Page 1 Trajectory measurements
Faculty: Radio and special training
Speciality: Technical protection of the information
Topicality. This work is devoted to research methods and data processing algorithms unsynchronized data the measurements in a secure automated measurement and information complexes.
Despite many years of experience in solving problems of processing the measurements, there is no universal method that allows high quality to process measurements in real conditions. The reason is that the real dimensions contain besides the signal is a priori unknown and a number of factors complicating the processing of measurement information. These factors include systematic and random (regular) in sinfulness, as well as the anomalous dimension. Statistical characteristics of errors of measurement, implemented in the measuring experiment, as a rule, only approximately describes the rated values. The measurement error is naturally determined by measuring the means-shaft, and the terms of the measuring experiment, which is generated by the large variety of options, consideration of which is difficult to develop a universal method of processing measurement results. Therefore, in the selected subject area is now a significant place in the processing of measurement is manual labor of skilled operator-handler. At the same time, science has led to new mathematical metods, allows the creation of new efficient algorithms for processing the measurements, such as adaptive and robust estimation, and wavelet technology, a significant contribution to the development of which have made Johnston J., Donoho D., Zhdanyuk B.F., Lawson C., Malyutin J.M., Friedland B., Hampel F., Hughbert P., Hanson. R., Ekalo A.V. etc.
Any qualitative method of statistical treatment of TRI requires knowledge of numerical characteristics of errors. Calibration of the mathematical model of error is directed at the estimation of these characteristics. Comparison of the passport of uncertainty of the measuring means with the actual evaluation can also be judged on the quality and stability of its work on the required preventive measures on it and has re-cial practical value. As a result of the processing of external tracking more accurate model of measurement error can improve the quality of results, for example, estimates of the parameters of motion of the object of research.
Applying the hypothesis of the additive model of measurement errors in the paper we consider the following of its components: anomalous (singular-molecular) measurement, regular (rapidly changing) and systematic error (Zhdanyuk, 1978), including the error of timing measurements. Research methods and algorithms for estion of these parameters on the results of measurements is the main task of work.
Purpose of the is the development and research methods and processing algorithms unsynchronized measurements in the protected-calving automated measurement and information complex.
Objective. In the process of achieving the goal of the following tasks will be:
- Review of methods of processing information;
- Modeling unsynchronized data of different types;
- Develop methods and algorithms unsynchronized data;
- Analysis of simulation results;
- Stability of the algorithm and testing of the algorithm;
Methods. We used the apparatus theory of random processes and filtering, mathematical analysis and linear algebra, modeling theory, methods of computational mathematics.
Reliability and validity of the research confirms the results of Xiamathematical modeling and experimental investigations.
The practical significance of the work lies in the fact that its findings are specifically aimed at the solution of applied problems associated with pre-treatment data and aim at increasing the accuracy and reliability of the results of treatment-trajectory measurements.
External instrumentation designed to measure of parameters of the trajectories of aircraft — the coordinates, velocity, angular position in space, etc. For external instrumentation used radio (radar, phase direction finders, radio range finders) and optical (kinoteodolity, kinoteleskopy, laser long-range action) means. Optical means external instrumentation have high accuracy, but their use is limited to weather conditions, radioteckhnical means, yielding an optical exactly, independent of meteoevents, have a lot of modifications and widely used.
Modern means of external instrumentation characterized mnogoparametrichnostyo (measured not just contacts, but also forming the velocity vector, the difference of the coordinates, etc.). multi-channel (ensures a means of measuring the parameters of multiple vehicles), long-range, high accuracy, reliability, as well as the degree of automation enables data processing on computers and gain parameters of the trajectory of the aircraft to recially time. Placement of external instrumentation than on earth, but on a special plane — airplane command post — provides a significant expansion of the zone of their action, conduct test flights of aircraft with the measurement of the trajectory in any region of the country (without the creation of ground measuring trace). However, this is significant, but degrades synchronization external instrumentation and the definition in the location of airborne command post in the space.
Using indirect measurement tools can determine the primary parameters — the components of position vectors and velocity of the aircraft (the viewing angle, distance, direction cosines of the angles of sight, the derivatives of these quantities) — and for them depending on the method of measuring the trajectory parameters are calculated trajectory of the aircraft. The method of measurement (direction finders, rangefinder, azimuth, rangefinder, the difference-rangefinder) is selected depending on the required accuracy of the trajectory parameters and test areas. Direction-finding method for external instrumentation is based on measuring the direction of the line of sight of the flying machine by two means, remote from each other at a distance, called the base; realized kinoteodolitami or phase direction finder. Azimuth-range-finding method is to determine from one measuring point vector components of the aircraft in the polar coordinate system is implemented or radar range finder and Rain-optical means to measure the angular position. Ranging method (or its modification — rangedifference method) is implemented by three or more range finders, remote from each other.
