JPS59210328A - Interpolation system for sample data - Google Patents

Abstract

PURPOSE:To suppress undesirable waviness which occurs where variation in sound speed with depth is very large by estimating a gradient at each sample data position previously, and performing interpolation on the condition based upon the estimated values. CONSTITUTION:The sample data sequence of a continuous signal inputted from an input terminal 1 is stored in a register 2, and a mean gradient calculating means 3 read the sample data sequence successively and calculates and stores the mean gradient of each section in a register 4. Further, gradient interpolating means 5 access mean gradients successively, and calculates and stores estimated values of the gradients at sample data positions in a register 6. When the gradient values are calculated, a signal interpolating means 7 reads sample data out of the register 2 and the estimated gradient values out of the register 6 and calculates and stores the parameter of the interpolation function of an sound speed profile in each section divided by the sample data in a storage means 8 together with boundary depth.

Description

DETAILED DESCRIPTION OF THE INVENTION (Technical Field) The present invention relates to a sample data interpolation method for functionally approximating original continuous information based on sample data from continuous information.

Numerical calculations based on sound ray theory and wave theory are performed to predict the propagation characteristics of sound waves in the ocean, but this requires data on the vertical distribution of sound speed in seawater (hereinafter referred to as the sound speed profile). It is necessary as In calculations based on sound ray theory, if there is a discontinuity in the vertical change in the gradient of the sound speed with respect to depth, problems such as an imaginary focal line or a discontinuous change in sound pressure occur in calculating the sound intensity. As a means to solve this inconvenience, (1) perform correction using higher-order approximation theory;

(2) Approximate the sound speed profile by a function with a continuous gradient.

There are two methods, one of which is method (2).
A method of sound velocity profile interpolation using the following equation has been conventionally used.

C2(z)-Ca2[1-Ka (Z-Za)2)
' (1) Here, Z represents the depth and C(Z) represents the speed of sound. Also, Ca.

Ka and Za are constants determined to fit the sample data. If sample data changes rapidly, several functions must be interpolated by force.

The procedure of the conventional interpolation method will be explained. The depth and sound speed values of the sound speed profile data are Z,,C,, respectively.

Let l 1 = 1.2, . . . 2M. Interpolation is performed in the following steps.

(1) Set the sound velocity tolerance for interpolation.

(2) Three or more pieces of data are taken out in order from the seabed or sea surface, and the parameters Ca, Ka, and Za of the interpolation function (1) are determined by least squares approximation. The accuracy of the interpolation results is checked at the depth of the sample data, and if the tolerance is satisfied at all depths, data is added one point at a time and the interpolation is restarted. If you are not satisfied,
Leave the previous interpolation result. In this way, as much sample data as possible is interpolated with one function within the range that satisfies the tolerance. This is designated as C1[F]).

(3) If it is possible to interpolate up to the m-th data in the previous section, interpolate the data of three or more points from the (m-1)th data using the same method as in the previous section, and obtain the nomurameters Ca', Ka', Define Za'. Let this function be 04(Z).

(4) (m-z, LJth sample data depth 2
Interpolation is performed for the section from m- to the m-th sample data depth- so that the following four conditions are satisfied.

C(Zm-1)-C4(zm,,-1)C'(zm)-
C14 (zm) where prime (ri represents differentiation by argument. (1)
Equation (2) has three undetermined parameters, whereas Equation (2) has four conditions, so all conditions up to 1 cannot be satisfied. Therefore, the interval is zm, <ζ<
Divide into two at a depth ζ of Zm(M or -1>ζ>Z,) and each section is C2(Z).

Interpolation is performed using two functions C3(Z).

In addition to the four conditions in equation (2), the parameters of C2(z) and C3(z) are: C2(ζ) = C, (ζ) (3) C4(ζ) = C', (ζ) be determined to satisfy. The depth ζ is C2(Z
,,)+C (visual −1) (ζ−ζ1)=c, (z□)+
C5 (Z□) (ζ-view) Obtain according to (4). however,
ζ obtained by equation (4) is the interval (zm-1' zm
) When going outside, use the following values.

(5) For further sample data, (
By repeating the same method as in 3) and (4), it is possible to realize interpolation that satisfies the condition that the speed of sound and the gradient of sound speed are continuous.

This conventional method is very effective in that it can uniquely perform interpolation given sample data and a tolerance, and can interpolate well if the sample data changes smoothly. In areas where the speed of sound changes sharply with depth, such as the surface layer of seawater or the seasonal thermocline, undesirable ridges may form.

In order to suppress this type of distortion, it is necessary to add sample data to important points, but this work requires experience and intuition.

(Problem to be solved by the invention) The present invention estimates the slope at each sample data position in advance and performs interpolation using the estimated value as a constraint, thereby eliminating the above-mentioned inconvenience without relying on experience or intuition. This will be explained in detail below.

(Structure and operation of the invention) The present invention will now be described in detail. If the Zannor value (Z,, C4), i=1, 2,...2M of the function C(Z) is given, and a person interpolates by hand after looking at it, the currently drawn To determine the slope of the part where you are, refer to the positions of several sample data before and after it. AKi
ma modeled this process as follows.

