METHOD OF ASCERTAINING NAVIGATIONAL INFORMATION

Abstract: A method is disclosed of ascertaining navigational information for at least one mobile platform (81) in terms of at least one angular coordinate by transmitting a signal having defined characteristics from at least one transmitter (20, 83) and receiving with at least one receiver (22).

Description: This invention relates to a method of ascertaining navigational information. According to Karwarth in the Journal of the Institute of Navigation , Vol. 24, No.1, pp. 105-120, January 1, 1971, the basic objective of area navigation is to position in real time with appropriate accuracy one or more mobile platforms with reference to some known coordinate system. The number of coordinates needed depends upon whether the course of the mobile platform can be charted on a known surface or must be described in three-dimensional space as in the respective cases of a ship at sea and an aircraft. The ability to chart a course based on past, present and future desired positions is a principal element in distinguishing an area navigation system from navigation using point-to-point or "homing" approaches such as VOR/DME (VHF Omnidirectional Range/­ Distance Measuring Equipment). Positions are established in all cases by signal transmission between the mobile units and at least one transmitter of known location. The transmissions can be electromagnetic (including optical) or acoustic in any medium including air. Two basic methods are normally used to obtain positions: Positions may be determined from a sufficient number of range measurements to known reference locations by using what is commonly known as "range -range" systems, or positions may be determined from a sufficient number of range differences to known reference locations, by using what is commonly known as "hyperbolic"systems. In each case a sufficient number is at least equal to the number of coordinate values needed. Direct ranging involes calculation of inter­ sections of the circles or spheres of uniform range from each reference location to the mobile unit. By contrast, the locus of equal range difference from the mobile unit to a pair of reference locations are hyperbolae or hyperboloids of revolution. Again, positions are calculated by intersection of curves or surfaces, but in this case related to the hyperbolae, hence the name hyperbolic systems. An exemplary task of area navigation might be the positioning of a ship at near shore distances. In range-range operation only two shore stations are needed while a hyperbolic system requires three. Three shore stations admit calculation of two independent range differences. As a general rule, hyperbolic systems offset a disadvantage in requiring one or more known reference location than the simpler range system by not requiring either a time standard or an active transmitter on the ship. As for the transmitted signals, a variety of differing modes of operation are possible. Ranges can be determined from signal transmission time between the mobile unit and a reference location if the signal initiation time is known, a time standard is available, and a signal propagation velocity is also known. The simplest means for establishing known initiation times is to transmit signals only in response to some interrogation. Alternatively, if trans­ missions are synchronized to occur at regular time intervals, time differences are readily determined, with no interrogation step needed, using only a local clock and a propagation velocity. Again, signal transmissions themselves can consist of continuous waveforms (typically sinusoids), intervals of continuous signal transmissions, or sequences of pulses. The choice of transmitted signal reflects consideration of the information desired, mode of operation (range-range versus hyperbolic), noise effects, and the extent of Doppler distortions among other factors. Continuous waveforms are the most robust signals in the presence of noise backgrounds since correlation-type receivers may take advantage of the extreme signal duration. Such signals have no resolution in time and are used principally with hyperbolic systems to establish time-differences by making phase comparisons with reference signals. Where the transmitter-receiver relative velocity is not insignificant in proportion to the signal propagation velocity, Doppler effects shift the frequencies of continuous waveforms. Frequency shifts may be viewed as errors since they distort subsequent correlation steps and thus degrade phase comparisons; however, if such shifts are measured, they do relate to velocity information should this be desired. Use of continuous signals over intervals provides time resolution as well as opportunities for correlation detection, but over shorter data windows. Again, any Doppler effects may be viewed either as constituting an error in range determination or if measured, velocity infor­ mation. The tolerance of such signals to noise effects is of course diminished in direct relation to their shortened duration. In the limit, as duration is shortened, pulsed signals must be considered which when taken individually offer no opportunity to measure Doppler effects. Hence significant transmitter-receiver relative velocities will be noted as range errors for such systems. These signals are also most affected by the presence of noise, but afford the greatest resolution in making a direct time measurement. It follows that the alternative methods of operation that exist constitute attempts at optimizing a number of