INTERWEAVED MATRIX UPDATING COORDINATE CONVERTER

• US 3,763,358 A
• Filed: 10/21/1971
• Issued: 10/02/1973
• Est. Priority Date: 10/21/1971
• Status: Expired due to Term

• Current Assignee: Donald R. Cargille
• Original Assignee: Donald R. Cargille
• Inventors: Cargille, Donald R.
• Primary Examiner(s): Botz, Eugene G.
• Assistant Examiner(s): Smith, Jerry
• Application Number:
  US05/186,870
• Time in Patent Office: 712 Days
• Field of Search: 235/150.2,150.25,150.26,150.27,150.31,152,164 73/178R 444/1
• US Class Current: 708/442
• CPC Class Codes: G06F 7/548 Trigonometric functions; Co-ordinate transformations

Abstract

A coordinate converter system for high speed and accurate updating of a direction cosine matrix which describes the relative orientation of one orthogonal coordinate frame such as a body frame to another frame such as a stable frame in response to rotations of both frames. The coordinate converter utilizes an interweaved series-parallel-reversal type algorithm that allows simultaneous cosine updating for both the body frame and the stable frame rotation without additional adders, while requiring only three word times for updating for body rotation. The system includes nine DDA dual adders operating in parallel in which the body update computations of the cosine matrix is maintained at full speed and the adders unused by the body frame computations are utilized during each word time to provide the stable frame computations. Because the algorithm updates the cosine matrix in response to both body frame and stable frame rotations with reversing computations when input incremental rotation pulses are received, a high degree of accuracy is provided without undesirable interactions due to the simultaneous processing of body frame and stable frame rotations. Thus the coordinate converter performs simultaneous calculations of the cosine matrix for both the body frame and the stable frame rotations and operates at a fast speed and with a high degree of resolution of the body motion. The invention herein described was made in the course of or under a Contract or Subcontract thereunder with the Navy.

Claims

1. A computer for updating a cosine matrix in response to rotations of the axes of a first and a second coordinate frame, said cosine matrix representing the cosine functions between each axis of the first frame relative to each axis of the second coordinate frame comprising:

arithmetic means including nine digital differential analyzer means, one for each cosine function of said cosine matrix, said cosine matrix having cosine functions arranged in first, second and third rows, each with three columns, and timing means coupled to said arithmetic means to control the updating of said cosine matrix in a reversible sequence relative to said columns and said rows respectively for said first and second coordinate frame rotations, said sequences being performed simultaneously for updating iN response to rotations of the first and second coordinate frames, said timing means controlling the digital differential analyzer means so that the column sequence of each row reversible sequence of the updating for said second coordinate frame rotations, reverses in response to a reversal of the sequence of the columns resulting from the updating for the first coordinate frame rotations.

2. A computer for updating a cosine matrix in response to rotations of the axes of a first and a second coordinate frame, said cosine matrix representing the cosine functions between each axis of the first frame relative to each axis of the second coordinate frame comprising:

arithmetic means including nine digital differential analyzer means, one for each cosine function of said cosine matrix, said cosine matrix having cosine functions arranged in first, second and third rows, each with three columns, and timing means coupled to said arithmetic means to control the updating of said cosine matrix in a reversible sequence relative to said columns and said rows respectively for said first and second coordinate frame rotations, said sequences being performed simultaneously for updating in response to rotations of the first and second coordinate frames, said timing means controlling the updating of said cosine functions relative to rotation of said first coordinate frame so as to have a reversible sequence for each row of updating said cosine function of said second and third columns, said first and third columns and said first and second columns, and relative to rotations of said second coordinate frame so as to have a reversible sequence for updating said cosine functions in said second and third rows sequentially for said first, second and third columns, for updating said cosine functions in said first and third rows sequentially for said first, second and third columns, and for updating said cosine functions for said first and second rows sequentially for said first, second and third columns, and in which said timing means controls updating of said cosine function relative to rotation of said first coordinate frame in a first frame period having three word time periods with one word period for each of updating the second and third columns, the first and third columns and the first and second columns of said reversible sequence and controls updating of said cosine functions in response to rotations of said second coordinate frame in three first frame periods each having three word time periods, with the cosine functions for each column being updated during a different word time period of each first frame period.

3. The computer of claim 2 in which said timing means controls updating of said cosine functions in response to rotations of said second coordinate frame so that the updating sequence of said first, second and third columns is a reversible sequence during each updating of rows opposite from the reversible sequence in response to rotations of said first coordinate frame of updating columns two and three, columns one and three and columns one and two, and reverses in response to a reversal of the sequence of updating in response to rotations of said first coordinate frame.

4. A system for updating a matrix of cosines of first, second and third rows and first, second and third columns in response to variations of orientation of first and second coordinate systems, said variations of first coordinate systems occurring at a faster rate than the variations of the second coordinate system, comprising:

arithmetic means responsive to said variations for updating the cosines of said matrix, and including nine digital differential analyzers, and control means coupled to control said arithmetic means for updating said cosines in a first reversible sequence of columns for each row for the variations of said first coordinate system and in a second reversible sequence of rows for each column for the variations of said second coordinate system, said first and second revErsible sequences being performed simultaneously, said first and second reversible sequences respectively updating relative to the columns in each of said rows and relative to the rows in each of said columns, second and third cosines, the first and third cosines and the first and second cosines, said control means includes timing means to control the updating of said first reversible sequence of columns to be performed in three word time periods, and the updating of said second reversible sequence of rows to be performed in three reversible coordinate frame periods, each including three word time periods.

5. The system of claim 4 in which the timing means controls said second reversible sequence so that a reversible sequence of columns is updated during each coordinate frame period and is of a predetermined reversal sequence relative to the reversal sequence of said first reversible sequence, and reverses as a function of reversals of said first sequence.

6. The system of claim 5 in which said timing means further controls said second reversible sequence so that for each word time period, cosines are updated of a column that is not being updated in the first reversible sequence.

7. The system of claim 5 in which the first coordinate system is the body frame and the second coordinate system is the stable frame and including a source of body frame rotation signals and a source of stable frame rotation signals and in which said control means includes multiplexing means at each digital differential analyzer for reversing said first reversible sequence and said second reversible sequence respectively in response to said body frame rotation signals and said stable frame signals.