US2762565A - Anti-aircraft gun computer - Google Patents

Description

Seggi. M

, 3956 E. E. LEMAN ET AL ANTI-AIRCRAFT GUN COMPUTER 5 Sheets-Sheet l Filed June 5 ACTUAL VELC/TY 0555/?!/59 DATA VELC/TY TARGE ACTUAL PATH NORTH w M m s w R X M U M x0 n JN VEN TORS. E Ljbznan,

pi?, E956 E. E. LEMAN ETAL 2,752,555

ANTIIRCRAFT GUN COMPUTER Filed June 5, 1950 3 Sheets-Sheet 2 N INVENTORS. s MEL/ibm ANTI-AIRCRAFT GUN CGNIPUTER Earl E. Libman, Brooklyn, Aaron D. Fialkow, New York,

Sohn W. Bozeman, Baidwin, and irving Gerst, Brookiyn, N. Y., assignors to Contro instrument Company, Zinc., Brooklyn, N. Y., a corporation of New York Application June 5, 1950, Serial No. 166,192

13 Claims. (Cl. 23S-61.5)

ri`his invention relates to computers and has particular reference to a system for computing a forecast of the future position of a moving target and of the direction in which a projectile should be launched so that it will hit that target.

In computers or' this nature, the computation of future target position customarily proceeds on the assumption that the target will continue to move from the position it occupies at the moment of projectile launching with the instantaneous velocity and direction it has at said moment, and that the data of instantaneous position, Velocity and direction of the target given by a tracking mechanism is adequate. However, the data thus obtained does not necessarily represent the true position, velocity and direction of the target.

Therefore, in accordance with the present invention and in order to obtain a more accurate forecast of future target position, the computation of such position, while it proceeds on the rst of the above mentioned assumptions that the target will continue to move with the velocity and direction it has at the instant of tiring a projectile thereat, further utilizes computed values of target velocity and direction that are obtained by operating upon data received from a tracking mechanism over a period of time just preceding the launching of said projectile.

The above rand other objects of the invention will be made apparent from the following description and drawings which illustrate a preferred embodiment of the inventive idea.

ln the drawings:

Fig. l is a diagram representing the observed data of a targets path, the actual path of the target, and the errors distinguishing these paths from each other;

Fig. 2 is a diagram representing the coordinate axes to which the computation is referred;

Fig. 3 is a diagram showing the time history of one of the observed coordinates of the target path and of the corresponding coordinate of the least squares path, to be hereinafter dened, along with the various symbols used in the computation;

Fig. 4 is a diagrammatic view illustrating the components which comprise a preferred embodiment of the invention; and

Fig. 5 is an enlarged fragmentary plan view of a voltage recording mechanism shown in Fig. 4.

General principles When a tracking mechanism follows a moving target, it oscillates or hunts about its position, and the data furnished by said mechanism contains errors, and even if the data of position deviates from that targets true position in small measure so that the positional data obtained therefrom can be considered to be quite accurate, the velocity data, especially with reference to direction, may be enormously in error. As illustrated in Fig. l, the positional error shown at C constantly varies, but, if the tracking device is an accurate one, the position indicated will always be in the immediate neighborhood of the actual position of the target. However, the observed data at the instant of tiring indicates a movement of the target toward B which is different from the actual direction of motion of the target toward A. Hence, although the error in position may be very small, the error in direction may, nevertheless, be large, as indicated by the angle D.

in order to make a forecast of the future position of the target (based on the assumptions previously indicated) so that a projectile can be tired to hit the same, it is necessary to know the target position, velocity and direction at the instant said projectile is launched thereat, and a means to make an accurate determination of these quantities is essential. To make such a determination, all that is available is a continuous record of observations of target behavior. From this, by the means hereinafter shown, a path can be determined which closely approximates the true path taken by the target and from which may be determined the direction and velocity information required to launch a projectile at said target in order to hit the same.