If the composition of primary parameters does not include derivatives, the velocity of the aircraft is calculated by differentiating the coordinates.
Be exposed to radiation and all the other goals and, in particular those which are located the same distance from the radar station (call these goals, for example, 2 and 3) as the test target 1.
Naturally, the radio waves reflected from the targets 1, 2 and 3, simultaneously reached the point 0, where the radar station. In this case, the signal at the point 0 there is a simple addition of three signals. This value-cheat, and that the total signal would also have the same form as the representation-tion, whether present or absent detectable target.
This means that regardless of the situation, the presence or absence of targets in the general case at the entrance to the radar receiver is always a signal of the same species-quasiharmonic oscillation.
Let us now consider the processes occurring after is pre-excitations of received signals of antenna paths and entering it on the input pa-diopriemnogo radar device.
Since the radar has to deal with very low signal, whose intensity is comparable with the intensity of their own noise-atoms of the radio receiver radar (often a useful signal even multi-th lower noise signal), we must bear in mind that the input of the radar tional receiver is constantly affected by the noise signal, which, as it follows from the general theory, also has a kind of quasi-harmonic oscillations. Moreover, its amplitude and phase are random functions of time.
Therefore, in all cases related to the presence or absence of targets, even in cases of monitoring free space on the entrance radio receiver radars are always affected by a quasiharmonic oscillation with random amplitude and phase.
Represent the signal, affecting the input of the radar in the form of two components, first of which relates to detect signals, the second to all OS-gations, including the noise signal.
From the foregoing it is clear that strictly to solve the task Principles-cially impossible, especially on the results of any single measurement in a fixed time.
First, we note that accurately answer the question is whether or not a permitted purpose elements are found, essentially impossible. This answer can only be the nature of the assumptions of quantitative estimates of mi which may make some probability reliability of this assumption. Consequently, an adequate mathematical apparatus for detection problems, and the majority of radar targets, can methods of mathematical statistics and probability theory.
Second conclusion to be drawn from the review is that suf-faith opinion of the value of the parameter n can be increased by increasing the observation time, ie, increasing the interval functions Uin (t), are analyzed.
Finally another conclusion that can be done by analyzing a common position equation, lies in the fact that the difference in the form of functions Uin (t) in the presence or absence of goals is the difference between statistical laws that govern the random functions Uin (t).
Try to figure out what principles should lay in the processing of the received signal to an error committed in this case in response to a question on whether the goals were somehow, and this will try to understand the types of errors that will inevitably arise in the process of deciding on the presence or absence of target.
To understand the emerging types of errors, consider a simple situation where the background reflections are missing or they simply can be ignored.
Let radio transmitter radar produces some processing of the received signal. In this case, the output of the receiver signal is formed, which is a function of the additive mixture received signal and intrinsic noise receiver. This enables the amount of output voltage is represented as follows: Uout (t) = f (Un (t) + nUs (t))
In this formula, Un (t) — intrinsic noise the radio receiver is always present in the mixture and is always applied to the input of this mouth-nal; Us (t) — signal caused by the reflection of detectable targets, which is present in mixture called only if the target (n = 1) in The observed resolution element.
Whatever the function f (z), in all cases, the decision about the presence or absence of targets will be taken at some fixed instant of time t = t1, that is, as a result of a single measurement. Writing is a strict answer to the question 'What is the ratio n, the principal is not possible. How to be in this case? What should be the decision rule? Surprisingly, the answer to the second question, regardless of the method of receiving ICDO-signal (a function of the form f (z)) is quite simple and obvious. The only possible decision rule may be made only by the threshold rule. It boils down to that if the input voltage Uin (t) is greater than some value (threshold) U0, then it must be assumed that the goal is, but if there is a reverse situation, you should recognize that no goal.
Dismantled the situation allows us to see that the procedure for making D-tion at a threshold rule, ie the process of discovery, accompanied by errors of two types. Consider these errors.
