Cross-range Errors Research Articles

Efficient Gaussian Mixture Modeling of Long-Range 2D Radar Measurements

In some practical radar systems of interest, the standard EKF linearization approach applied to a nonlinear measurement transformation is ineffective. In particular, if measurements are performed in polar coordinates and the crossrange error is much greater than the range error, then the true error region in Cartesian space is no longer well approximated by a Gaussian distribution. This effect is known as the “contact lens” problem, and various approaches have been proposed to alleviate it, including particle and Gaussian mixture (GM) filters. In this work, a method is presented for modeling Cartesian converted measurement distributions which suffer from the contact lens effect using Maximum Likelihood (ML) GM parameters. In order to allow an efficient implementation of this process in a GM Kalman filter, a normalization of the ML parameters is introduced so that parameters can be computed offline and efficiently stored in a lookup table. Simulation results are presented to illustrate the method and confirm the results.

Analytical entry guidance for no-fly-zone avoidance

This paper is devoted to designing an analytical entry guidance for steering a hypersonic glide vehicle of high Lift-to-Drag ratio (L/D) in the presence of numerous No-Fly Zones (NFZs). The NFZ constraints pose serious challenges to the guidance design: (1) because there is no engine to provide thrust, the vehicle needs to manage the energy of motion carefully and cannot perform avoidance maneuvers arbitrarily; (2) due to disorder distribution of NFZs, there are multitudinous complicated cases to consider. As the basis of the guidance, the adopted 3-D analytical glide formulae are improved by posing a more accurate Earth-rotation compensation model. Then, the guidance uses the new downrange formula to plan longitudinal reference profile according to the energy-management requirement, and mainly employs the new crossrange formula to schedule proper bank reversals under the NFZ and terminal-position constraints. Here, a complex but rigorous scheme is proposed for fast planning bank-reversal sequence based on six analytical iteration algorithms, which are designed to search the nearest trajectory point to NFZ, to adjust the existing bank reversals or add a new one for NFZ avoidance, and to regulate the last bank reversals for eliminating terminal crossrange error, respectively. The scheme begins with two bank reversals and then gradually adds more bank reversals according to the needs of avoiding the NFZs. As the scheme prefers to adjust the existing bank reversals to address the NFZ constraints, it commonly requires only a few bank reversals. The superior performance of the guidance is verified by sufficient trajectory simulations in disturbed environments.

Omnidirectional autonomous entry guidance based on 3-D analytical glide formulas

An autonomous entry guidance law is developed based on 3-D analytical glide formulas, where the downrange formula is used to plan the longitudinal reference profile in order to meet the downrange and final energy requirements, and the crossrange formula is used to regulate the bank reversals in order to eliminate the crossrange error. As the analytical glide formulas ignore the effects of the Earth׳s rotation, a series of strategies is proposed for compensating these effects, which provides the guidance with the capability of steering the hypersonic glide vehicle with high Lift to Drag ratio (L/D) to any place of the world accurately. The compensation strategies can be summarized into two parts: (1) the reference profiles are properly adjusted by roughly evaluating the effects of the Earth׳s rotation on the aerodynamic profiles over the whole flight, which can compensate most of the effects; (2) the current effects are accurately evaluated and then the guidance commands are slightly modulated for compensating the remaining effects. Due to careful design, the strategies will not result in drastic changes in the Angle of Attack (AOA) and can keep the bank angle almost constant during most of flight.

Entry guidance with real-time planning of reference based on analytical solutions

In this paper, first, we develop new analytical solutions to hypersonic gliding problem. In the derivation of these solutions, we propose an innovative method based on spectral decomposition for solving a special type of linear system with variable coefficients, where the system matrix can be expressed as the product of a scale function and a constant matrix. Next, we design an entry guidance based on these analytical solutions. In the guidance, the downrange analytical expression is used to plan the longitudinal reference profile satisfying the downrange requirement in real time. Two bank reversals are needed to eliminate the crossrange error. The first is planned by the crossrange analytical expression such that the second is at a specified point near the end of the flight. After the first bank reversal is performed, the second is slightly corrected using the trajectory simulation. Because the longitudinal reference profile and bank reversals are planned onboard, the entry guidance can handle various urgent tasks and deal well with large dispersions in the initial conditions, aerodynamic model and atmospheric model.

Construction of the reachability region with regard to the attitude motion of a descent module at reentry with near-circular velocity

A model of the general motion of the descent module that includes the motion of its center of mass and the attitude motion is constructed. An improved estimate of the reachability region in the case of descent in the disturbed Earth atmosphere is obtained. A terminal descent control algorithm with three bank angle reversals for the simultaneous elimination of predicted downrange and cross-range errors with regard to the constraint on the tolerable load factor n tol ≤ 3 is used.

