Navigation Measurements Research Articles

Autonomous spacecraft navigation and control for comet landing

The autonomous guidance, navigation, and control operations during the landing phase of the Comet Nucleus Sample Return mission are described and the associated performance of the onboard system is analyzed in terms of landing accuracy and relative velocity at touchdown. Two descent scenarios are developed and investigated: a slow descent strategy that optimizes the operation of an onboard laser mapper and a fast descent strategy that relies only on microwave measurements for navigation. It is demonstrated by means of Monte Carlo simulations that the first scenario provides a more accurate landing, whereas the second one is a suitable alternative to the case where the complex laser system has failed. Equatorial and polar descent orbits to a landing site on the comet equator are considered. Models of the comet, spacecraft dynamics, and instrument measurements are described, and the main features of the onboard algorithms are outlined. These models and algorithms are incorporated into a simulation software that is used to generate typical time histories of the spacecraft dynamical state during the landing phase.

Simple solutions for hyperbolic and related position fixes

Navigation fixed from range differences to three stations and an additional piece of information are investigated. It is shown that if the additional information is the navigator altitude, or the range difference to a fourth station, the computation of the navigation fix is reduced to finding the roots of a quadratic. If the additional information is the range to another station, or that the navigator is on the Earth ellipsoid, the fix can be obtained by solving a quartic. By emphasizing the underlying geometric interpretations, these fixes and their simple solutions are made clear. The derivations also show that the same solution algorithms are applicable if the basic navigation measurements are range sums instead of range differences.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Confidence Approach in the Dynamic System State Estimation Problem

The report considers the problem of determining dynamic plant state estimates under the influence of random and uncertain factors acting separately or jointly. The quality criterion of the estimates obtained is a probability of an estimate error not exceeding a certain pre-set threshold.In oraer to obtain these estimates, the authors sug-gest the generalized minimax (confidence) approach developed by them; the essence of this approach consists in reducing the original probability problem to an equivalent minimax problem of deterministic structure. In terms of this approach the authors present a formulation of the conditions which make it possible to generate data processing algorithms with the properties mentioned above. The authors also suggest using the optimization of the measurement procedure according to the probability criterion as an additional way of improving the estimation accuracy. In order to solve this problem, an approach has been developed which uses the analytical properties of the Riccati type equation and makes it possible to reduce the nonlinear problem of optimization of the measurement procedure in a dynamic system to a linear one with respect to phase variables. In order to obtain the optimal schedules of navigation measurement in specific engineering problems, an effective modified Krylov-Chernousko-method-based numerical procedure has been developed.

Relativistic Reduction of Astrometric Observations

The nonuniqueness of the quasi-Galilean coordinates of general relativity leads to the emergence of unmeasurable coordinate-dependent quantities in astronomical practice. One may offer three possible ways to overcome the related difficulties: 1.developing theoretical conclusions only in terms of measurable quantities2.using arbitrary coordinates and developing an unambiguous procedure for comparing measurable and calculated quantities3.agreement to utilize one and only one coordinate system.In this paper we prefer the second way. After formulating the heliocentric planetary and geocentric satellite equations of motion, the general technique for relativistic reduction in astrometry and geodynamics is developed. Specific algorithms for the reduction of absolute and relative measurements are derived for the one- and the two- body problem. For illustration, the relativistic reduction of stellar parallaxes, Doppler satellite observations, navigation measurements with the aid of satellites and radiointerferometric measurements are presented in detail.

Rotations in Navigation

Wing Commander Anderson, the author of The Principles of Navigation in which he emphasized the essential unity of philosophy which underlies all forms of navigation, has further developed this concept in two papers in this Journal published in 1980, ‘Navigational Measurements’ and ‘The Magic of Animal Navigation’ (Vol. 33, pp. 33 and 444). In the present paper he examines further in non-mathematical terms some of the difficulties met with in the analysis of rotations in navigation, including the effects of the Earth's rotation on its axis.

Accurate INS Transfer Alignment Using a Monitor Gyro and External Navigation Measurements

A particular alignment mechanization for a nonmaneuvering vehicle is described which uses a monitor gyro to estimate the slave inertial navigation system (INS) equivalent east gyro drift rate and thus improves azimuth alignment. A state-space model of the dynamic system with measurements is developed. Results of covariance simulations employing Kalman filter estimation are presented for two master INS position update scenarios, one involving frequent and very accurate updates and the other including infrequent and coarse updates. The ef fects of position updates and the monitor gyro on the quality of transfer alignment are demonstrated and analyzed.