With radar observation two situations: the first - in the resolution element is a target (situation A), second — in an element of an authorization no goal (situation B). In both cases, the observer can take the one-but two solutions: either the goal is (decision 1), or it does not exist (decision 2). In this way, four possible options which can be conventionally denoted as: A1, A2, B1, B2. In this case two solutions — the A1 and B2 — are true, and the other two — A2 and B1 — false.
So, we are dealing with two types of erroneous decisions: 1) False alarm, when in the absence of a resolution element objectives adopted a decision on its availability (option B1, corresponding to the probability is the probability of false alarm, it is usually denoted by the letter F). 2) Skipping purpose as when in the presence objective decision about its absence (option A2; the corresponding probability is the likelihood of missing targets, it is usually indicated by the difference 1 — D).
Two other solutions are true. 1) The correct detection, when the presence of objective decision about its availability (option A1; the corresponding probability is the probability of a correct detection, it is usually denoted by the letter D). 2) Correct failure to detect when the absence of objective decision about its absence (option B2, the corresponding probability is the probability of correct detection, it is usually indicated by the difference 1 — F).
Whatever the goals and objectives nor stood in front of the radar, in all cases desirable to as little as possible to take wrong decisions. However, the threshold decision rule before the observer is the one and only one opportunity to "influence" on the situation: to change the value in the Horn of U0. Consider how the value of U0 affects the probability of false decisions listed above.
Growth threshold U0 naturally leads to a decrease in ve-probabilities of false alarm, but leads to an increase likelihood of missing a target. Conversely, reducing the threshold U0 reduces the probability of crossing targets, but entails increased the probability of false alarm.
Next major challenge facing the radar, is to ensure the accuracy of measurement of basic parameters and characteristics of the reflection of charged radio signals, indicating the spatial coordinates and the speed you radar targets, as well as the distance to that goal.
Detection of radar targets, as already mentioned, depends solely on the energy of the reflected signal does not depend on its form and shape. The accuracy of measurement parameters and characteristics of the receiving signals depends not only on their energy, but also on the shape of the transmitted signal. From the general theory that in order to ensure precision the definition of distance and speed of radar targets, the emitted signal must have as much as possible the length of time and have the widest possible spectrum. (The latter requirement means the complexity of the form of the signal, its as if the greatest difference from the very basic radar signal, which is the normal sinusoid.) Satisfies these requirements satisfy the so-called complex signals, which include the linear frequency-modulated signals, signals with a phase manipulation, noise-like signals and several others. Development and application of such signals, special sections devoted to radar. The impossibility of presenting all the problems of radar in one article does not allow more residual novitsya on this issue. Note the paradox, that the best criterion for the accuracy of simultaneous measurement of long-range Step up to the goal and its speed is the ideal noise signal.
Increasing the duration of the regular (smooth) can increase the pulse-lichit range and uniqueness of the measurement of velocity (as well as the accuracy of the measurement of angular coordinates), but reduces the resolution and accuracy of the measurement range. A radical way to solve this contradicts — the transition to complex signals.
To improve the accuracy of distance measurements by use of complex signals used pulses with linear frequency modulation (LFM) and phase-shift keyed pulses. The application of pulses with chirp improves resolution and accuracy of measurement distance obtained; same resolution and accuracy of measurement speed without deteriorating.
In nonlinear reflection from the object of artificial origin-tion spectrum of the signal into the realm of the second, third, fourth harmonics. Naturally, the width of the spectrum of the reflected signal is used in the nonlinear radar, will be greater than that of the transmitted signal at its of basic frequency. It is obvious that an increase in the spectrum, increases base signal, and hence the compression ratio of the radio pulse with chirp. This in turn provides an additional improvement in resolution and accuracy of measurement range without sacrificing resolution and accuracy for speed.
During the work it was found that the width of the spectrum of the reflected signal, is n times larger than the width of the spectrum of the probe signal (n — number of harmonics), however, the lowest RMS estimates range achieved with discoveries of objects at the third harmonic radiating wave.
In nonlinear radar signal to noise ratio at the harmonics is usually very small. However, it is known that during the passage of signal through a nonlinear element changes shape law distribution of the envelope of the noise source. This property can be put in a basis new method of detection of objects with non-linear electrical characteristics, was to compare the degree of differences in implementations of noise probing signal and the signal response.
Advantage of this method of detection of non-linear object is the reception at the fundamental frequency signal. The latter allows to significantly simplify the procedure for optimal on-processing signal in the receiving part of the detector and to avoid a significant reduction in SNR.