trade-offs which interact with some complexity. The hardware requirement, operations costs, efficiencies and effectiveness in terms of achievable accuracy are all essential ingredients that play roles in the optimization. Navigation systems based on the present invention may generally serve as replacements for such systems and others. The present invention involves the application of dis­ persion to signal phase. The phenomenon of dispersion is well known in optics. By way of an appropriate background regarding this principle in order to understand its application to the present invention, an appropriate definition of dispersion, a presentation of the distinguishing characteristics of normal and anomalous dispersion, and a description of various embodiments of dispersion may be found in Sommerfeld, Mechanics of Deformable Bodies , Acadmic Press, New York 396 p, 1950 (see in particular pp. 172-206, 2nd printing 1956), and Longhurst, Geometrical and Physical Optics , Longman, 592 p, 2nd Edition, 1967 (see in particular p. 452 and Fig. 20-4). It is necessary to distinguish also the phase-angle rotation undergone by a signal in traveling through a dispersive medium or in post-critical angle reflection from a mere time delay. If the angular frequencies contained within the spectrum of a signal having bandwidth range from a value ω₁ to a greater value ω₂, the phase spectrum of the signal over that range will be some function f(ω), ω₁ ≦|ω|≦ω₂. After traveling through a dispersive medium the change in phase of the signal, which characterizes the degree of dispersion, can be described in first approximation by Δf(ω) = ϑ₁ + ϑ₂ ω where ϑ₁ and ϑ₂ are constants which depend only on the medium and the distance travelled within the medium. The value of the constant ϑ₂ describes the delay of the signal, that is, it is the increment of time that the signal has undergone in traveling through the medium or simply the signal travel time. The phase angle rotation is given by the value of the constant ϑ₁. Because phase is an angular measure, two signals of like amplitude spectra whose phase spectra differ by an integral multiple of 2π are identical and hence indistinguishable. It is therefore customary to replace any value of ϑ₁ that is equal to or greater than 2π by the residue of ϑ₁ modulo 2π or in common terminology by the remainder after dividing ϑ₁ by 2π. Values of ϑ₁ modulo 2π other than O andπ correspond to changes in the signal shape. According to the present invention there is provided a method for ascertaining navigational information for at least one mobile platform in terms of at least one angular coordinate by transmitting from at least one transmitter and receiving with at least one receiver at least one signal which is not a member signal but which can be transformed to a member signal by a linear filtering operation, the signal having a band of contiguous frequen­ cies with no frequency missing over a defined frequency bandwith, the method comprising the steps of: changing the shape of the signal by encoding a distinction in phase over a plurality of individual fre­ quencies of the band of contiguous frequencies in accor­ dance with at least one angular coordinate of navigational information, while propagating the signal from the trans­ mitter to the receiver; receiving the propagated signal, measuring the phase of the received signal, and decoding the angular coordinate from the encoded distinction in phase. Certain of the signal processing techniques used for this invention may conveniently employ the methods described in US-A-4114153 to which attention is directed. The term "member signal" is defined below. Signals which are member signals or which can be transformed to member signals are referred to generically herein as "constituent signals". The description refers for simplicity to the use of signals which are member signals, but it is to be noted that the invention as claimed is limited to signals which are not member signals but which can be transformed to member signals by a linear filtering operation. Component signal trains of constituent signals convey all of the navigational information. The component signals which may be concurrently propagating are always separable and distinguishable from one another by some combination of frequency content, polarization character, and constituent signal pattern. Member signals formed after reception and preliminary processing are made up from base signals which are required in accordance with the present invention to have four basic properties to be discussed below. Broad-beam, broad-band transmitters produce component signals which illuminate the navigation area. Broad-beam, broad-band receivers detect these signals. Angular coordinate information is phase encoded in constituent signals by reflective or transmissive mechanisms. All encodings can be substantially characterized by an additive increment to the phase angle consisting of a constant and a second complementary constant which multiplies the frequency. This approximation to the phase effect of dis­ persion is essentially the first two terms of a Taylor series developed over frequency, the independent variable. In effect, the shape of a constituent signal is changed by encoding a distinction in phase in accordance with the angular coordinate information. Angular coordinates are referred either to receiver or transmitter locations, and either the receiver or the trans­ mitter can constitute the known location, depending on the particular embodiment. Component signal