Systolic VLSI array for implementing the Kalman filter algorithm

A method of solving equations having matrix and vector terms in real time, said method comprising the steps of:

• mapping a first equation, having both matrix and vector terms, into an equivalent equation which is represented in matrix-only values that represent the matrix and vector terms of said first equation;
• applying signals representing the matrix-only values of the equivalent equation to a systolic processing array;
• and
• triangulating and nullifying the signals in said systolic processing array whereby a real time solution to the matrix and vector terms of said first equation appears as an output signal from said systolic processing array.

A method of implementing a Kalman filter algorithm for a real-time solution, said method comprising the steps of:

• arranging the vector and matrix terms of said Kalman filter algorithm into matrix-only terms of a Faddeeva algorithm, which matrix-only terms represent both the matrix and vector terms of the Kalman filter algorithm;
• representing the terms of the Faddeeva algorithm as electrical signals;
• inputting the electrical signals into a systolic processing array;
• and
• processing the electrical signals in the systolic processing array to obtain a real-time solution to said Kalman filter algorithm.

A method of implementing the Kalman filter algorithm for a real-time solution to variable terms in the algorithm, said method resulting in an implementation of the Kalman filter algorithm and comprising the ordered steps of:

• (1) arranging the vector and matrix terms of said Kalman filter algorithm into a Faddeeva algorithm which includes matrix-only terms;
• (2) placing cell elements according to the size of the matrix to solve the matrix-only terms of the Faddeeva algorithm in a systolic array;
• (3) steering electrical signals, representing the matrix-only terms of the Faddeeva algorithm into cell elements of the systolic array;
• and
• (4) obtaining from the array, real-time output signals indicative of a real-time solution to said Kalman filter algorithm.

Apparatus for solving equations having a matrix and vector terms in real time, said apparatus comprising:

• means for mapping a first equation, having both matrix and vector terms, into an equivalent equation which contains matrix-only values that represent both the matrix and vector terms of said first equation;
• a systolic array, with an appropriate number of cell elements according to the size of matrix to provide a real-time solution of said matrix-only values, connected to said mapping means;
• and
• means for applying electrical signals representing the matrix-only values to said systolic processing array for solution thereof.