Of the methods suited to operate upon the observed, data of the target path to obtain a close approximation to the true targets path during the immediate past, and from which the velocity and direction of the target at the instant of projectile launching may be computed, the method and underlying theory utilized in this invention will now be described.

lt is shown in the theory of probability that, from a series of observations in which the errors of observation constitute a normal probability distribution, the most probable value of the observed quantity results from the application of the method of least squares. in the present invention, these statistical considerations are applied to the observed path of the target to determine the most probable target path during a time interval in the immediate past.

The targets actual motion during the immediate past can be closely represented by the following set of parametric equations:

where the As, Bs and Cs are literal coethcients to be determined, by the application of the method of least squares, from the observed data, and t is time measured from some arbitary initial instant. indeed, for practical military iiights, the above set of equations, with 11:3, is suicient to closely represent the targets history over a suthciently small period of time, for n=3 is the lowest degree for which the set represents a three-dimensional curve whose curvature and torsion at any point may assume any values. The equations are thus In order to determine the coeiiicients by the method of least squares, it is necessary that these values be such that the sum of the squares of the distances at each instant, during a fixed time interval in the immediate past, between the path represented by the equations (which will be called the least squares path) and that represented by the observed data, be a minimum. This may be accomplished by utilizing the mathematical expression for the distance between the observed position of the target at any time and the corresponding point (at that time) on the least squares path. The observed position is known and the expression for the position on the least squares path contains the unspecified coeicients. Thus an expression may be obtained for the square of that distance agreaeee and by adding together all such expressions during some known interval just prior to ring there is obtained a summation which contains the unspecified coefficients. By well lgnown methods ot` mathematics, the coefficients may then be so determined that this sum is a minimum. This determination gives the equation of the most probable target path of the type indicated which can be obtained from the observed data.

By mathematical differentiation of the equation of the least squares path, the present target velocity vector is obtained. Then, by extrapolating along that vector for a distance equal to its magnitude multiplied by the time of projectile flight, the advance position of the target is obtained. The usual methods of ballistics may then be used to convert this advance position to the orders required to position the projectile launching device.

Mathematical analysis Consider the horizontal plane through the present gun position. Choose a set of axes through the gun position such that the positive directions of the axes of x, y and z point North, East and Up, respectively, as shown in Fig. 2. The target at the present instant 2:11, has the following polar coordinates: present compass bearing present elevation above the horizontal e and present range R. These are the observable data which are usually obtained from the sighting mechanism.

Let x, y and z represent the corresponding rectangular coordinates of the target. Then, if r is the projection of R on a horizontal plane,

Since these are computed from the observed polar coordinates, they may be termed the observed rectanguiar coordinates.

The following analysis will be carried out for x alone. The analysis for y and for z is exactly similar and reed not be repeated.

As shown in Fig. 3, which iigure is a plot of the variations i x with respect to time, the diterence at any in stant t between the observed x coordinate and the corresponding X coordinate of the least squares path is X( t) -x(t). The sum of the squares of these differences over an arbitrary period of 2q seconds just prior to the present instant t=p is equal to the integral The most probable value of the X-coordinate at a given time D is determined by selecting values for the coefcients Au, A1. Az and As in Equations l such that t=pe2q The velocity of :t target flying along the least squares path at instant t is XU) where X(t) is intended to mean dX(t) dt [X(t) x(tWdt--minimum is used, so that the projectile is actually directed to hit the point whose x-coordinate is The targets least'squares path is given by Equations l.

if, for convenience, time is measured from an arbitrarily chosen instant q seconds prior to the present instant and this time is indicated by the variable s, there is obtained, by substituting t=pq+s (Fig. 3) in Equations l, the following expression for XU) and, of course, similar expressions for )'(t) and Z(t),

where the as are functions of p and q.

Similar substitution in equation 4 gives:

The values of the as that make the integral a minimum are, by the well known methods of calculus:

Fhrt-5K2] known by Equations 9, and from Equations 8 all of the as are known and, therefore, the coecients in the Equation 6 for the X coordinate of the least squares path are now known. Differentiation of Equation 6 with respect to t gives and so by Equation 5, xA is known.