transmissions can be sent in response to interrogation, at regular time intervals or at random, depending on the selected mode of operation. In all cases the angular coordinate information will be conveyed by the distinction in phase which changes the signal shape. Processing the received component signals to identify constituent signals may be described after formation of member signals by a phase-invariant quadrature-matched-filtering operation which is described in the above U.S. patent. Member signal basic properties and processing of the re­ ceived component signals are complementary in that frequency shifts resulting from relative motion between the transmitter and receiver affect neither the arrival-time measurements nor the phase-encoded angular coordinate information. The processing includes measurement of member signal phase and a decoding from the measured phase of the encoded angular coordinate information. Radial/relative velocity components or relative velocity information between mobile platforms and a known location and radial range or distance information may also be conveyed by the component signals. Such determinations are possible if the initial time interval between constituent signals, the initiation times of constituent signal trans­ missions, the signal propagation velocity in the medium, and a time standard are known or predetermined. Having both range and angular coordinate information allows development of a navigation system which can operate using only a single base station. Since utilization of phase information is an important feature of the invention, several corrections to compensate for phase distortions are included. Distortions accompany­ ing member signal design and entering during processing are some which fall in this category. The broad beam nature of the transmitters used in this invention suggests lower signal energy levels in any particular direction than might be achieved with a narrow beam system. Rapid repetition of these broad beam signals can however overcome an energy-level deficit. Further, the ability to impart angular coordinate information offers opportunities to overcome ambiguities of skywave reflections in electromagnetic embodiments and multipath reflections in sonar application. By encoding sufficient redundancy in the constituent signals, any phase distortions imparted by the propagation medium may be measured as a part of the decoding operation. This feature adds significantly to the present invention. The ensuing description includes a description of how the phase distortion for sound waves caused by propa­ gation in water for frequencies in the vicinity of 1.2 mhz can be characterized as a function of the propagation path length. In the accompanying drawings: Fig. 1 shows the time and frequency domain properties of a design base signal pair having respectively odd and even symmetry; Fig. 2 shows schematically a generalized system having a single transmitter and receiver for carrying out the method of the present invention; Fig. 3 shows a processing sequence for the embodiment of Fig. 2; Fig. 4 shows the sequence of operations of the naviga­ tional information estimator of Fig. 3; Fig. 5 shows an elementary electromagnetic area navi­ gation system having a single base station; Fig. 6 shows schematically binary encoded member signals at known intervals for establishing time references; Fig. 7 shows an experimental apparatus used to characterize the phase distortion caused by the dispersive properties of water at 1.2 mhz; Fig. 8 shows digitized received member signals for the apparatus of Fig. 7, after transmission through water, and their frequency analyses; and Fig. 9 shows experimental results indicating the relationship of the phase distortion of member signals at 1.2 mhz with their propagation distance through water. Fig. 1 shows a pair 10 of base signals 11, 12 from which a member signal may be designated. A single member signal is formed as a linear combination of a pair of base signals as defined in above mentioned US-A-4114153. In mathematical terms this signal f(t) may be defined: f(t) = m f o (t) + n f₁(t), (1) where m and n are constants obeying the relationship m²+n² = 1, and f o (t), f₁(t) represent the base signals. The four requisite properties I-IV of the base signals f o (t) and f₁(t) are: I. f o (t) and f₁(t) share the common amplitude spectrum F(ω) 13 which is substantially flat over both its continuous bands at positive and negative frequencies and is essentially zero elsewhere. II. There is a finite time interval of duration α, before and after which both f o (t) and f₁(t) may be considered to be zero, in other words f o (t) and f₁(t) are pulses. III. f o (t) and f₁(t) are in quadrature or constitute a Hilbert transform pair. In other words, at each common frequency component the signals differ in phase by ninety degrees. IV. f o (t) and f₁(t) must be transformable to odd and even functions respectively about t = o, defined as the central coordinate value in their interval of definition of duration α, by a constant phase shift applied to all frequencies. Signals termed Klauder signals and Gabor signals described in applicant's referenced patent are in fact representative types of signals appropriate for use as the base signals f o (t) and f₁(t). Mathematically these two signal types are defined as: Returning now to Fig. 1 (which corresponds to Fig. 12 of my referenced U.S. patent), there is shown a diagram of the time domain (10) and Fourier frequency domain (14, 15) properties of the Klauder