Extended High-Gain Observer for Mars Entry Guidance

To deliver a Mars entry vehicle to the prescribed parachute deployment point, active entry guidance is essential. This paper addresses the problem of Mars atmospheric entry guidance through drag tracking method with extended high gain observer. First, an extended high gain observer combined with feedback linearization is applied in drag tracking for Mars entry longitudinal guidance. The observer estimates the drag and drag rate for drag tracking, estimates the perturbation due to model uncertainty and disturbance, and compensate for the perturbation by canceling its estimate. Then, bank reversal is adopted in the lateral plane to reduce the cross-range error. Finally, Mars entry simulation is performed to assess the performance of the adaptive guidance law. The results demonstrate that the proposed guidance law exhibits good performance. DOI: http://dx.doi.org/10.11591/telkomnika.v11i2.1998 Full Text: PDF

Lateral Entry Guidance for Lunar Return Vehicles

A lateral entry guidance is designed based on azimuth error and crossrange error for a low L/D ratio lunar return vehicle. The conventional technique to determine the bank sign is according to the crossrange error, which might cause large crossrange deviation during Kepler phase if azimuth error at skip out point is large. This paper develops a combined lateral guidance logic to minish accumulate crossrange error caused by azimuth error during Kepler phase. The lateral logic decides the value of crossrange threshold by constantly predicting the crossrange at skip out point. The azimuth error at skip out point is regulated to a small value by only one bank reverse through online adjusting reversal threshold. The effect of earth rotation is compensated by moving the landing site to opposite direction. During the second entry, the lateral logical is designed based on the crossrange error to achieve precise lateral control. The lateral guidance logic is validated by numerical simulations. Monte Carlo simulations show that the proposed lateral guidance logic can deliver the vehicle to the desired landing site in the presence of large initial dispersions and disturbance.

Neural network-based sliding mode variable structure control for Mars entry

To deliver a Mars entry vehicle through the Martian atmosphere to the prescribed parachute deployment point, active Mars entry guidance and control is essential. This article addresses the problem of Mars atmospheric entry control by a neural network-based sliding mode variable structure control (NNSMVSC) to reduce the effect of the bounded uncertainties on the atmospheric density and aerodynamic coefficients. First, NNSMVSC is designed to robustly track the prescribed nominal trajectory under high uncertainties and to effectively reduce the downrange error. Then, the heading alignment logic is adopted in the lateral plane to reduce the cross-range error. Finally, the validity of the control algorithm proposed in this article is demonstrated by computer simulation analysis.

Command generator tracker based direct model reference adaptive tracking guidance for Mars atmospheric entry

In order to accurately deliver an entry vehicle through the Martian atmosphere to the prescribed parachute deployment point, active Mars entry guidance is essential. This paper addresses the issue of Mars atmospheric entry guidance using the command generator tracker (CGT) based direct model reference adaptive control to reduce the adverse effect of the bounded uncertainties on atmospheric density and aerodynamic coefficients. Firstly, the nominal drag acceleration profile meeting a variety of constraints is planned off-line in the longitudinal plane as the reference model to track. Then, the CGT based direct model reference adaptive controller and the feed-forward compensator are designed to robustly track the aforementioned reference drag acceleration profile and to effectively reduce the downrange error. Afterwards, the heading alignment logic is adopted in the lateral plane to reduce the crossrange error. Finally, the validity of the guidance algorithm proposed in this paper is confirmed by Monte Carlo simulation analysis.

재진입 비행체의 진입 및 착륙단계 경로 생성 및 퍼지제어기 설계

재진입 비행체의 Approach & Landing단계는 Steep Glideslope 단계, Circular Flare 단계, Flare Maneuver 단계로 이루어지며, 본 논문에서는 실시간 경로 생성을 위하여 기하학적 조건을 이용한 기준궤적 생성 알고리즘을 사용하였다. 이를 통하여 재진입비행체의 착륙 안정성을 고려한 기준궤적을 빠른 시간 안에 생성할 수 있다. 그리고 본 논문에서는 비선형 시스템에 대하여 강건성을 가지는 Mamdani Fuzzy PD Controller를 통한 종방향 및 횡방향 제어기를 설계하였다. 또한 Downrange 와 Crossrange의 초기 오차를 포함하는 시뮬레이션을 수행하여, 제안된 Fuzzy 제어기의 우수한 성능을 확인하였다. The approach and landing phase of a re-entry vehicle is composed of Steep Glideslope phase, Circular Flare phase, Flare Maneuver phase. The trajectory planning algorithm with geometric parameters is studied in this paper for on-board trajectory planning. This algorithm generate reference trajectory rapidly considering safe landing of re-entry vehicle. In this paper, the Mamdani Fuzzy PD type controller for longitudinal and lateral control is designed which has robustness of nonlinear system. In addition, the simulation is performed including initial downrange and crossrange errors, and the results shows that the proposed fuzzy logic controller has good performance.

Entry Configurations and Performance Comparisons for the Mars Smart Lander

The Mars Smart Lander (MSL, renamed and redefined as the Mars Science Laboratory) will provide scientists with access to previously unachievable landing sites by providing precision landing to less than 10 km of a target landing site with landing altitude capability to 2.5 km above the Mars Orbiter Laser Altimeter geoid. Precision landing is achieved by using the aerodynamic forces on the entry body to aeromaneuver through the Martian atmosphere during the entry phase of flight. The entry body is designed to provide aerodynamic lift. The direction of the aerodynamic lift vector, defined by the vehicle bank angle, is commanded by the onboard entry guidance, to converge downrange and crossrange errors by parachute deploy, while meeting the parachute deploy constraints. Several approaches and entry body configurations for providing aerodynamic lift can be considered, including axisymmetric capsule configurations with offset c.g.s using ballast or packaging, aerodynamically shaped capsule-type configurations, and alternate configurations such as mid-lift-to-drag-ratio vehicles. The design considerations, entry configurations, and entry performance of the Mars Smart Lander are described.