Following an analogous process for Y and Z, YA and ZA are obtained which give the rectangular coordinates of the advanced point at which the projectile is launched to obtain a hit. By converting these back into polar coordinates, the data, after ballistic corrections, for training and elevating a gun or other projectile launching apparatus, and the range for which the fuse of the projectile should be set, are known.

The computer ln actual practice, target range, elevation and bearing may be obtained from a tracking device such as a radar, or an optical sight and range nder. The elevation and bearing thus obtained will be available, mechanically, as angular displacements from the axes of the tracking device. From a radar, the range will be available as a arcanes A voltage; and from an optical range finder, as a mechanical angular displacement which may be converted to a voltage.

The voltage representing range is introduced into the computer by way of the leads 5 and 6 (Fig. 4) thus energizing the rotor 7 of the resolver 8, which rotor is positionable by means of 'the shaft 9 with respect to the mutually perpendicular stator coils 10 and 11. The Shaft of the resolver 8 is positioned by the mechanical input of target elevation and, therefore, the voltage induced from the rotor into the stator coils will be, respectively,

R sin e=z, and

R cos e=r which outputs are respectively on the leads 12, 13 and 14, 15.

The voltage on leads 14 and 15, proportional to r, is

introduced into the rotor 16 of the resolver 17 which is similar in construction to the resolver 8 and whose shaft 18 receives the mechanical input of target bearing and positions the rotor 16. The voltages then induced in the stator windings 19 and 2l) are r sin =y and r cos =x Thus, there is obtained the rectangular coordinates x, y and z of the targets present position.

Since the subsequent operations performed by the computer are the same for each of the coordinates x, y and z it will be suicient, as before, to trace the operations performed upon the x coordinate alone, it being understood that similar treatment is accorded the y and z coordinate data before they are recombined finally at the output.

To the voltage representing the instantaneous value of x from leads 23 and 24, is added a biasing voltage of magnitude (L-B) by placing the secondary 59 of transformer 57 in series between leads 24 and 24a, where L is the window width and B is a quantity of maggnitude greater than the maximum negative value of x and is such that L-(B-l-x) and B-l-x are always positive. The alternating voltage on the primary 58 of transformer 57 is supplied by leads 28 and 29 from the same source as that supplied to leads 5 and 6 of resolver B.

The voltage L-(B-t-x) actuates the galvanometer and causes its pen 30 to trace an opaque area 31 on a transparent surface or ribbon 32 of width L-(B-l-x). Since the window 39 in the mask 39' directly above the surface 32 is of width L, there is then left a transparent portion whose width is B-l-x. The ribbon 32 is carried by the rollers 33 and 34 and is of sucient width to accommodate without overlapping the three traces made by the galvanometers 25, 26 and 27. The roller 34 is driven under the window 39, whose length is two inches, at the rate inches per second by means of the gears 35 and 36, the speed selector 37 into which q is set, and the time motor 38. This quantity q, which is arbitrarily chosen, may be of the order of seconds, and is introduced by means of the hand wheel 40, which turns the shaft 41 whose threaded portion 42 causes the traveling nut 43 to vary the position of the elements of the selector 37, and thus the speed of the drive to roller 34.

Since the ribbon 32 is running at a speed of inches per second, the time it requires to move two inches is 2q, so that the window 39 covers the sampling time 2q.

By Figs. 3 and 5, s is time measured from the midpoint of the sampling time interval 2q, and the ribbon running at the speed moves relative to the midpoint of the window and in the time s will move the distance Q which, by Equation l0 is w. Therefore, it follows from Figs. 3 and 5 that w measures the distance along the window 39 from the midpoint to the point on the said ribbon corresponding to the instant t.

ln the time dt. the strip moves a distance La q which equals dw from Equation l() (Fig. 5). In an elementary piece of the ribbon at distance w from the center line of the window and of width dw, the transparent area is (B+x).dw.