base signal pair termed f o (t) (refer to Equation (2A) which illustrate the four requisite properties (I through VI) for base signals. It is important to recognize that any signal which occupies a band of contiguous frequencies having no fre­ quency missing over the defined bandwidth, or a signal which has frequency bandwidth, can be simply transformed in character to that of a member signal by a linear filter­ ing operation. As a member signal it will have a structure as described in terms of a base signal pair. The filters described by Wiener in Extrapolation, Interpolation and Smoothing of Stationary Time Series , M.I.T. Press, Cambridge, 1949, are particularly suited to such task. Hence any signals having frequency bandwidth may be employ­ ed in the manner of this invention by including as a step in the processor a transformation of that signal to member signal character. For clarity of presentation the embodiments included herein will be described in terms of signal transmissions having the form of member signals. It will be readily understood by those skilled in the art that each embodiment may employ appropriate signals of more general nature by providing a suitable linear filter operation step in the processor, and the claims herein are directed to this possibility. Figure 2 shows a generalized system for carrying out the present invention, which employs a single transmitter 20 and receiver 22. The transmitter 20 produces at least one component signal 25. A component signal is a train of member signals which is always separable and distinguisha­ ble from other component signals by some preselected combination of frequency content, polarization character and member signal pattern. In cases such as for sonar signals where the polarization character is alike for all signals, the polarization character drops out as a possible distinguishing feature. A discussion on polarization character or state is presented by A.S. Marathay in Optical Engineering, Vol. 15, No.4, p. SR 80-81, July-­ August, 1976. For the navigation system of Fig. 2, it is required that a transmitted component signal 25 be received directly, but that somewhere along the propagation path a mechanism interacting with the signal phase be encountered. Such an element can be a phase lens or phase encoding mechanism. Element 21 performs this function. Component signal 25 which propagates with known velocity encounters phase encoding mechanism 21 and is subsequently received by receiver 22. The received component signal 26 is forwarded to the processing sequencer 23 and processing outputs are sent on to the navigational information estimator 24. The role of the phase encoding mechanism 21 is to encode in each member signal information about one or more angular coordinates as a phase distinction. Also, the phase distinction for each angular coordinate must be unambiguously related to that coordinate. Further, the phase distinction over the applicable frequency band for any given value of the angular coordinate must be repre­ sentable in good approximation by: G(ω) = ϑ o + ϑ₁ω (3) where, ϑ o is constant phase, ϑ₁ is a complementary constant multiplying the angular frequency ω. ϑ o , ϑ₁ are functions of the angular coordinate thus making G(ω) a function of the angular coordinate. The code for the angular coordinate is contained in the explicit relation between the coordinate and G(ω). Property I as given earlier for the underlying base signals must be substantially retained even after the action of the phase encoding mechanism 21. Equation (3) will be recognized as comprising the first two terms of a Taylor series expansion. Hence the character of this approximation is based upon development of the received member signal phase spectrum as a Taylor series with truncation of the series after the second term. For the i th member signal of a component signal, the following notation will be used: ϑ io + ϑ il ω to approximate the measured phase. Attention is directed to European Patent Application No 81305350.1 (EP-A-0056517) from which the present application is divided and in which are described various phase lenses which may be used in the method of the present invention. The phase lenses may phase encode the outgoing signals or the incoming signals. The phase lenses disclosed in EP-A-0056517 encode the transmitted signals by propagating them through a dispersive medium so that the degree of dispersion varies in accordance with the angular coordinate, or by reflecting them from a surface at an angle beyond the critical angle. The navigational information for the generalized embodiment of Fig. 2 can be recovered by processing the received component signal 26 through the processing sequencer 23 which is shown in detail in Fig. 3. In Fig. 3 each member signal of the pattern within each component signal must be identified and timed. The mathematical analysis of the operational sequence is given in my referenced patent. Such analysis describes how basic properties I through IV enable individual member signals to be identified and correctly retain arrival time and phase encoded angular coordinate information in spite of appreciable distortions which may be present owing to relative motion between the transmitter and receiver. Also, a phase-invariant quadrature matched-filter process­ ing sequencer employing analogously designed signals was described by Speiser and Whitehouse at a symposium on Spread Spectrum Communications held at the Naval Electronics Laboratory Center, San Diego, March 13-16, 1973. Member signals are