOTEC), and the Air Force Space Command (AFSPC). Both "open air" aeronautical and astronautical test needs were considered. The study solicited requirements for existing and future programs, extrapolated existing and planned test capabilities out into the future, then compared the two to identify future shortfalls in capabilities and specific actions that are necessary to insure that the future program needs can be met. Three critical types of testing were identified that cannot be satisfied with existing or planned instrumentation. These are: large area testing (LAT), over the horizon testing (OTH), and space weapons testing (SWT). A major deficiency was also uncovered in end game scoring for air and space intercepts, where inadequate capability exists to perform the required vector miss-distance measurement. This paper is important to the telemetering community because it identifies the Global Positioning System (GPS) as the primary time space position information (TSPI) system for all future open air testing. GPS provides a passive capability that permits each vehicle to determine its own precise TSPI. Means must be provided, however, for the vehicle to relay its position to the appropriate range control center. The paper shows that the problems with down linking telemetry, aircraft buss data, digital audio, digital video, and TSPI collectively represent the need for a very capable datalink. Likewise, the need to uplink commands, synthetic targets, synthetic backgrounds, and target control information also represents the need for a very capable datalink. With its extensive expertise in RF linkages, the telemetering community is ideally suited to address this need for a robust datalink for the future of T&E.

Recently, autonomous vehicles have received worldwide attentions from academic research, automotive industry and the general public. In order to achieve a higher level of automation, one of the most fundamental requirements of autonomous vehicles is the capability to respond to internal and external changes in a safe, timely and appropriate manner. Situational awareness and decision making are two crucial enabling technologies for safe operation of autonomous vehicles. This thesis presents a solution for improving the automation level of autonomous vehicles in both situational awareness and decision making aspects by utilising additional domain knowledge such as constraints and influence on a moving object caused by environment and interaction between different moving objects. This includes two specific sub-systems, model based target tracking in environmental perception module and motion planning in path planning module. In the first part, a rigorous Bayesian framework is developed for pooling road constraint information and sensor measurement data of a ground vehicle to provide better situational awareness. Consequently, a new multiple targets tracking (MTT) strategy is proposed for solving target tracking problems with nonlinear dynamic systems and additional state constraints. Besides road constraint information, a vehicle movement is generally affected by its surrounding environment known as interaction information. A novel dynamic modelling approach is then proposed by considering the interaction information as virtual force which is constructed by involving the target state, desired dynamics and interaction information. The proposed modelling approach is then accommodated in the proposed MTT strategy for incorporating different types of domain knowledge in a comprehensive manner. In the second part, a new path planning strategy for autonomous vehicles operating in partially known dynamic environment is suggested. The proposed MTT technique is utilized to provide accurate on-board tracking information with associated level of uncertainty. Based on the tracking information, a path planning strategy is developed to generate collision free paths by not only predicting the future states of the moving objects but also taking into account the propagation of the associated estimation uncertainty within a given horizon. To cope with a dynamic and uncertain road environment, the strategy is implemented in a receding horizon fashion.

This research is a novel approach to enabling Unmanned Aerial Vehicle (UAV) navigation and target finding and tracking missions under uncertainty in cluttered and GPS-denied environments. A novel framework, implemented as a modular system, formulates the missions as online Partially Observable Markov Decision Processes (POMDP). The online POMDP computes a motion policy that balances multiple mission objectives optimally. The motion policy is updated while flying based onboard sensor observations. This research provides an enabling technology for UAV missions such as search and rescue, biodiversity assessment, underground mining and infrastructure inspection in challenging and natural environments.

