JPH03188552A - Gain parallel calculating device for kalman filter - Google Patents

Abstract

PURPOSE:To shorten the gain calculating time by providing an input and two outputs on each data memory and using a basic arithmetic unit which performs the computing operations in parallel with each other in plural steps and stores repetitively the result of the matrix calculation in a data memory. CONSTITUTION:Each basic arithmetic unit 1 consists of a multiplier 4, an adder/ subtractor 5, and an internal register 6 and also is provided with two inputs, an output, and a division function. The matrix data is inputted to a data memory from a central arithmetic processor and then outputted to each unit 1 from the data memory. These units 1 carry out the computing operation in parallel with each other in plural steps and stores repetitively the results of the matrix calculation, i.e., the intra-matrix calculation, the adverse matrix calculation, and the matrix transposition calculation into the data memory. Thus the single operation of the Kalman filter gain calculation is completed without performing the middle transfer of data to the central arithmetic processor. Thus, the gain calculating time is shortened and this calculating device can be applied in real time to the signal processing operation.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a calculation device used for high-speed gain calculation of a Kalman filter used in signal processing, image processing, etc.

[Conventional technology]

For high-speed gain calculation of conventional Kalman filters, a device using a systolic array type matrix inner product calculation device 8t as shown in FIG. 7 has been used.

FIG. 8 shows the configuration of the basic arithmetic unit shown in FIG. 7.

Dyne calculation of a Kalman filter consists of matrix inner product calculation, inverse matrix calculation, and transposed matrix calculation, but in the conventional device shown in FIG. 7, only matrix inner product calculation is performed by matrix inner product calculation device 8, and other calculations are performed by central processing unit 9 is going.

[Problem to be solved by the invention]

In conventional devices, in one Kalman filter gain calculation (re), the inverse matrix calculation and the transposed matrix calculation are performed from the matrix inner product calculation results, so it is necessary to transfer data from the matrix inner product calculation device to the central processing unit.

(2) When performing further matrix inner product calculations from the matrix inner product calculation results, it is necessary to transfer data between the data memories of the matrix inner product calculation device via the central processing unit.

Therefore, it is necessary to transfer data several times between the central processing unit and the matrix inner product calculation device, and it takes a long time to calculate the gain of the Kalman filter once, making it difficult to apply it to signal processing in real time. Ta.

The present invention aims to provide a device that solves these problems.

[Means for Solving the Problems] A Kalman filter gain parallel calculation device according to the present invention is a Kalman filter dyne calculation device comprising n basic calculation units 1, n data memories 2, and a central processing unit 3. Each basic arithmetic unit consists of a multiplier 4, an adder/subtractor 5, and an internal register 6, and has two inputs, one output, and a division function, and each data memory has one input and two
The one basic arithmetic unit 1 is arranged in an n×n two-dimensional array, and the first output from each of the n data memories is arranged in a row to which it is assigned. a second input of the elementary arithmetic unit connected in parallel to the first input of the n elementary arithmetic units and arranged in the first row of the column to which the second output from each data memory is assigned; Connect the outputs of the basic arithmetic units arranged in the first to nth rows to the second inputs of the next basic arithmetic units in the same column, and The output of each basic device arranged in the same column is connected to the input of the data memory assigned to the same column.

[Effect]

Matrix data is input from the central processing unit to the data memory, and data is output from the data memory to each basic processing unit. Each basic arithmetic unit performs multiple steps of calculation in parallel, and stores the results of matrix calculations (matrix inner product calculation, matrix inverse calculation, matrix transposition calculation) in data memory. One Kalman filter gain calculation is completed without data transfer with the

〔Example〕

Embodiments of the apparatus of the present invention are shown in FIGS. 1 to 6.

(1) Device configuration example In FIG. 1, the number of basic arithmetic units is n x n = 3 x
3=9, the configuration of a Kalman filter gain parallel calculation device according to an embodiment of the device of the present invention will be shown.

The part surrounded by the dotted line in FIG. 1 is the part showing the features of the present invention. FIG. 2 shows the internal configuration of the basic arithmetic unit shown in FIG. 1.

Each basic arithmetic unit includes a multiplier 4, an adder/subtractor 5, an internal register 6, and a division table 7), and has two inputs and one output. In the embodiment of FIG. 1, the basic arithmetic unit 1-1~
1-9 are arranged in a 3x3 two-dimensional array, and the first output of the data memory 2-1 is connected to the basic arithmetic unit 1-1.1-:1.
, 1-3. Similarly, the first outputs of the data memories 2-2 and 2-3 are connected to the basic arithmetic unit J-4,
, 1-5.