identified for each of the significant peaks detected by element 57. Arrival times can be computed for each member signal with the use of a time standard; however, signal transmission times only can be determined if the signal initiation times are distinct and known. The phases of the member signals can be computed using the alternatives represented by elements 58 and 59. If the method using arctangents of ratios by element 58 is elected, then if more than single member signal is involved, these must be in quadrature. Again, the applicable signal processing is given in the above U.S. patent. The navigational information estimator 24 of Figs. 2 and 3 is outlined in detail in Fig. 4. In both Figs, 3 and 4, a subscript, or the first subscript of a doubly subscripted quantity refers to the number of an individual member signal of the pattern within a component signal. Processing sequencer outputs 60 and 61 are both arrival times t i for the member signals and their phase functions. Since the two term Taylor expansion will be taken to approximate the phase functions, these quantities will consist of either the constant terms ϑ io if the calcula­ tion of 58 is used, or both ϑ io and ϑ il , if the alterna­ tive 59 is selected. The constants are complementary in that should the ϑ il not be determined as in the calcula­ tion of 58, they will nevertheless be known by prior measurement or theoretical calculation and so can be supplied by alternate means should this be required. Element 62 of Fig. 4 calculates member signal interval times. If interval times 71 are initially pre­ determined, then in conjunction with the signal propagation velocity V of the medium 75, radial relative velocity components can be calculated according to element 63. Signal transmission times can be computed from the member signal arrival times t i as in element 64 if member signal initiation times 72 are known. Such transmission time is corrected as indicated for phase terms linearly varying with frequency (elements 73, 72). Among such correction terms would be ϑ il which are either measured or complemen­ tary known as previously discussed, and any linear phase terms of the encodings. Radial range estimates between transmitter and receiver can be made according to element 65 using any computed signal transmission time T i (from element 64) and correcting for the signal propagation velocity in the medium. Provision is made in 65 for any known radial/­ relative velocity component as may have been previously determined by element 63. The decoding of the angular coordinates of element 66 is relatively straightforward. First, correction is made to the measured constant phase for any constants introduced by the base signals (element 77). Such constants might result from the use of a pair of base signals rotated in phase by a constant X from base signals as defined having symmetry and anti-symmetry properties, respectively (Property IV). Also, the base signals used in the process­ ing sequencer 23 may contribute constant phase modifica­ tions to the measure member signal measured phases. If a single angular coordinate is encoded in each member signal, only the measured phase need to be associa­ ted with the angular coordinate via the known code imposed by the phase lens according to the present invention. Where more than one angular coordinate is encoded in each member signal, a somewhat more complex, but simultaneous decoding scheme is employed as described in the echo location embodiment shown in Fig. 7 of my referenced U.S. patent. In this case at least one angular coordinate must be encoded differently in different member signals. Also, the codes must be independent and at least sufficient in number to permit a simultaneous solution for the angular coordinates. If there are redundant codes, a least squares solution can be applied. The following exemplary circumstance is illustrative of a situation where more than one encoded angular coordinate is present. Assume that for two member signals which constitute a component signal, the measure constant phases ϑ oo and ϑ₁ 1 are determined. The two angular coordinates which are encoded are  o and ₁. The constant phase encoding for  o will be taken as  o /h o for both member signals, where h o is taken as a known constant. For ₁ on the other hand, the encoding will be ₁/h₁ for the first member signal and ₁/h₂ for the second one, where h₁ and h₂ are known constants. Now the measurements ϑ oo and ϑ₁ o may be related to  o and ₁, by the simply developed set of equations: Simultaneous solution of equations (4) gives: which is the desired simultaneous decoding. The embodiment of Fig. 2 has been set forth in generalized terms since in navigation applications the present invention may be practiced when either the receiver 22 or the transmitter 20 is at a known location. Further, with the present invention, the component signal may be sent off in response to interrogation or at regular intervals. Also, the nature of the particular signals sent may be either acoustic or electromagnetic (including optical). Further, the same or other trans­ mitters may be used to produce other component signals concurrently, and that these other component signals can be received and processed in an analogous manner to give still other estimates of navigational information. Since viable navigation systems of this type (as described by Fig. 2) may operate according to any or all of the possibilities cited above according to the principles already set forth, a specific illustration of one alter­ native from the foregoing embodiments is given to help in understanding the present invention. Fig. 5 shows an elementary area navigation system having a single base station 80 at a known location. Receiver 22 onboard mobile platform (i.e. an aircraft, ship or other vehicle or vessel) 81 is able to establish bearing angle , radial range, and radial velocity with respect to this base station. The navigation area is defined by two limits, the first comprising a line 84 of zero phase distortion in which the reflection is precisely at the critical angle, a second line 85 being defined by the effective physical limit of a reflector 82. Between limiting lines 84 and 85 there is a constant phase encoding ϑ o that varies with the bearing angle . The encoding of a distinct phase according to the bearing angle  is established by reflective means 82, the critical angle for the particular reflective material being β c . A broad band source 83 of pulsed electromagnetic radiation is required. Such a source for signals having frequency bandwidth may be designed employing principles analogous to the Travitron developed by Ikor, Inc., of Burlington, Massachusetts, which was reported by the New Scientist, p. 285, August 6, 1970. Source 83 of Fig. 5 sends binary encoded pulses trains of member signals which repeat on a five minute clock cycle that is precisely controlled. The pulse sequences are sent at five-second intervals according to the code shown in Fig. 6. Seven time slots or windows are defined to apply for each pulse train sequence. The first read-in or clocking window 101 is always occupied by a pulse 111. The other time slots 102 through 107 represent successive powers of two from 2⁰ to 2⁵. The absence of a pulse in any slot represents a 0 in the corresponding position of the binary code. The presence of a pulse 112 represents a 1. Thus for example, at the line representing a time of two minutes, zero seconds of the five minute clock cycle the decimal representation of the assigned binary code is 25 and is represented by pulses (i.e. ones) in slots 101, 102, 105, 106 and the absence of pulses in slots 103, 104, and 107 to yield the code sequence 1100110 which, on inversion to customary numerical order and removal of the lead-in one, yields the equivalent binary number 11001. Note that the time of member signal initiation can be determined by simple recognition of the binary code. If a mobile platform remains stationary for several intervals at a known location, sufficient information will be received to calibrate a relatively low quality (and correspondingly inexpensive) time standard. With such a calibration achieved, the member signal initiation times are subse­ quently known. Each of the component signal trains consists of no less than two member signals, and each signal is of a nature previously described (Properties I through IV). An appropriate frequency band in the case of electro­ magnetic near shore navigation might be 100-500 mhz. The system shown in Figs. 5 and 7 thus require no interroga­ tion of the transmitter and can provide redundant naviga­ tional information by the conventional range-range approach, should there be additional base stations. From the foregoing description alternative imple­ mentations of the generalized embodiment of Fig. 2 using transmitter interrogations, or having known receiver locations and mobile transmitters, or employing only the encoding of angular coordinates will become readily apparent to those skilled in the art. Again, it is important to emphasize that methods employing phase encoded angular coordinates according to the present invention may be used with conventional approaches such as the range-range operation, where more than one range determination may be made, and that standard statistical procedures for combining and up­ grading the accuracy of redundant measurements may be employed. It is useful at this point to relate features of the present invention to the considerations presented in the background for the invention. First, although member signals are pulse-like, they still are of sufficient duration to benefit from correlation detection, but also to suffer from Doppler distortions. Hence, a phase invariant correlation and detection scheme which com­ plements the signal design is employed. If velocity information is desired more than one member signal is required. While sequences of member signals provide good redundancy and signal-to-noise ratio advantage, their very duration limits the ability to resolve changes in the relative velocity if this too is changing. The defined class of member signals and signals which can be processed to be member signals have a remarkable ability to bear angular coordinate information as a distortion-resistant phase encoding. Several important practical advantages accrue to this invention owing to this ability and two particularly sophisticated extensions of the basic generalized embodiment of Fig. 2 will be described below. Certain practical matters first should be taken into consideration. A rather standard approach to developing angular coordinate information in the prior art is to scan in the sense of the angular coordinate with a narrow beam transmitter, as in the case of a conventional radar system. Use of the narrow signal beam allows great concentration of signal energy, and has consequent advantages in noisy environ­ ments. One disadvantage, however, is that the time duration of the scanning cycle may leave portions of the navigation area without signal coverage for unacceptable time