Les Moments ont été largement utilisés dans la reconnaissance de formes et dans le traitement d'image. Dans cette thèse, nous concentrons notre attention sur les 3D moments orthogonaux de Gauss-Hermite, les moments invariants 2D et 3D de Gauss-Hermite, l'algorithme rapide de l'attribut de cohérence et les applications de l'interprétation sismique en utilisant la méthode des moments.Nous étudions les méthodes de suivi automatique d'horizon sismique à partir de moments de Gauss-Hermite en cas de 1D et de 3D. Nous introduisons une approche basée sur une étude multi-échelle des moments invariants. Les résultats expérimentaux montrent que la méthode des moments 3D de Gauss-Hermite est plus performante que les autres algorithmes populaires.Nous avons également abordé l'analyse des faciès sismiques basée sur les caractéristiques du vecteur à partir des moments 3D de Gauss -Hermite, et la méthode de Cartes Auto-organisatrices avec techniques de visualisation de données. L'excellent résultat de l'analyse des faciès montre que l'environnement intégré donne une meilleure performance dans l'interprétation de la structure des clusters.Enfin, nous introduisons le traitement parallèle et la visualisation de volume. En profitant des nouvelles performances par les technologies multi-threading et multi-cœurs dans le traitement et l'interprétation de données sismiques, nous calculons efficacement des attributs sismiques et nous suivons l'horizon. Nous discutons également l'algorithme de rendu de volume basé sur le moteur Open-Scene-Graph qui permet de mieux comprendre la structure de données sismiques.

Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2005.
Bottasso, Carlo, Committee Chair ; Hodges, Dewey, Committee Member ; Bauchau, Olivier, Committee Member. Includes bibliographical references.

In April 2010, approximately 4.9 million barrels of oil were accidentally released into the Gulf of Mexico during the Deepwater Horizon Macondo Mc252 Oil Spill. Some of the surface oil was carried by prevailing winds and currents and reached the coast of Louisiana impacting marsh and marine ecosystems. One and a half years after this incident, a set of oiled marsh samples (2 grab samples) coupled with nearby subtidal and intertidal cores (12 cores) were collected from Barataria Bay, Louisiana to determine the probable source of petroleum residues present and to characterize the chemical composition of the oil. Plus, pre-spill core which was collected from Barataria Bay in 2007 was analyzed to identify the background hydrocarbon composition of the area. Polycyclic aromatic hydrocarbons (PAH), total petroleum hydrocarbons (TPH), biomarker, and stable carbon isotope compositions of selected samples were detected using a GC-MS and an elemental analyzer Conflo system coupled to a DeltaPlusXP isotope ratio mass spectrometer. The comprehensive chemical data allowed us to classify the pre and post-spill samples into 4 Groups. According to this classification, Group 1 and Group 2 samples had the highest concentrations of petroleum-derived hydrocarbons. Group 3 and background samples, on the other hand, was dominated by biogenic signatures. Although a direct connection between the detected and spilled Macondo oils results are complicated due to confounding factors (e.g., already present hydrocarbons and weathering processes), our biomarker data indicates that both oils have similar signatures. This close genetic relationship was also identified by stable carbon isotope analysis. The impact of the Macondo Mc252 Oil Spill in Barataria Bay appears to be limited to areas closer to the source. The oil has undergone moderate weathering and has penetrated into, the at least, the top 9 cm sediments. Additionally, to examine the decadal-scale history of sedimentation in these marshes, a sediment core was analyzed for the radioisotope 137Cs. The observed sedimentation rate of 0.39 cm/yr shows that oil pollutant input into Barataria Bay has been ongoing for at least 50-60 years.

In Remaindered Life Neferti X. M. Tadiar offers a new conceptual vocabulary and framework for rethinking the dynamics of a global capitalism maintained through permanent imperial war. Tracking how contemporary capitalist accumulation depends on producing life-times of disposability, Tadiar focuses on what she terms remaindered life—practices of living that exceed the distinction between life worth living and life worth expending. Through this heuristic, Tadiar reinterprets the global significance and genealogy of the surplus life-making practices of migrant domestic and service workers, refugees fleeing wars and environmental disasters, criminalized communities, urban slum dwellers, and dispossessed Indigenous people. She also examines artists and filmmakers in the Global South who render forms of various living in the midst of disposability. Retelling the story of globalization from the side of those who reach beyond dominant protocols of living, Tadiar demonstrates how attending to remaindered life can open up another horizon of possibility for a radical remaking of our present global mode of life.