Multitarget tracking using geographically separated radars

Joint search data technology by geographically separated radars has drawn attention. In this technique, the observation data of several radars placed in a geographically wide area are collected for tracking processing. A characteristic of this technique is the reduction of the cross range error that is a problem in single radar. Hence, improved tracking capability is expected. However, for realization it is necessary to take into account the deviations of the coordinate axes between the state variable vector of the target and the observation vector for the observation model of the tracking filter. In this paper, the difference in the coordinate axes is studied. JPDA (Joint Probabilistic Data Association), a multitarget tracking algorithm making use of the observation information of radars placed at several locations, is studied. In order to evaluate the effectiveness of the present technique, computer simulation is carried out. It is found that the tracking performance is improved over the conventional method of using only one radar. © 2002 Scripta Technica, Electron Comm Jpn Pt 1, 85(5): 34–47, 2002

Multitarget tracking using geographically separated radars

AbstractJoint search data technology by geographically separated radars has drawn attention. In this technique, the observation data of several radars placed in a geographically wide area are collected for tracking processing. A characteristic of this technique is the reduction of the cross range error that is a problem in single radar. Hence, improved tracking capability is expected. However, for realization it is necessary to take into account the deviations of the coordinate axes between the state variable vector of the target and the observation vector for the observation model of the tracking filter. In this paper, the difference in the coordinate axes is studied. JPDA (Joint Probabilistic Data Association), a multitarget tracking algorithm making use of the observation information of radars placed at several locations, is studied. In order to evaluate the effectiveness of the present technique, computer simulation is carried out. It is found that the tracking performance is improved over the conventional method of using only one radar. © 2002 Scripta Technica, Electron Comm Jpn Pt 1, 85(5): 34–47, 2002

Autofocus and super-resolution synthetic aperture radar image formation

An FFT (fast Fourier transform) based parametric algorithm, referred to as MCCLEAN, is devised for cross-range phase error compensation in SAR (synthetic aperture radar) imaging. It can be used as an independent autofocus approach for the SAR imaging of a large scene. The authors also present a similarly structured algorithm for simultaneous autofocus and super-resolution SAR image formation of a small scene or small region of interest (ROI) in a large scene. Examples are provided to illustrate the performance of the proposed algorithms.

Explicit expressions for debiased statistics of 3D converted measurements

The method for tracking based on Kalman filter with debiased consistent converted 2D measurements was given and discussed by D. Lerro et al. (1993) and Y. Bar-Shalom et al. (1993). In this work explicit expressions for debiasing compensation terms and debiased covariance statistics related to the 3D case are presented. The proposed procedure can be employed in active sonar systems or long range radar systems especially when the cross-range errors are significantly large relative to the range errors.

Tracking with Consistent Converted Measurements vs the EKF

In tracking applications target motion is usually best modeled in a simple fashion using Cartesian coordinates. However, in most systems the target position measurements are provided in terms of range and azimuth (bearing) with respect to the sensor location. This situation requires either converting the measurements 10 a Cartesian frame of reference and working directly on converted measurements or using an Extended Kalman Filter (EKF) in mixed coordinates. An accurate means of tracking with debiased consistent converted measurements is presented which accurately accounts for the sensor inaccuracies over all practical geometries and accuracies. This method is compared to the mixed coordinate EKF approach as well as the standard converted measurement approach discussed in [1] and [4] which is an acceptable approximation only for moderate cross range errors. This new approach is shown 10 be more accurate in terms of position and velocity errors and provides consistent estimates (i.e. compatible with the filter calculated covariances) for all practical situations. The combination of parameters (range, range accuracy, and azimuth accuracy) for which debiasing is needed is presented in explicit form.

Tracking with debiased consistent converted measurements versus EKF

In tracking applications target motion is usually best modeled in a simple fashion using Cartesian coordinates. Unfortunately, in most systems the target position measurements are provided in terms of range and azimuth (bearing) with respect to the sensor location. This situation requires either converting the measurements to a Cartesian frame of reference and working directly on converted measurements or using an extended Kalman filter (EKF) in mixed coordinates. An accurate means of tracking with debiased consistent converted measurements which accounts for the sensor inaccuracies over all practical geometries and accuracies is presented. This method is compared with the mixed coordinates EKF approach as well as a previous converted measurement approach which is an acceptable approximation only for moderate cross-range errors. The new approach is shown to be more accurate in terms of position and velocity errors and provides consistent estimates (i.e., compatible with the filter calculated covariances) for all practical situations. The combination of parameters (range, range accuracy, and azimuth accuracy) for which debiasing is needed is presented in explicit form. >