1-6 and 1-1, 1-8. Connect to the first input of 1-9.

The second output of data memory: l-1, 2-2, 2-3 is the second output of basic arithmetic unit 1-1.1-2゜1-3, respectively.
Connect to the input of

Basic arithmetic unit 1- arranged in the 1st to 2nd rows
The outputs of 1.1-2.1-3.1-4.1-5゜1-6 are the basic arithmetic unit 1 arranged in the next row of the same column.
-4.1-5.1-6゜1-7.1-8.1-9 second
Connect to the input of

Basic arithmetic unit 1-7゜1-1 located in the third row
1.1-11 outputs are respectively data memory 2-1.2
-2. Connect to the input of 2-3.

A central processing unit 3 providing matrix data to be calculated is connected to a data memory 2-1.2-2.2-3.

(2) Kalman filter gain calculation The calculation formula for the 247 matrix of the Kalman filter is the following three formulas.

■Z = P -KHP ■P = FZF'+ GQG" ■l(= P H(HPH"+R)"'Here, each character represents a matrix, its order is , t is a positive integer, Z , P, F, Q, G・k×kL
, R...tXt K...kXt H...tXk.

The Kalman filter dyne parallel computing device of the present invention is applicable if the order n is n≧MAX (k, t). It was. Even if k and t are integer multiples of n, even if I is larger than i.

This method can be applied to expansion into a small matrix of matrix tn×n.

Here, assuming h=t, the calculation formula for ■■■ is (Case 1)
D=C+MUXB (Case 2) D=C+AXBT However, A # s p c t o Fih Indicates that the

■Z = P -KHP 1) /'=KXH 2) Z = P -r ■ = P H(HPH"+R)"-'1) Φ=HP 2) Ω=R+ΦH? 3) Ω = Inverse matrix of Ω 4) F=PH 5) K = TI'Ω-1 (Case 1) (Case 1) (Case l) (Case 2) (Inverse matrix) (Case 1) (Case 1) (Case 1) (Case 2) (Case 1) (Case 2) Kokote, 7', A, x, Σ , Φ, Q, are FijkXk matrices.

(3) Matrix inner product calculation example (including transposed matrix) Based on the device configuration example in (1), the case of a 3×3 matrix with υ, k:++:3 is shown in (2) (Case 1), (Case An example of the calculation of 2) is shown below.

First, it is assumed that the first column of matrix data is provided to the data memory 1, the second column to the data memory 2, and the third column to the data memory 3 from the central processing unit. Since the matrices of the calculation results below are also stored in the same allocation, it is possible to perform matrix calculations that include the matrix of the calculation results.

(Case 1) Calculation procedure 10 of D=C+AXB: Give the elements of matrix B from the second output of each data memory to the internal register of each basic arithmetic unit.

The assignment is written in the part showing the basic arithmetic unit in FIG. At this time, four steps of calculation are required.

Step 2. A matrix inner product operation is performed using the data input cetance shown in FIG. However, the input data to the multiplier output from the internal register of each basic arithmetic unit is allocated in all steps and is 9B elements. After six steps, all elements of the matrix are stored in the data memory as shown in FIG.

(Case 2) D = C + A X BTO calculation Calculation procedure 1st issue The output is given to the internal register of each basic arithmetic unit.

The allocation is shown in Figure 4. At this time, four steps of calculation are required.

Step 2. According to the nine data person sequence shown in Figure 4,
The inner product calculation is performed in the same way as in case 1.

After six steps, all elements of the matrix are stored in the data memory as shown in FIG.

(4) Inverse matrix calculation The inverse matrix of a kXk matrix person is calculated by A7' = adj A/ l A l.
Here, adjA is the person's total factor matrix, and IAI is the person's determinant.One determinant is expressed by the product, sum, and difference of O elements of the matrix, and the elements of the total factor matrix are calculated by the minor determinant. Ru.

Therefore, each element of ^-1 can be found by multiplying matrix elements, sum-difference, and performing one reciprocal calculation.

Therefore, in the Kalman filter parallel computing device of the present invention, the product and sum of arbitrary matrix elements in the data memory.

