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END_VAR

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銆�銆�濡傛灉鎴戜滑鎯充紶閫掓暟缁勮�ユ�庝箞鍔炲憿锛屼緥濡傚皢鏁扮粍浣滀负涓�涓�鍙傛暟浼犻�掔粰鍑芥暟鍧楋紵鏁扮粍鍚嶅氨鍍廋璇�瑷�涓�鐨勬寚閽堬紝鍙�浠ョ洿鎺ヤ紶閫掓暟缁勫悕锛屼緥濡侫:=FUN(B)銆備篃鍙�浠ョ洿鎺ョ敤鏁扮粍鍚嶇粰鍙︿竴涓�鏁扮粍璧嬪�硷紝渚嬪�侫:=B銆�
銆�銆�鏁扮粍鐨勫ぇ灏忓彲浠ュ湪瀹氫箟鏃惰�句负鍥哄畾鍊硷紝鍦ㄧ▼搴忔墽琛岃繃绋嬩腑濮嬬粓淇濇寔涓嶅彉銆傝繖鏍锋墍鏈夌殑鐭╅樀杩愮畻鍑芥暟閮藉彧鎺ユ敹杩斿洖鍥哄畾澶у皬鐨勬暟缁勩�備絾鏄�杩欐牱缂栧啓鐨勭▼搴忔病鏈夐�氱敤鎬э紝閬囧埌涓�涓�鏂扮殑闂�棰樻垨鑰呭姞鍏ユ柊鐨勬潯浠舵垜浠�灏辫�佷慨鏀规暟缁勫ぇ灏忥紝寰堢箒鐞愩�傛湁涓�涓�鏂规硶鏄�浣跨敤鍙�鍙橀暱搴︽暟缁� [2,3]锛圓rrays of variable length锛夈�備絾鏄�娉ㄦ剰锛屽彲鍙橀暱搴︽暟缁勫彧鑳界敤浜嶸AR_IN_OUT澹版槑涓�锛屼笉鑳界敤鍦ㄥ叾瀹冨０鏄庝腑锛堜緥濡俈AR鎴栬�匳AR_IN锛夛紝涓嬮潰鎴戠粰鍑轰袱涓�渚嬪瓙銆�
銆�銆�绗�涓�涓�渚嬪瓙鏄�璁＄畻涓や釜鍚戦噺鐨勫唴绉�锛屽皢鍏跺畾涔変负鍑芥暟锛團UN锛夛紝澹版槑閮ㄥ垎濡備笅銆侷nner 鍑芥暟鐨勮繑鍥炲�兼槸REAL绫诲瀷锛岃緭鍏ユ槸涓や釜鍙�鍙橀暱搴︾殑涓�缁存暟缁勶細v1鍜寁2锛屼簩鑰呴暱搴﹀繀椤荤浉绛夛紝娉ㄦ剰v1鍜寁2鐨勫畾涔夋斁鍦ㄤ簡VAR_IN_OUT涓�锛岃�屼笉鏄疺AR涓�銆�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

FUNCTION Inner : REAL;[/align]VAR
	i:LINT;
END_VAR
VAR_IN_OUT
   v1: ARRAY[*] OF REAL;    //杈撳叆鍚戦噺1
   v2: ARRAY[*] OF REAL;    //杈撳叆鍚戦噺2
END_VAR

鍑芥暟涓讳綋閮ㄥ垎濡備笅銆傚湪閬嶅巻鏁扮粍鍏冪礌鏃朵娇鐢ㄤ簡绯荤粺鑷�甯︾殑LOWER_BOUND鍜孶PPER_BOUND鍑芥暟鏉ヨ幏鍙栨暟缁勭殑涓婁笅鐣屻��

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

Inner:=0;[/align]FOR i:=LOWER_BOUND(v1,1) TO UPPER_BOUND(v1,1) BY 1 DO 
	Inner:=Inner+v1[i]*v2[i];
END_FOR;

鍑芥暟浣跨敤鐨勬柟寮忓�備笅銆傝�ュ嚱鏁扮敱浜庝娇鐢ㄤ簡鍙�鍙橀暱搴︾殑鏁扮粍锛屾墍浠ヤ笉闄愬埗杈撳叆鍚戦噺鐨勭淮鏁帮紝瀵逛簬浠绘剰缁存暟鐨勬暟缁勯兘鍙�浠ョ粰鍑烘�ｇ‘鐨勭粨鏋溿��

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

result:=Inner(v1,v2);[/align]

绗�浜屼釜渚嬪瓙鏄�涓や釜鐭╅樀鐩稿姞锛屽０鏄庨儴鍒嗕唬鐮佸�備笅锛�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