Summary Due to the rapid increase in the amount of seismic volumes, the traditional seismic interpretation mode based on manual structure interpretation and single-horizon automatic tracking has encountered many challenges. The seismic interpretation of large or super-large 3-D seismic surveys is facing serious accuracy and efficiency bottlenecks. Aiming to the goal of improving the accuracy and efficiency of seismic interpretation, we propose a dynamic seismic waveform matching technology based on the sparse dynamic time warping algorithm under the guidance of the relative geological time volume theory, and realize multi-horizon simultaneous tracking based on the technology. Has been verified by a model and a real seismic volume, it can realize simultaneous horizon automatic tracking, full spatial tracking and high-density tracking, and can significantly improve the accuracy and efficiency of structure interpretation.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.

Macroeconomic summary Annual inflation continued to rise in the first quarter (8.5%) and again outpaced both market expectations and the technical staff’s projections. Inflation in major consumer price index (CPI) baskets has accelerated year-to-date, rising in March at an annual rate above 3%. Food prices (25.4%) continued to contribute most to rising inflation, mainly affected by a deterioration in external supply and rising costs of agricultural inputs. Increases in transportation prices and in some utility rates (energy and gas) can explain the acceleration in regulated items prices (8.3%). For its part, the increase in inflation excluding food and regulated items (4.5%) would be the result of shocks in supply and external costs that have been more persistent than expected, the effects of indexation, accumulated inflationary pressures from the exchange rate, and a faster-than-anticipated tightening of excess productive capacity. Within the basket excluding food and regulated items, external inflationary pressures have meaningfully impacted on goods prices (6.4%), which have been accelerating since the last quarter of 2021. Annual growth in services prices (3.8%) above the target rate is due primarily to food away from home (14.1%), which was affected by significant increases in food and utilities prices and by a rise in the legal monthly minimum wage. Housing rentals and other services prices also increased, though at rates below 3%. Forecast and expected inflation have increased and remain above the target rate, partly due to external pressures (prices and costs) that have been more persistent than projected in the January report (Graphs 1.1 and 1.2). Russia’s invasion of Ukraine accentuated inflationary pressures, particularly on international prices for certain agricultural goods and inputs, energy, and oil. The current inflation projection assumes international food prices will increase through the middle of this year, then remain high and relatively stable for the remainder of 2022. Recovery in the perishable food supply is forecast to be less dynamic than previously anticipated due to high agricultural input prices. Oil prices should begin to recede starting in the second half of the year, but from higher levels than those presented in the previous report. Given the above, higher forecast inflation could accentuate indexation effects and increase inflation expectations. The reversion of a rebate on value-added tax (VAT) applied to cleaning and hygiene products, alongside the end of Colombia’s COVID-19 health emergency, could increase the prices of those goods. The elimination of excess productive capacity on the forecast horizon, with an output gap close to zero and somewhat higher than projected in January, is another factor to consider. As a consequence, annual inflation is expected to remain at high levels through June. Inflation should then decline, though at a slower pace than projected in the previous report. The adjustment process of the monetary policy rate wouldcontribute to pushing inflation and its expectations toward the target on the forecast horizon. Year-end inflation for 2022 is expected to be around 7.1%, declining to 4.8% in 2023. Economic activity again outperformed expectations. The technical staff’s growth forecast for 2022 has been revised upward from 4.3% to 5% (Graph 1.3). Output increased more than expected in annual terms in the fourth quarter of 2021 (10.7%), driven by domestic demand that came primarily because of private consumption above pre-pandemic levels. Investment also registered a significant recovery without returning to 2019 levels and with mixed performance by component. The trade deficit increased, with significant growth in imports similar to that for exports. The economic tracking indicator (ISE) for January and February suggested that firstquarter output would be higher than previously expected and that the positive demand