A light source 44 is energized by way of the leads 45 and 46. This light source must be of constant intensity. Of the various ways for obtaining such constancy the following is given as an illustration. The lens system 47 focuses the light upon the photocell 48 that controls the activity of the amplifier 49, which amplifier controls the power delivered to the light source. This arrangement causes the power delivered to said source to vary in such a Way as to maintain its brightness constant. In order to electrically manipulate the computing devices receiv ing the light after transmission through the ribbon 32, it is desired that the light be modulated with the line frequency. The following is given as an illustration of one way to secure this desideratum.

A lens system 5l) causes a part of the light from the source to be columnated and these parallel rays are transmitted through three sets of polarizing filters 5l and associated polarizing cells 52, said sets being angularly disposed relative to each other about the light source 44 and each being individual to one of the coordinates x, y and z. Two of said sets direct their rays, respectively, to the mirrors S3 and 53b and thence to the windows 39 and 3971 while the rays from the third set are transmitted directly to the window 39a. Each polarizing cell is activated by connection to leads 23 and 29 so that the light therethrough changes its plane of polarization at line frequency, and the combined filter 51 and cell 52 of each set therefore modulates the parallel rays in intensity at the rate at which the cell 52 is caused to change its plane of polarization. The parallel rays emanating from the three lens systems are thus caused to pass through the windows 39, 39a `and 39b to the associated mirrors 55, 55a and SSb of the three optical systems shown; and since the computations for the coordinates x, y and z are effected in the same manner, the following detailed description will be confined to the optical system obtaining its light through the window 39.

The amount of light coming through this window will be determined by the transparent area which. in turn, is the entire window area diminished by the opaque portion written into that area by the galvanometer pen 30. It has been shown that the light through the narrow ribbon of width dw (Fig. 4) -is (B+x)dw and Ithus the light through the entire window is (12) V21 [B+x1dw This light is caused to fall on the mirror 55, which mirror is so constituted as to permit 3%; of the light incident thereon to be transmitted therethrough and the remaining A to be rellected therefrom. The reflected light passes through the uniform filter and falls on a photoelectric cell 56. The voltage produced thereby is proportional to the integral (12). This integral is, by Equation 9,

which is the entire light falling on photocell 56 and is therefore the voltage output of amplifier 61.

The remainder of the light, which was transmitted through the mirror 55, falls upon the mirror 62, which mirror is similar to the mirror 55 in that part of the light incident thereupon is transmitted and the remainder is reflected. One-third of the light incident upon the mirror 62 is reflected therefrom. That passing through the ribbon of width dw at distance w from the window midpoint point is, as before, proportional to (B-i-x) dw which light then passes through the filter 63 whose transmission varies along its vertical length, so that at a point distance w from its midpoint it transmits the fraction l/2 (1+w) of the light falling upon it. Since w lies in value between +1 and 1, it follows that /2(1lw) is always positive and not greater than l. Thus the light (B+x)dw from the ribbon of width dw, after passing through the filter. is 1/z(l+w)(B-lx)dw, and the entire light through filter 63 is, by Equation 9.

which is the entire light that falls upon the photocell 64 and the voltage output of amplifier 65 is Kr-l-(Ko-l-ZB). The remaining two-thirds of the light transmitted through the mirror 62 is incident upon the mirror 66 which, like the foregoing mirrors, transmits one part and reects another part of the light incident thereon. Onehalf of the light incident thereon is reflected and passes through a tilter 67 whose transmission, at a point distance w from its midpoint, is the factor wz of the incident light so that the entire light falling on the photocell 68 is proportional to .V +1 J-i by Equation 9. This is,` therefore, the output of amplitier 69.

The remainder of the light transmitted through the mirror 66 causes the image in the window 59 to fall upon the filter 70 whose transmission at any point distance w from the midpoint is the fraction 1/:(l,'-w3) of the incident light so that the entire light falling on photocell 71 is by Equation 9. Thus. the output of amplier 72 is Ka-l-(Ko--2B).

The transformer 57 has two additional windings 73 and 74, the winding 74 yielding a voltage 2B and the winding 73 appears on its secondary 80.

