813,126. Radio navigation. GAUDILLERE, P. C. April 20, 1956 [April 28, 1955], No. 12095/56. Class 40 (7). Relates to a radio navigation system comprising two spaced fixed transmitters A and B, a spaced relay station P1 and a receiving station P2. In one mode of operation, i.e. " objective " mode, P1 is mobile, P2 is fixed and there is produced at P2 an indication of the position of P1 in terms of a hyperbolic co-ordinate with A, B as foci and an elliptical co-ordinate with A, P2 as foci, Fig. 2 (not shown). In order to reduce ambiguities P2 is preferably located adjacent the base line AB; if P2 is adjacent A the ellipses become circles and a direct measure of distance is obtained; if P2 is adjacent B the ellipses and hyperbolae have common foci and intersect at right angles. In another mode of operation, i.e. " subjective " mode, P1 is fixed, P2 is mobile and there is produced at P2 an indication of the location of P2 in terms of intersecting hyperbolae with foci at A, B and A, P1, Fig. 3 (not shown). The equipment at stations A, B, P1 and P2, Fig. 4 (not shown), is the same for all modes of operation. Station A transmits short pulses of recurrence period T1 and station B transmits pulses of recurrence period T2 and of duration equal to or slightly greater than (T1 - T2), T1 and T2 being such that the system recurrence period T = NT1 = (N + 1)T2, when N is an integer and (T1 - T2) is small compared with T1. The A and B pulses are received at P1 and at P2 and at each station a coincidence pulse Z is derived from each received A pulse which coincides with a received B pulse, the coincidence pulses Z1 derived at P1 being transmitted to P2 which comprises means for determining the time interval i between the received Z<SP>1</SP>1 pulses and the coincidence pulses Z2 generated at P2. Alternatively the transmitters may be modulated in any known form, e.g. A.M., F.M. or P.M., by recurrent signals, e.g. sinusoidal signals, having recurrent periods T1 and T2 respectively, corresponding pulse signals of the required duration being derived at P1 and P2; in this case the carrier frequencies for the A and B signals must be different. If hyperbolae defined by r A - r B = nc(T 1 - T2), c being the velocity of radio waves, are constructed for all positive and negative values of n up to n = N and if the area between two hyperbolae corresponding to (n - 1) and n is called the nth channel then it is shown that a receiver located in the nth channel will detect a coincidence between pulses transmitted from A and B at times nT1 and nT2 respectively measured from the start of a sytem recurrence period T. Accordingly if P1 and P2 are situated respectively in the nth and n<SP>1</SP>th channels, the timing I 1 and I 2 of the coincidence pulses Z1 and Z2 are P1 and P2 is given by and the required time internal i is given by T1 is chosen such that R is always fractional. In the objective mode of operation P2 is fixed and therefore n<SP>1</SP> + r2 A are known. Hence the hyperbolic channel occupied by P1 is given by n = Q + n<SP>1</SP> and the value of R defines an ellipse with foci at A and P2 given by the equation r1 A + r = cRT1 + r2 A . In this mode of operation the signals Z1 transmitted by the mobile station P1 may be also coded according to identity or altitude. In the subjective mode of operation P1 is fixed and therefore n and r1 A are known. Hence the hyperbolic channel occupied by P2 is given by n<SP>1</SP> = n - Q and the value of R defines a hyperbola with foci at A and P1 given by the equation r - r2 A = cRT1 - r1a. The time interdal i may be determined at P2 by an electronic counter initiated and terminated by the coincidence pulses Z2 and Z<SP>1</SP>1 or by applying the coincidence pulse Z<SP>1</SP>1 to intensity modulate a C.R.T. having a rectangular raster the vertical timebase (recurrence period T) being triggered by the coincidence pulse Z2 and the horizontal timebase (recurrence period T 1) being triggered by the A pulses received at P2 so that the values of Q and R are indicated by the vertical and horizontal positions of the image spot. By using non-linear timebases the position of the image spot may be arranged to indicate the geographical position of the mobile station on a map superimposed on the screen of the C.R.T.