shock observed at the end of 2021 could be fading slower than anticipated. Imports in consumer goods, retail sales figures, real restaurant and hotel income, and credit card purchases suggest that household spending continues to be dynamic, with levels similar to those registered at the end of 2021. Project launch and housing starts figures and capital goods import data suggest that investment also continues to recover but would remain below pre-pandemic levels. Consumption growth is expected to decelerate over the year from high levels reached over the last two quarters. This would come amid tighter domestic and external financial conditions, the exhaustion of suppressed demand, and a deterioration of available household income due to increased inflation. Investment is expected to continue to recover, while the trade deficit should tighten alongside high oil and other export commodity prices. Given all of the above, first-quarter economic growth is now expected to be 7.2% (previously 5.2%) and 5.0% for 2022 as a whole (previously 4.3%). Output growth would continue to moderate in 2023 (2.9%, previously 3.1%), converging similar to long-term rates. The technical staff’s revised projections suggest that the output gap would remain at levels close to zero on the forecast horizon but be tighter than forecast in January (Graph 1.4). These estimates continue to be affected by significant uncertainty associated with geopolitical tensions, external financial conditions, Colombia’s electoral cycle, and the COVID-19 pandemic. External demand is now projected to grow at a slower pace than previously expected amid increased global inflationary pressures, high oil prices, and tighter international financial conditions than forecast in January. The Russian invasion of Ukraine and its inflationary effects on prices for oil and certain agricultural goods and inputs accentuated existing global inflationary pressures originating in supply restrictions and increased international costs. A decline in the supply of Russian oil, low inventory levels, and continued production limits on behalf of the Organization of Petroleum Exporting Countries and its allies (OPEC+) can explain increased projected oil prices for 2022 (USD 100.8/barrel, previously USD 75.3) and 2023 (USD 86.8/barrel, previously USD 71.2). The forecast trajectory for the U.S. Federal Reserve (Fed) interest rate has increased for this and next year to reflect higher real and expected inflation and positive performance in the labormarket and economic activity. The normalization of monetary policy in various developed and emerging market economies, more persistent supply and cost shocks, and outbreaks of COVID-19 in some Asian countries contributed to a reduction in the average growth outlook for Colombia’s trade partners for 2022 (2.8%, previously 3.3%) and 2023 (2.4%, previously 2.6%). In this context, the projected path for Colombia’s risk premium increased, partly due to increased geopolitical global tensions, less expansionary monetary policy in the United States, an increase in perceived risk for emerging markets, and domestic factors such as accumulated macroeconomic imbalances and political uncertainty. Given all the above, external financial conditions are tighter than projected in January report. External forecasts and their impact on Colombia’s macroeconomic scenario continue to be affected by considerable uncertainty, given the unpredictability of both the conflict between Russia and Ukraine and the pandemic. The current macroeconomic scenario, characterized by high real inflation levels, forecast and expected inflation above 3%, and an output gap close to zero, suggests an increased risk of inflation expectations becoming unanchored. This scenario offers very limited space for expansionary monetary policy. Domestic demand has been more dynamic than projected in the January report and excess productive capacity would have tightened more quickly than anticipated. Headline and core inflation rose above expectations, reflecting more persistent and important external shocks on supply and costs. The Russian invasion of Ukraine accentuated supply restrictions and pressures on international costs. This partly explains the increase in the inflation forecast trajectory to levels above the target in the next two years. Inflation expectations increased again and are above 3%. All of this increased the risk of inflation expectations becoming unanchored and could generate indexation effects that move inflation still further from the target rate. This macroeconomic context also implies reduced space for expansionary monetary policy. 1.2 Monetary policy decision Banco de la República’s board of directors (BDBR) continues to adjust its monetary policy. In its meetings both in March and April of 2022, it decided by majority to increase the monetary policy rate by 100 basis points, bringing it to 6.0% (Graph 1.5).