The output voltage Kol-2B of amplifier 61 in opposition series with the output voltage Ki-l-(Kol-ZB) of amplifier 65, puts voltage K3 across the primary 34 of transformer 85. This transformer having a 1:2 winding ratio yields on its secondary 86 the voltage 2Ki.

The output voltage X24-36B of amplifier 69 in opposition series with the output voltage 6B of the secondary 73 puts voltage K2 across the primary 91 of transformer 90. This transformer having a 4:3 Winding ratio, the voltage fKz appears on its secondary 92.

The output voltage Ka-i-(Ko-I-ZB) of amplifier 72 in opposition series with the output voltage Kn-l-ZZB of amplier 61 puts voltage K3 across the primary 94 of transformer 95. This transformer having a 2:7 winding ratio yields on its secondary 96 the voltage 7/2K3.

By means of the leads 99, the secondaries 96, 92, 86 and are placed in series so that the voltage which appears across the leads 23 and 101 is equal to K [-f-zKmLKnLgtnl This expression is multipled by by means of the shaft `41, the gears 102 and the cam 103, whose cam surface has for its generating expression and is driven bythe shaft 4l.

The follower 104 whose position is then proportional to carries the sliding Contact 195 of a potentiometer 106 which is joined at its ends to the leads 23 and 101. The voltage from the tap 107 to the lead 23 `vill therefore be the voltage across the entire potentiometer multiplied by the factor i. e., giving This voltage is then multiplied by the time of ight T, as required by Equation 5. giving TX(p) by means of the positionable tap 11,28 of potentiometer 169 which connects the tap 107 to lead 23. The position of tap 108 is made proportional to time of flight T by being driven by the traveling nut on the shaft 110 which, by means ofthe gears 111, 112, 113, 114 and the shafts 115, 116, 117, is turned proportionally to T by the output shaft 118 of the time of flight computer 119 which may be of a construction similar to that shown in U. S. Patent 2,403,543, dated Iuly 9, i946.

The voltage thus obtained across leads 121 and 122 is TX(p) and this, in series with the voltage x available from the resolver 17 on the leads 23 and 24, yields the sum T'p) +x(p) which, by Equation 5, is xa which is the rectangular cordinate of the target position at the time T in the future.

The mechanism above described for the computation of x is duplicated in Fig. 4 for y and z which are converted into Ya and Za, and like numerals are employed to designate similar parts with the addition to said numerals of the subscripts a and b denoting the different portions of the mechanism for the computation of y and z. respectively.

The voltages represented by xt. ya and za are amplied. respectively, in the amplifiers 123, 124 and 125. The amplified voltages representative of xa and ya are combined in the combining mechanism 126 which has two eld coils 127 and 12S so arranged as to have their respective fields at right angles to each other. The rotor 129 has two coils 130 and 131 andthe voltage induced in said rotor is amplified in amplifier 132 and used to excite the motor 133 to drive the shaft 134 which positions said rotlor. if any voltage is induced in the coil 130, the motor will be energized and will continue to drive the shaft 134 until said coil is so positioned that the voltage induced therein is zero; that is to say, it is parallel to the resultant field produced by xa and ya. The coil 131 will therefore be at right angles thereto and have an output voltage proportional to this resultant field which from equations similar to (2), but with subscripts a, corresponds to ra and the position of the shaft 134 by the same equations will be proportional to the advance bearlng a The Voltage proportional to ra on coil 131 is amplified in the amplifier 135 and energizes winding 136 of the combining mechanism 137 whose remaining winding 138 .is energized by za. In the same way as for the element 126, the winding 139 whose output is amplified in the amplifier 140 will drive the motor 141 which in turn will position the rotor 142 until the coil 139 has no voltage induced therein. The position of the shaft 143, which is coupled by means of the gears 144 and shaft 145 to the motor 141, will therefore represent es and the output of the coil 146, the advance range Re to the target.

The advance target range Ra. is amplified in amplier 147 and is used to position a servomotor 148 making this range available as adisplacement by means of gears 149 on the shaft 150.