The Role of Time in Navigation

Time is so much a part of everyday experience that no thought is normally given to the meaning of the word. The scientific measurement of a quantity such as time, however, requires the definition of a gauge as a standard of measurement that is reasonably invariant to human experience and the creation of a measurement language capable of independent empirical reproduction so that one laboratory can share experience with another using only a written language to do so.Time as a means of scientific measurement for navigation requires a further extension of this experience to independent reproduction on a moving craft.

Chapter 7 - WITHDRAWN: Navigation Measurements

This book has been withdrawn as the rights have been returned to the author.

Measurements in Navigation

Measurements in Navigation

NAVIGATION REQUIREMENTS FOR GEOPHYSICAL EXPLORATION *

AbstractMarine geophysical work requires accurate navigation on a continuous basis. A repeatability of 150 m CEP (circular error probable) with sequential positioning of 15 m CEP is usually acceptable. Quoted figures for many presently available navigation systems yield nearly the required accuracy. In actual operations, however, such accuracies may not be achieved, and usually the performance actually realized cannot be determined for want of independent measurements for comparison. If more redundancy in navigation measurements were available on an integrated basis, the limitations of individual systems would no longer be so critical and the accuracy of measurements could be assessed in real time. Failures in navigation continue to occur. Such failures usually result from ignorance of the capabilities of the navigation system and limitations and consequent choice of a system which is not appropriate to the demands of a particular survey. The points to be covered in work standards are listed.

COMPUTER SYSTEMS FOR REAL‐TIME MARINE EXPLORATION

The goals of the Gulfrex are to perform marine exploration and to conduct research and development in the various facets of marine exploration. The Gulfrex is equipped with various geologic and geophysical data‐gathering instruments along with a highly sophisticated navigational package. Computerized control systems were designed to output data in real time so that preliminary interpretations could be made concurrently with data collection. One system, based on an EMR‐6130 computer, handles multichannel seismic data. This system includes routines for real‐time demultiplexing, normal moveout, stacking, and deconvolution. Output of demultiplexed data is to magnetic tape and optionally to paper records. Output of moveout‐corrected, stacked data is to a visual monitor and to magnetic tape via a PDP‐8 computer. Deconvolution may be applied to either the single‐channel traces or the stacked traces. A moveout‐corrected, CDP group is output to a paper record every 24 shots so that estimates of average velocities can be made for a normal‐moveout correction. Another system, designed for a PDP‐8 computer, is used to collect data from devices interfaced to it. These include single‐channel seismic data, gravity and magnetic measurements, and navigational measurements such as course, speed, ship position, and direction. Deconvolved single‐channel seismic data are plotted in real time on a visual monitor along with a corrected gravity profile, magnetic profile, speed, course, and time of day. A map of the ship’s course is plotted in real time on a drum plotter Inquiries may be made of the system for current position in latitude and longitude.

One-Way Radio Range Measurements for Surveying and Navigation

Atomic clocks did reach a perfection during the last years that it becomes likely to have position fixing by such clocks in the near future. Theoretically this was proposed sometimes in the past decades. Now we have two systems used for navigational purposes, the McDonnell Collision Avoidance System, well known to air navigation experts, using crystal clocks, and a geophysical surveying system, ANA,* developed by the “Gesellschaft fur praktische Lagerstattenforschung”, Hannover, using Rubidium atomic clocks. Two ground stations are equipped with such clocks, a third is installed in an aircraft for time comparison with the ground-based clocks. The difficulty to use the mentioned systems over longer periods as it would be necessary for maritime use, consists in the synchronization. There exist some proposals, till now not realistic and rather complicated, which would render possible to extend both methods to a general use for aircraft and ships. The further development of atomic clocks seems to be very promising.

Statistical estimation in inertial navigation systems.

Although navigation systems have generally been developed by solving exactly the dynamic equations of motion, in reality the navigation problem is a statistical one since there are unpredictable errors in the measurements. The advent of very powerful navigation computers makes it possible by using statistical filtering techniques to retrieve more of the information contained in the navigation measurements. The navigation system is thus developed here as an information-filtering problem rather than a simulation of a deterministic physical system. The Kalman optimum linear filter is found to apply to the navigation problem if some technique is used to account for possible non-Gaussian maneuver accelerations. A major problem in the application of statistical techniques is the tremendous amount of computation required. Two methods are suggested which greatly reduce the amount of computation with a minimum degradation in the performance of the system. In one method, physical considerations are used to divide the total filter into smaller, simpler filters. In the other method, the optimum gains are precomputed and approximated by simple functions in the flight computer. The details are given for the alignment and calibration of an inertial platform using statistical filtering.