Since difference operations and divisions are possible, inverse matrix calculations are possible.

(Example of Inverse Matrix Calculation) An example of inverse matrix calculation of a 3×3 matrix will be described based on the device configuration example in (1).

1) Calculation of determinant The inverse matrix IAI of the 3×3 matrix A is I A I=a11(azza5s agzazs)−
alz(azlasg-asti2g)+a1s(&z
1as2-a31azz).

The data input sequence for the calculation of the first term is shown in FIG.

Similarly, IAI is calculated by calculating the sum of the second and third terms, and the result is stored in the data memory.

2) Calculation of 1/IAI The division in the device configuration example (1) can be performed by performing convergence calculations using two multiplications and addition/subtraction using an approximation of the reciprocal using the division table.

3) Each element of the inverse matrix B-A-1 is bl 1 = (1/ IA I ) x (a22'55
- asza2a)b1z= (1/IAI)x(as
zalx-aszall)b1a= (1/IAI)X
(azzazs-atsazz)bz1= (1/A
I) x (azaasl-a2tass)bzz= (1
/IAI)X(&5iat1-a!11m1rib2B
= (1/IAI)X(alsazt-allaza)
bs1= (1/IA I)X(121m52-
a2z'51) bsz= (1/IAI)X(151
112-aszall) bss-(1/IAI)X(a
11a2z-a12a21) 0 e.g. bs
s is calculated using the 1/IAIt calculated in 2) according to the data input sequence shown in Figure 6, and the result is stored in the data memo IJ.
JK is stored.

〔Effect of the invention〕

Since the present invention is configured as described above, it produces the effects described below.

(1) Conventional equipment uses a Kalman filter as shown in Figure 1.

In line with the r-in calculation, data transfer between the central processing unit and the matrix calculation device, which was required at least nine times, is no longer necessary.

(2) Therefore, the time required to calculate the Kalman filter gain for one time can be significantly shortened, and the range of application to actual signal processing etc. can be expanded.

[Brief explanation of drawings]

FIG. 1 is a diagram showing the configuration of a dyne parallel computing device for a Kalman filter according to an embodiment of the present invention, FIG. 2 is a diagram showing the configuration of the basic arithmetic device in FIG. 1, and FIG. 3 is an embodiment of the present invention. The figure which shows the data input sequence of the matrix inner product calculation (case 1) concerning. FIG. 4 shows matrix inner product calculation (case 2) according to the embodiment of the present invention.
), FIG. 5 is a diagram showing the data input sequence of determinant calculation according to the embodiment of the present invention, and FIG. 6 is the inverse matrix required IRcbss according to the BAo embodiment of the present invention.
), FIG. 7 is a diagram showing a conventional Kalman filter dyne parallel computing device, and FIG. 8 is a diagram showing the configuration of the basic arithmetic device 1o in FIG. 7. 1.1-1 to 1-9...Basic arithmetic device,! , 2-
DESCRIPTION OF SYMBOLS 1-2-3... Data memory, 3... Central processing unit, 4... Multiplier, 5... Addition/subtraction device, 6... Internal register, 7... Division table, 8 ...Matrix inner product calculation device, 9...Central processing unit, 1o-1 to 1
o-9...Basic arithmetic unit, 11-1 to 11-3...
Row data memory, 12-1 to 12-6... Column data memory, 13°14.° Latch, 15... Multiplier, 1
6... Addition/subtraction device.

Claims (1)

[Claims] In a Kalman filter gain calculation device consisting of n^2 basic arithmetic units (1), n data memories (2), and a central arithmetic unit (3), each basic arithmetic unit performs multiplication. It consists of an adder/subtractor (4), an adder/subtractor (5), and an internal register (6), and has two inputs, one output, and a division function, and each data memory has one input and two outputs, and the n^ The two basic arithmetic units (1) are arranged in an n×n two-dimensional array, and the n basic arithmetic units (1) are arranged in a row to which the first output from each of the n data memories is assigned. connected in parallel to a first input of the arithmetic unit, and a second output from each data memory connected to a second input of the elementary arithmetic unit arranged in the first row of the assigned column; The output of each basic arithmetic unit arranged in the first to nth rows is connected to the second input of the basic arithmetic unit arranged in the next row of the same column, and A Kalman filter gain parallel calculation device characterized in that the outputs of each basic device are connected to the inputs of data memories allocated to the same column.