The time of projectile flight is a function of the advance target range and elevation. Since this is a function of two variables, a three-dimensional cam is generally employed, although this is not the only method available, to compute the time of projectile flight from such data. The mechanism 119 represents such a time of iiight computer which may employ any of the well known methods of taking into account such characteristics and when operated by range Ra, as supplied by servomotor 148, by way of shafts 151 and 152 and gears 153, and advance elevation by way of shafts 145, 154 and gears 155, it Will compute the time of ght for the projectile so that it may be launched on a collision trajectory. The tiene of ilight thus computed is the time of iiig'nt which, by way of shaft 118, gears 114, etc., is introduced into the computation of the coordinates on shaft 119 to position the variable taps of potentiometers 109, 109a and 109b.

To avoid complicating the drawings with mechanisms old in the art, no means are shown for the usual corrections required in ballistics for wind velocity, change in projectile launching velocity, supereievation and the like. Means to accomplish these functions may be driven by the outputs of future target coordinates as they are produced by the mechanism disclosed, and the manner of their accomplishment is immaterial to the manner in which these future target coordinates are evolved.

The realization of the gun positions by the use of the principles described above to the known positions occupied by the target may be accomplished by means other than those specifically disclosed herein. The required integrations might, for example, be performed by ball and table integrators and the required multiplications, divisions, additions and subtractions by means of linkages, potentiometers or other means known to the computing art. The embodiment herein shown and described, together with the method of computation, constitutes the invention, and said embodiment is intended merely to illus trate rather than to limit anddene the mode of realization and scope of the invention, reference being had to the appended claims for that purpose.

What is claimed is:

1. An apparatus for computing the direction in which a projectile launching device must point in order that a projectile launched therefrom will score a hit on a moving target, said apparatus comprising input means for the observed spherical coordinates of target position, computing means coacting with said input means for continuously determining, by computations eected by said computing means and depending upon the coordinates of every observed position that the target occupies during an arbitrary interval in the immediate past, the most probable actual path being followed by said target and the velocity of said target in said most probable path, said computing means including, in combination, means responsive to said input means for resolving said observed data of every target position into rectangular coordinates, means for forming a continuous record of each of said rectangular coordinates of target position so resolved, means for sensing the entire record of each of said recorded rectangular coordinates of target positions as recorded over said arbitrary interval in the immediate past, optical means including a system of associated light reflectors and filter elements coacting with said sensing means, means responsive to said optical means for converting each of said sensed records to yield one component of the velocity of the target in said most probable path, means to utilize the components thus obtained for extrapolating along the line parallel to the tangent ot' said most probable path and through the observed position of the target at the instant of projectile launching to determine a point whose distance along said tangent from said observed target position at said instant is the product of the time of projectile iiight and of the velocity of said target in said computed path, means for computing the projectile time of ight, and means to convert the coordinates of said extrapolated point into range and angles of train and elevation for the projectile launching device.

2. An apparatus for computing the direction in' which a projectile launching device must point in order that a projectile launched therefrom will score a hit on a moving target, said apparatus comprising input means for the observed spherical coordinates of target position, computing means coacting with said input means to continuously determine, by computations depending upon the coordinates of every observed position that the target occupies during an arbitrary interval in the immediate past, the most probable path of said target during said interval, said computing means including, in combination, means responsive to said input means for resolving said observed data of every target position into rectangular coordinates, means for forming a continuous record of each of said rectangular coordinates of target position so resolved, photometric means including coacting light filters and photo cells for sensing the entire record of each of said recorded rectangular coordinates of target positions as recorded over said past arbitrary interval, optical means including a system of associated light reilectors and filtering elements coacting with said sensing means, means responsive to said optical means for converting each of said sensed records to yield one component of the velocity of the target in said most probable path, means to utilize the components, thus obtained for extrapolating along the line parallel to the tangent of said most probable path and through the observed position of the target at the instant of projectile launching to determine a point whose distance along said tangent from said observed target position at said instant is the product of the time of projectile ight and of the velocity of said target in said computed path, means for computing the projectile time of flight, and means to convert the coordinates of said extrapolated point into range and angles of train and elevation for the projectile launching device.