periods. The system of the present invention is omnidirectional or at least broad beam by nature. Any diminution of signal level accompanying this feature may be overcome by frequent repetition of the signal patterns over time and the develop­ ment of statistical models relating the information from one time to the next. In fact, the work of R. E. Kalman as reported in the Journal of Basic Engineering (ASME Trans­ actions), Vol. 82, Pages 35-45, 1960, and the subsequent work on Kalman filters by others offers an ideal analytical vehicle to update the navigation information display 67 of Fig. 4. The navigation system described herein would at no time leave the navigation area without signal coverage for any significant time period. Also, the ability to label the signal transmission paths with angular coordinates will solve an important problem occurring in long range navigation systems that use either electromagnetic or acoustic signals. For electro­ magnetic signals the skywave or ionospheric reflection sometimes may not be readily distinguished from directly transmitted signals. Submarine navigation systems similarly have multipath signal arrivals caused by reflections from the surface and bottom of the sea, which similarly may not be conveniently distinguishable from direct transmission paths. With the present invention, direct signal paths can be distinguished from secondary paths in terms of an angular coordinate, so that a new basis for identification of the direct signal is developed. It follows from the ability to label signal transmission paths with angular coordinates, that a mobile platform such as shown in Fig. 5, once positioned, may position other mobile platforms relative to itself from their reflected signals or echoes. The transmitter and mobile platform carrying the receiver being at known locations constitute an echo location system. Finally, one must consider the possibility that phase distortions may be impressed into the member signals by properties of the signal propagation medium itself. The presence of such distortions may not necessarily be anticipated or even recognized. An excellent case in point involves the use of water as a propagation medium for acoustic signals centered around the frequency 1.2 mhz. Such transmissions are often used as small scale simulations of radar and microwave systems. An experimental study using the techniques of this invention will be described below and documents and measures the hitherto undetected phase distortion or dispersive property of water at the cited frequency. In this study, the constant phase term, which will be taken to characterize the phase effect of water as a disper­ sive transmission medium, was sought for the frequency band 0.95-1.45 mhz (roughly centered about 1.2 mhz). For the range of water transmission paths between two and seven centimeters in length, the constant phase distortion was estimated to be 16.7°/cm. Figs. 7, 8 and 9 describe this particular study. Fig. 7 shows a schematic arrangement of the apparatus. A Datapulse Model 101 signal generator 120 was used to drive a transmitting transducer 121 which sends a narrow acoustic beam to a receiving transducer 122 through water 123 in an immersed open glass tube 124. Transmitter 121 and receiver 122 were crystals having circular faces 1.905 centimeters in diameter, while the glass tube inner diameter measure 3.175 cm. Received waveforms were recorded on Polaroid photographs from a Tektronix type 561A oscilloscope 125. The wave forms were subsequently digitized at a sample interval of .122 µ-­ sec using a Wang calculator (not shown) with an interfaced digitizer (not shown). Fig. 8 shows plots of the digitized received member signal waveforms for propagation distances from zero to ten centimeters through the water. Owing to the physical size of the transducer, only distances beyond 1.5 centimeters become representative of the far field signal transmissions. Also, owing to the transducer beam width, results beyond 7.5 centimeters may be expected to show tube sidewall inter­ ference effects. In Fig. 8 amplitude and phase spectra are also shown for the received member signals. The origins for the phase spectral calculations are the time samples at or just before the member signal origins as would be determined following the processing sequence of Fig. 3. In this case, the correlation operations 52, 53 of Fig. 3 are performed with a Klauder signal base pair occupying the frequency band of 0.89 to 1.48 mhz and the origins selected are based on the peak times identified by element 57. Hence the phase spectra and the identification of characteristic constants over the significant frequency band represent the operations of element 59. The simple behavior of the phase spectra over the significant frequencies which results from appropri­ ate choice of the member signal origins are to be noted. In Fig. 9 the detected constant phases as calculated from the phase spectra over the band of significant frequencies (Fig. 8 and element 59 of Fig. 3) are plotted against the propagation distance, as are the constant phases computed according to element 58 of Fig. 3. The two calculations produce remarkably similar results, which imply a simple linear relationship 130 between the constant phase distortion (imparted by the water) and the propagation path length. As stated earlier, the slope of this relationship is estimated to be 16.7° of constant phase rotation for each centimeter of travel. Hence, if signal phase distortions are present in the propagation