FUNCTION MatAdd: BOOL;[/align]VAR_IN_OUT
   A: ARRAY[*,*] OF REAL;   //杈撳叆鐭╅樀
   B: ARRAY[*,*] OF REAL;   //杈撳叆鐭╅樀
   C: ARRAY[*,*] OF REAL;   //杈撳嚭鐭╅樀
END_VAR
VAR
	i:LINT;
	j:LINT;
END_VAR

鍑芥暟涓讳綋閮ㄥ垎濡備笅锛�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

FOR i:=LOWER_BOUND(A,1) TO UPPER_BOUND(A,1) BY 1 DO [/align]	FOR j:=LOWER_BOUND(A,2) TO UPPER_BOUND(A,2) BY 1 DO 
		C[i,j]:=A[i,j]+B[i,j];
	END_FOR;
END_FOR;

璇ュ嚱鏁扮殑浣跨敤鏂瑰紡濡備笅锛屾敞鎰廙atAdd鍓嶉潰娌℃湁璧嬪�肩�﹀彿锛�:=锛夛紝鑰屾槸鐩存帴鎶婃兂瑕佽祴鍊肩殑鏁扮粍浣滀负鍙傛暟浼犻�掔粰浜嗚繖涓�鍑芥暟锛堢殑绗�涓変釜杈撳叆鍙傛暟C锛夛紝C鏁扮粍閲屼繚瀛樼潃鎴戜滑鎯宠�佺殑缁撴灉銆�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

MatAdd(Mat1,Mat2,Mat3);[/align]

3.3銆�鐭╅樀姹傞��

銆�銆�LU鍒嗚В娉曠殑鍏蜂綋ST浠ｇ爜濡備笅锛屽熀鏈�涓嶤璇�瑷�鐗堟湰涓�鏍凤紝鍙�鏈変竴涓�鍦版柟涓嶅悓锛欳璇�瑷�鍙�浠ヤ娇鐢ㄦ寚閽堬紝浣嗘槸ST璇�瑷�鐨勬寚閽堜笉澶�濂界敤锛屾墍浠ユ垜浠�涓嶅緱涓嶆尐涓�鎿嶄綔鐭╅樀涓�鐨勬瘡涓�鍏冪礌锛屽�艰嚧浠ｇ爜鐣ラ暱銆�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

	FOR i:=0 TO n-1 BY 1 DO [/align]		maxA:=0.0;
	    imax:=i;
		FOR k:=i TO n-1 BY 1 DO 
			absA:=ABS(A[k,i]);
			IF absA>maxA THEN
				maxA:=absA;
				imax:=k;
			END_IF
		END_FOR;
		
		IF imax<>i THEN
			//pivoting P
			j:=P[i];
			P[i]:=P[imax];
			P[imax]:=j;
			//pivoting rows of A
			FOR k:=0 TO n-1 BY 1 DO 
				tmp[k]:=A[i,k]; 
			END_FOR;
			FOR k:=0 TO n-1 BY 1 DO 
				A[i,k]:=A[imax,k]; 
			END_FOR;
			FOR k:=0 TO n-1 BY 1 DO 
				A[imax,k]:=tmp[k]; 
			END_FOR;
		END_IF
			
		FOR j:=i+1 TO n-1 BY 1 DO 
			A[j,i]:=A[j,i]/A[i,i]; 
			FOR k:=i+1 TO n-1 BY 1 DO 
				A[j,k]:=A[j,k]-A[j,i]*A[i,k]; 
			END_FOR;
		END_FOR;
	END_FOR;

瀹屾垚LU鍒嗚В鍚庯紝涓嬮潰鍐嶆眰閫嗗氨瀹规槗浜嗭紝浠ｇ爜濡備笅銆�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

	FOR j:=0 TO n-1 BY 1 DO [/align]		FOR i:=0 TO n-1 BY 1 DO 
			IF P[i]=j THEN
				IA[i,j]:=1;
			ELSE
				IA[i,j]:=0;	
			END_IF;	
			FOR k:=0 TO i-1 BY 1 DO 
				IA[i,j]:=IA[i,j]-A[i,k]*IA[k,j];
			END_FOR;
		END_FOR;
		FOR i:=n-1 TO 0 BY -1 DO 		
			FOR k:=i+1 TO n-1 BY 1 DO 
				IA[i,j]:=IA[i,j]-A[i,k]*IA[k,j];
			END_FOR;
			IA[i,j]:=IA[i,j]/A[i,i];
		END_FOR;
	END_FOR;