3. The method of computing the most probable advanced coordinates of a targets position at a time of flight T in the future, which method consists in continuously observing and recording the observed instantaneous coordinates (x, y, Z) of a targets position, deterspaanse "i1 A l'. mining the Values of the coetflcients At, Bt, Cl (1:1, 2. n) of a computed curve of the form so that said curve best represents the actual positions of the target, determining from the computed curve the instantaneous rate of change of target position X, Y, Z on that curve and extrapolating at the determined rate of change and for the time T along a line through the observed target position at the present instant and parallel to the tangent to the computed curve at that instant to obtain the most probable target coordinates at said time of ight in the future. r'

4. The method of computing the most probable advanced coordinates of a target position at a time of ight T in the future which consists in continuously observing and recording7 the instantaneous observed coordinates (x, y, z) of a targets position, determining the values of the coeticients At, B1, Ct (i=l, 2, n) of a computed curve of the form so that the sum of the squares of the differences between the coordinates represented by said computed curve at any instant and the corresponding coordinates of the observed target position at that instant over an arbitrary interval of time in the immediate past is a minimum,` determining from the computed curve the instantaneous rate of change of target position along that curve, and extrapolating at the determined rate of change and for the time T along a line through the observed target position at the present instant andparaliel to the tangent to the computed curve at that instant to obtain the most probable target coordinates at said time of flight in the future.

5. The method of computing the most probable advanced coordinates of a tarvets position at a time of flight T in the future which consists in continuously observing and recording the observed instantaneous coordinates (x, y, z) of a targets position, determining the values of the coefficients Ai, Bt, Ct (z'=1, 2, n) of a computed curve of the form so that the sum of the squares of the differences between the coordinates represented by said computed curve at any instant and the corresponding coordinates of the observed target position at that instant over an arbitrary interval of time in the immediate past is a minimum with the value of n being restricted to n3, determining from the computed curve the instantaneous rate of change of target position along that curve, and extrapolating at the determined rate of change and for the time T along' a line through the observed target position at the present instant and parallel to the tangent to the computed curve at that instant to obtain the most probable target coordinates at said time of ight in the future.

6. The method of computing the most probable advanced coordinates of a target position at a time of tiight T in the future which consists in continuously observing and recording the instantaneous observed coordinates tr. y, z) of a targets position; determining the values of the coefficients At, Bt. Ci (1:1, 2, computed curve of the form .11) cfa" so that the sum of the squares of the differences between the coordinates representedtby said curve at any instant and the corresponding coordinates of the observed target position at that instant over an arbitrary interval of time inthe immediate past is a minimum with the value of n being restricted to n-3, determining from the computed curve the instantaneous rate of change of X, Y, Z and considering the same to be the target velocity at that instant, and extrapolating at the determined rate of change and for the time T along a line through the observed target position at the present instant and parallel to the tangent to the computed curve at that instant to obtain the most probable target coordinates at said time of flight in the future.

7. An apparatus for computing the direction in which a projectile launching device must point in order that a projectile launched therefrom will score a hit on a moving target, said apparatus comprising input means for the observed data of target position, computing means coacting with said input means for continuously determining, by computations depending upon the coordinates of every observed position that the target occupies during an arbitrary interval in the inmediate past, the most probable path of said target during said interval, said computing means including, in combination, means responsive to said input means for resolving said observed data into rectangular coordinates, means to form a continuous record of each coordinate, photometric means for simultaneously sensing the entire records of all said coordinates during said past arbitrary interval, optical means including a system of associated light retlcctors and tiltering elements coacting with said sensing means, said light reilectors each reflecting a portion of the light from said sensed records, a plurality of transformers having windings connected to said optical means for converting said sensed records to yield the various components of target velocity in said most probable path, means connected to said transformers for utilizing said various components to extrapolate along a line parallel to the tangent of said most probable path and through the observed position of the target at the instant of projectile launching to determine a point whose distance along said tangent from said observed target position at said instant is the product of the time of projectile flight and of the velocity of said target in said computed path, means for computing the projectile time of flight, and means to convert the coordinates of said extrapolated point into range and angles or' train and elevation for the projectile launching device.