The gradient c'(z,) at 2=2 is determined as a function of five points, including two points before and after it, as shown in the following equation.

Here, g is the average slope g of the interval (Zi 'Zi-1)
□-(C□+1 'i)/(Zi+1 ''□)(
7). When the denominator of equation (6) is zero, C'
(Zl) is given by the following formula.

C'(Z□) -(gi-1+g1)/2
(8) To determine the slope at both end sample data points, g-1'go' and gM l gM+
You need to set it to 1. These are assumed as follows.

g-, =go=g1 ・gM+1 = gM=
gM-1 (9) MacKin no n etc. is this Ak
The sound velocity profile was approximated by a polynomial using the ima method. However, Z, (Z(Zl, -1, i = 1
, 2, "', M-1, the above (
By applying the method in section 4), a sound velocity profile that allows the sound ray path and sound intensity to be calculated analytically is realized. Moreover, since the slope at each sample data point is estimated in advance and the estimated value is used as a constraint condition, the occurrence of undesirable waviness is suppressed.

Next, examples of the present invention will be described. FIG. 1 is a detailed explanatory diagram of the present invention. In the figure, 1° sample data input terminals 2, 4, 6, register 3, average gradient calculation means for calculating the average gradient between each sample data.

5... Gradient interpolation means 7 for calculating the estimated value of the gradient at the sample data position based on the average gradient information of each section calculated by the average gradient calculation means 7... The sample data and Signal interpolation means 8 which calculates the parameter of the interpolation function in each section using the estimated gradient value; storage means which stores the parameter of the interpolation function.

Next, the operating principle of this device will be explained. The sample data string of the continuous signal input to input terminal 1 is also stored in register 2.
is stored in The average gradient calculation means 3 sequentially outputs the sample data string stored in the register 2, (7)
And by equation (9), the average slope g, ,i in each section
= -1, 0, 1,...1M.

Calculate M+1 and store it in register 4. The gradient interpolation means 5 sequentially calls the average gradient gi stored in the register 4, and calculates the sample value according to equations (6) and (8).
An estimated value C' of the gradient at the data position is calculated and stored in the register 6.

When the estimated gradient value is calculated, the signal interpolation means 7 inputs the sample data AiJ from the register 2 (2, .

cl), (zl, c2). Still register 6
The gradient estimated values C1, , C/2 are called from. Next, the position of the boundary ζ when dividing the interval (21, 22) into two
1 is calculated using equations (4) and (5). Section (Z4
．． ζ1) and the interpolation function in the interval (ζ1'''2), respectively, as CF+(Z)=CaF1[I Ka, , (
Z-Zal,)2)-1Z,<Z<ζ1(]0) c, % (z) 2Ca, ”2[II Ka
12 (Z Za12 )2]” ζ1<z<Z2
Anyway, the following six conditions CF"Zl) -C12 C12(Z2) -C22 Show (zl)201 C+12(Z2) = "2
(11) "i'1 (ζ1) = R2 (ζ1) CI'1 (ζ1) ""1'2 (ζ1) is made simultaneous to obtain the parameter Ca11.K, ]11. Zall,
Ca12+Ka12. Za12 is calculated and the result is stored in the storage means 8.

Repeat the same procedure for i = 2, 3 p...1M-1 and repeat the same procedure for 1,6 rammeters C211, Ka, , c
a2.2 p I(a□2 lZa s 2 is calculated and stored in the storage means 8.

Boundary depth Z., l::l,...2M1ζ, i=1.
2゜1
1...1M-1 are also stored in the storage means 8 at the same time.

As explained above, in the embodiment of the present invention, the sample
The gradient of the function at the data position is estimated with reference to the two sample data positions before and after it, and the interpolation function is determined using the estimated gradient as a constraint, resulting in interpolation results that often occur with conventional methods. Inconvenient ridges can be suppressed without relying on experience or intuition.

(Effects of the Invention) Since the present invention estimates the slope in advance and uses it as a constraint, it is possible to obtain a natural interpolation function similar to when a person visually draws an interpolation curve. Since this results in the same functional form as the function used in the 7 simulations of sound wave propagation, it can be used in sonar performance evaluation systems, etc.

[Brief explanation of the drawing]

Ru. 1...Input terminal, 2,4,6...Renostar, 3...
- Average gradient calculation means, 5... Gradient interpolation means, 7...
Signal interpolation means, 8... Storage means. Patent applicant Oki Electric Industry Co., Ltd. Patent application agent Megumi Yamamoto −

Claims (1)

[Claims] In a sample data interpolation method for functionally approximating an original sound speed profile from sample data of a sound speed profile in water, the sample data σ) means for calculating an average gradient between adjacent data; gradient interpolation means for calculating an estimated value of a gradient θ applied to the sample data point; and an interpolation function θ of the sound speed profile within each section delimited by the sample take from the sample data and the estimated gradient value. )para 7
- a signal interpolation means for calculating θ, and when the sound ray path and sound intensity are given in a closed form while maintaining gradient continuity, θ is
) A sample data interpolation method that uses a function that can be used to interpolate sample data.