medium, as described, the following description provides an embodiment for a navigation system which can measure such distortions and correct for them accordingly. The essentials for this embodiment have much in common with the method employed to encode more than one angular coordinate in a component signal. For this embodiment the phase distortions imparted by the medium are treated as one additional encoded angular coordinate. If sufficient redundancy is designed into the component signal, and a sufficient number of the encodings including the medium phase distortion are mathematically independent, then the medium phase distortion is developed as a part of the same simultaneous calculation for the angular coordinates. A specific illustration is given below to explain this general concept. Assume that two member signals constitute the particular component signal, and that the measured constant phases after processing according to Fig. 3 are ϑ oo and ϑ₁₀. The single angular coordinate  o is phase encoded as  o /h o in the first member signal and as  o /h l in the second one. A medium induced phase distortion  m is present in both member signals which have travelled over the same path. The following equations relate the measurements ϑ oo and ϑ₁₀ to the desired quantities  o and  m : Solving equations (6) gives the following separate values for  o and  m : When  m is calculated for many ranges, the phase distor­ tion of the medium can be rather simply characterized. Alternatively, if  m is believed to relate to the range in a functionally known manner and range estimates are available, then the decoding equations can be reformulated to directly estimate the parameters of the functional relationship. In sum, navigation systems which embody elements of the invention described herein offer several novel and highly desirable and useful alternatives for addressing the com­ promises which inevitably must be faced in developing area navigation systems.

Claims: 1. A method of ascertaining navigational infor­ mation for at least one mobile platform (81) in terms of at least one angular coordinate by transmitting from at least one transmitter (20, 83) and receiving with at least one receiver (22) at least one signal which is not a member signal but which can be transformed to a member signal by a linear filtering operation, the signal having a band of contiguous frequencies with no frequency missing over a defined frequency bandwidth, the method comprising the steps of: changing the shape of the signal by encoding a distinction in phase over a plurality of individual fre­ quencies of the band of contiguous frequencies in accor­ dance with at least one angular coordinate of navigational information, while propagating the signal from the trans­ mitter to the receiver; receiving the propagated signal, measuring the phase of the received signal, and decoding the angular coordinate from the encoded distinction in phase. 2. A method according to claim 1, wherein said measuring step includes determining the phase spectrum of the received signal. 3. A method according to claim 1 or 2, wherein said step of encoding comprises propagating the transmit­ ted signal through a dispersive medium so that the degree of dispersion varies in accordance with the angular coordinate. 4. A method according to any preceding claim, wherein said step of encoding comprises reflecting the transmitted signal from a surface at an angle beyond the critical angle. 5. A method according to any preceding claim, wherein the propagation medium between the transmitter and the receiver introduces phase changes into signals propa­ gating through the medium and including the addition steps of: forming at least one component signal compri­ sing at least two constituent signals each of which is transformable as aforesaid; encoding the distinction in phase in accor­ dance with the angular coordinate in at least one of the constituent signals, such encoding being independent of any phase changes introduced by the propagation medium and with the number of such independent encodings being greater than the number of angular coordinates; on receipt of the propagated signals, iden­ tifying within the received component signal the said con­ stituent signals; measuring the phases of the identified constituent signals; and separating the phase changes introduced by the medium from the angularly encoded phase. 6. A method according to any one of claims 1 to 4, wherein the navigational information is ascertained in terms of two angular coordinates and including the steps of: forming at least one component signal com­ prising two constituent signals each of which is trans­ formable as aforesaid; independently encoding the distinction in phase in accordance with each of the two constituent signals while propagating the component signal; on receipt of the propagated component signal identifying the constituent signals within the received component signal; measuring the phases of identified signals;and decoding angular coordinates from the measured phases and the independent encodings. 7. A method according to claim 1, wherein the phase of the propagated signal is substantially constant over its frequency bandwidth. 8. A method according to any preceding claim, wherein a portion of the distinction in phase of the signal which changes the signal shape is substantially constant over the frequency bandwidth of the signal.

Inventors: NEIDELL, NORMAN S.
Applicants: NEIDELL, NORMAN S.
Application year: 1981
Main classification: G01S1
IPC codes: G01S1