8. ln an apparatus for determining the most probable position of a moving object from approximate observations of its variable coordinates, a recording device adapted to produce a record of the approximate observations of one of said coordinates over a given time interval, filter means, input means for effectively presenting to said filter means the record produced by said recording device, said tilter means having portions thereo't` with relatively different transmission properties and being adapted to respond in non-uniform fashion to ditferent portions of the record presented by said input means according to predetermined functional relationships consistent with'the method of least squares, and output means responsive to the intelligence transmitted by said tilter means and adapted to combine the variant effects thereof according to predetermined relationships consistent with the method of least squares for providing an output signal which represents the most probable value of said one coordinate of said object as of a selected instant.

9. In an apparatus for determining the most probable position of a moving object from approximate observations of its variable coordinates, a recording device adapted to produce a record of the approximate observations of one of said coordinates over a given time interval, filter means comprising a plurality of lters, input means Yfor effectively presenting to each of said filters the record produced by said recording device, said lters having relatively diferentetransmission properties, and atleast some of said filters being adapted to respond in non-uniform fashion to different portions of the record presented by said input means, all according to predetermined relatiopships consistent with the method of least squares, and output means responsive to the intelligence transmitted by said filter means and adapted to combine the variant effects of each filter and the outputs of the several filters according to predetermined relationships consistent with the method of least squares for providing an out-put signal which represents the determined rate at which said one coordinate of said object is varying at a selected instamt.

i0. In an apparatus for determining the most probable position of a moving object from approximate observations of its variable coordinates, recording means adapted to produce individual records of thc approximate observations of the respective coordinates over a given time interval, filter means, input means for effectively presenting to said filter means the records produced by said recording means, said filter means comprising a plurality of filter devices, one for each of said records, each of said filter devices having portions thereof with relatively different transmission properties and being adapted to respond in non-uniform fashion to different portions of its respective input record according to predetermined relationships consistent with the method of least squares, and output means responsive to the intelligence transmitted by each of said iilter devices and adapted to cornbine the variant effects thereof according to predetermined relationships consistent with the method of least squares for providing output voltages that respectively represent the determined rates at which the coordinates of said object are varying at a selected instant.

l1. In an apparatus for determining the most probable position of a moving object as of a given time from apa records, each of said iilter devices having portions thereof with relatively different transmission properties and being adapted to respond in non-uniform fashion to different portions of its respective input record according to predetermined, relationships consistent with the method of Ileast squares, and output means responsive to the intelligence transmitted by each of said lter devices and adapted to combine the variant effects thereof according to predetermined relationships consistent with the method of least squares for providing output voltages that respectively represent the most probable coordinates of said object at a selected instant.

12. In an apparatus for `determining the most probable value of a variable from approximate observations thereof over a given time interval, a record medium, a recording device movable relative to said medium for graphically recording thereon the approximate observations of said variable in spaced relationship, function filter means for deriving from the record on said medium a predetermined interval function of the recorded values, and means for limiting at both extremities thereof the portion of said record which is electively presented to said function iilter means.

13. In an apparatus for determining the most probable position of a moving object from approximate observations of its variable coordinates over a given time interval, a record medium, a recording device movable relative to said medium for graphically recording thereon the approximate observations of at least one of said coordinates in spaced relationship, function filter means for deriving from the record on said medium a predetermined integral function of the recorded values according to the method of Ileast squares, and means for limiting at both extremities thereof the portion of said record which is effectively presented to said function filter means.

References Cited in the le ofV this patent UNITED STATES PATENTS 2,43 ,.178 Rajchman Feb. 17, 1948 2,442,383 Stewart lune l, 1948 FOREIGN PATENTS 597,026 GreatBritain Jan. 16, 1948 634,862 Germany Sept. 5', i936

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