瀹屾暣鐨勫崱灏旀浖婊ゆ尝杩�浠ｈ繃绋嬩唬鐮佸�備笅锛�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

FOR i:=0 TO 100 BY 1 DO[/align]		//Prediction
		x:=VecAdd(VecAdd(MatVecMul(F,x),u)); 
		P:=MatAdd(MatMul(MatMul(F,P),MatTranspose(F)),Q);
		//Update
		K:=VecMul(MatVecMul(P,H),MatInv(KroneckerProduct(H,P),MatTranspose(H))+Rc);
		x:=VecAdd(x,VecMul(K,z-Inner(H,x)));
		P:=MatMul(MatSub(IdentityMatrix(n),KroneckerProduct(K,H)),P);
	END_FOR;

鍥涖��鍏蜂綋妗堜緥

銆�銆�杩欓噷鎴戜滑鐢ㄤ竴涓�渚嬪瓙鏉ユ��楠屼唬鐮佺殑姝ｇ‘鎬э紝渚嬪瓙鏉ヨ嚜浜嶽4]锛屽叾涓庢枃鐚甗1]宸�涓嶅�氾紝鏄�涓�涓�灏忕悆鍋氳嚜鐢辫惤浣撹繍鍔�锛屼及璁″畠鐨勯珮搴﹀拰閫熷害銆�
銆�銆�鏂囩尞[4]缁欏嚭浜哅ATLAB浠ｇ爜锛屽�備笅銆傚綋鐒讹紝杩欓噷鍙�鏄�浠跨湡缁撴灉锛屽櫔澹扮敤randn鍑芥暟鐢熸垚銆傚洜涓烘槸浠跨湡锛屼负浜嗗�规瘮鍜岃�＄畻浼犳劅鍣ㄨ�傛祴鍊硷紝杩樺畾涔変簡鐪熷疄鐨勭郴缁熺姸鎬亁t銆備豢鐪熶腑锛岀湡瀹炵姸鎬亁t鏄�娌℃湁鍣�澹扮殑锛堝畬缇庣殑锛夛紝浼拌�″�兼槸鏈夊櫔闊崇殑銆�

[AppleScript] 绾�鏂囨湰鏌ョ湅 澶嶅埗浠ｇ爜

% Define the system[/align]N = 100;  % number of time steps
dt = 0.01;  % Sampling time (s)
t = dt*(1:N);  % time vector (s)
F = [1, dt; 0, 1];  % system matrix - state
G = [-1/2*dt^2; -dt];  % system matrix - input
H = [1 0];  % observation matrix
Q = [0, 0; 0, 0];  % process noise covariance
u = 9.80665;  % input = acceleration due to gravity (m/s^2)
I = eye(2);  % identity matrix
% Define the initial position and velocity
y0 = 100;  % m
v0 = 0;  % m/s
% Initialize the state vector (true state)
xt = zeros(2, N);  % True state vector
xt(:, 1) = [y0; v0];  % True intial state
% Loop through and calculate the true state
for k = 2:N 
xt(:, k) = F*xt(:, k-1) + G*u;  % Propagate the states through the prediction equations
end
% Generate the noisy measurement from the true state
R = 4;  % m^2/s^2
v = sqrt(R)*randn(1, N);  % measurement noise
z = H*xt + v;  % noisy measurement
%% Perform the Kalman filter estimation
% Initialize the state vector (estimated state)
x = zeros(2, N);  % Estimated state vector
x(:, 1) = [105; 0];  % Guess for initial state
% Initialize the covariance matrix
P = [10, 0; 0, 0.01];  % Covariance for initial state error
% Loop through and perform the Kalman filter equations recursively
for k = 2:N 
x(:, k) = F*x(:, k-1) + G*u;  % Predict the state vector
P = F*P*F' + Q;  % Predict the covariance
K = P*H'/(H*P*H' + R); % Calculate the Kalman gain matrix
x(:,k) = x(:,k) + K*(z(k) - H*x(:,k)); % Update the state vector
P = (I - K*H)*P; % Update the covariance
end
%% Plot the results
plot(t, x(1,:), 'b--', 'LineWidth', 2); 
hold on; plot(t, xt(1,:), 'r:', 'LineWidth', 1.5) 
xlabel('t (s)'); ylabel('x_1 = h (m)'); grid on; 
legend('Measured','Estimated','True'); 

鍙傝�冭祫鏂�

[1] 鍗″皵鏇兼护娉㈠櫒鍦≒LC绯荤粺涓�鐨勫疄鐜帮紝寰愭壙鐖憋紝鑷�鍔ㄥ寲鎶�鏈�涓庡簲鐢�, 2014.
[2] https://help.codesys.com/api-content/2/codesys/3.5.12.0/en/_cds_datatype_array/
[3] IEC 61131-3: Arrays with variable length
[4] A Kalman Filtering Tutorial for Undergraduate Students