A study of navigation measurement schedules for LEM rendezvous.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Sextant Sighting Performance for Space Navigation Using Simulated and Real Celestial Targets

the feasibility of using a hand-held sextant for taking navigation measurements from on board a manned spacecraft is being studied at Ames Research Center. It would be advantageous to use a reliable, light-weight, handheld instrument instead of a relatively complex, vehicle-mounted, automatic or semiautomatic device for taking such measurements if it provided sufficiently accurate angular measurements. The primary objective of the Ames research program is to determine the operational feasibility, scope of application, and accuracy of the manual measurement technique. A flight simulation facility has been used for examining navigator performance and the operational problems of the sighting task with hand-held sextants. Measurements of real star and lunar landmark angles are being obtained to evaluate the problems associated with absolute sighting accuracy. The accuracy typically considered necessary for space navigation is 10 arc seconds. A sighting experiment on board the Gemini spacecraft will be conducted to examine in a more realistic environment the feasibility and operational problems of using a hand-held navigation sighting instrument and to validate the results of ground-based investigations. The purpose of this paper is to describe some results of this program.

Optimization of Midcourse Velocity Corrections

The concept of a six-dimensional state space is used to develop the fundamental equations of linearized midcourse guidance. Both fixed endpoint (fixed-time-of-arrival) and variable endpoint (variable-time-of-arrival) problems are considered. It is shown that the variable-time-of-arrival problem can be simplified mathematically by the introduction of a special coordinate system, which is called the critical-plane coordinate system.A method is developed for determining the optimum time at which to apply a single midcourse correction the effect of which is to satisfy a set of position constraints. The correction is “optimum” in the sense that its magnitude is minimized. For a given nominal trajectory, the time of the correction depends on the predicted miss vector at the destination. The method is particularly simple to apply in the case of variable-time-of-arrival guidance; by exploiting the critical-plane coordinate system, a single curve can be prepared prior to the flight to indicate the optimum correction time as a function of a miss parameter which is determined from in-flight navigational measurements.Multiple-correction strategies are then investigated. A method is developed for determining an optimum schedule of midcourse corrections. The optimum schedule is the one for which the sum of the magnitudes of all corrections is minimized. It is proved that the number of corrections in an optimum schedule is no greater than the number of constraints to be satisfied at the nominal time of arrival at the destination.In position-constrained variable-time-of-arrival guidance there are only two constraints at the nominal time of arrival; hence there are at most two corrections in the optimum schedule. The optimum two-correction strategy is compared with the optimum single-correction strategy. It is shown that for certain ranges of the miss parameter two corrections can effect a saving in total magnitude of velocity correction, while in other ranges no improvement can be obtained from two corrections. A geometric construction, based on the theory of convex sets, is used to determine the ranges of miss parameter in which two corrections are preferable, and also the times and components of both corrections when they are preferable.It may be noted that the developments in this paper are deterministic rather than statistical. No consideration is given to the uncertainties of the navigational measurements; it is assumed that a sufficient number of measurements has been made during the flight so that the error in the predicted miss vector at the destination is negligible. The control action taken is determined by the predicted miss vector.

Translunar Midcourse Guidance

Optical and midcourse guidance and navigation requirements for the lunar mission are outlined. Techniques for meeting these requirements using an on-board guidance system are briefly described. Investigation of phenomena capable of providing navigation measurements are summarized. Instrumentation for possible use in orbital and midcourse navigation sightings is gellerally described.

The Nature of Astro Doppler Velocity Measurement

This paper deals with astro Doppler velocity measurement for space vehicle navigation. The measurement yields the relative velocity of the vehicle with respect to a star, and requires the use of electro-optical systems capable of measuring a small incremental change in the wavelength of propagated stellar energy. Such systems provide velocity data whose character and limitations are a function of the star's spectral radiation as well as the system instrumentation. This paper discusses the astro velocity data, its derivation, character, and limitations; and the Doppler velocity systems, their capabilities, limitations, and possible instrumentation.

Attitude control of space vehicles

The problem of sensing and controlling the angular orientation of a space vehicle is discussed. Optical, radio, and inertial methods of angle-sensing are described, and application of control torques by reaction jets, flywheels, radiation pressure, and gravitational gradient are compared. Requirements for angular accuracy likely to be imposed by maneuvering, performing measurements for navigation, making scientific measurements, radio communication, and solar cell orientation are described. Attitude control requirements and techniques for earth satellites and deep-space probes are compared. This discussion will not be published.

Inertia Navigation Systems

The object of this paper is to present various practical solutions to the problems of inertia navigation in a descriptive rather than a mathematical form. Inertia navigation is an automatic bump of locality, a dead-reckoning device which, starting from a known point, seeks to find position. Other dead-reckoning devices measure speed, which is only relative to the fluid sea or air. Inertia navigation measures accelerations, which are absolute, and hence builds up a measure of speed. The accelerometer is, therefore, a good starting point for our survey.