CN103699012A - Shooting calculation model of fire-fighting water monitor - Google Patents

Abstract

The invention relates to a shooting calculation model of a fire-fighting water monitor. The shooting calculation model comprises a shooting filter model and a shooting calculation model, wherein the shooting filter model is as follows: (1) a least square filter model; (2) a tracking and predicating self-adaptive filter algorithm: by combination of a least square identification algorithm and a Kalman filter, online identification and filtering can be realized, parameters a and b are obtained by identification of a filtering output result, a state transfer matrix of a target model in the Kalman filter is determined by the parameters a and b, and circulating calculation is carried out so, and the shooting calculation model is as follows: an encounter trajectory approximation method is mainly adopted, encounter water monitor future points are predicated by combination with the fire-control common method of a shipboard-artillery weapon system, and the influence of the weather condition to the reaching point of the water monitor is fully considered. The shooting calculation model has the advantages of fewer errors and high accuracy.

Description

Fire water monitor firing solution model

Technical field

The invention belongs to fire prevention field,

Background technology

Along with Modern Ships technical development, various types of naval vessels, for multiple-tasks such as maritime defense, patrol, anti-terrorisms, have proposed higher requirement to its security against fire.The fire characteristic in these places has: intensity of a fire development is rapid, fire scale is large, have explosion danger etc.Abroad the security against fire of this inflammable and explosive hazardous area is quite paid attention to, as the industrially developed country such as Japan, Britain, Germany have worked out corresponding law and standard, be clearly defined in above place and must be equipped with fire water monitor system.Fire water monitor system is installed in specific position, is linked with fire-fighting system, the very first time that can occur at fire, according to fire fighter, need to reach by remote control the object of quick extinguishing.In addition,, aspect anti-terrorism peacekeeping, utilize water cannon to tackle local and overseas lawless persons.

Needs in view of current naval vessels fire-fighting, native system can be according to commander's order or target indication, find in time, catch, follow the tracks of marine naval vessel or shore target, receive the own warship pitching that on-board equipment inertial navigation system detects in real time, rolling data, receive the hydraulic pressure of the water-pressure survey instrument detection of non-lethal intelligent water cannon itself, reception is from the target angle of optronic tracker, angular altitude, mixing console real-time resolving goes out the data-out of non-lethal intelligent water cannon orientation and pitching, control non-lethal intelligent water cannon orientation and elevation servo, complete the rescue to sea or opposite bank target, fire extinguishing, explosion-proof, anti-terrorism, anti-pirate, the task such as fight crime.

Existing fire water monitor is divided into and has or not control water cannon and remote control water cannon, and during without the fire at a target of control water cannon, deviation is large, precision is low, cannot be to the enforcement precision strike that strikes target; Remote control water cannon can be controlled the orientation of water cannon, just by control system, and for fire extinguishing, generally without fire control system, precision is not high, affected by wind speed, wind direction larger, and the remote bias current of water cannon is excessive, cannot time real correction.

Summary of the invention

In order to overcome the shortcoming of prior art, the invention provides a kind of fire water monitor firing solution model.Its error is little, and precision is high.

The present invention solves the technical scheme that its technical matters takes: comprise shooting Filtering Model and firing solution model; Described shooting Filtering Model:

(1), least squares filtering model is as shown in the formula expression:

y _i＝ax _i+b

$y=-\frac{2}{n}\mathrm{\Σ}{y}_i+\frac{6}{n(n+1)}\mathrm{\Σj}\·y_i$

$a=-\frac{6}{\mathrm{\ΔT}(n-1)n}\mathrm{\Σ}{y}_i+\frac{12}{\mathrm{\ΔT}(n^2-1)n}\mathrm{\Σj}\·y_i$

y _i＝Y _i-S _n-i

$\mathrm{\Σ}{y}_i=\mathrm{\Σ}{Y}_i-\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{S}_{n-i}$

$\mathrm{\Σj}\·y_i=\mathrm{\Σj}\·Y_i-\underset{i=0,j=1}{\overset{n}{\mathrm{\Σ}}}j\·S_{n-i}$

Sampled data sequence x _i(i=1,2,3...), the sampling period is △ T, and be ns observing time, and my warship voyage is S _ni;

(2), follow the tracks of and predict adaptive filter algorithm:

Least square identification algorithm, in conjunction with Kalman wave filter, can realize on-line identification filtering, by the identification of filtering Output rusults, obtains parameter a, b, by parameter a, b, determines the state-transition matrix of object module in Kalman wave filter, so cycle calculations;

T target state equation and observation equation is constantly

$\left[\begin{array}{c}{\stackrel{\·}{x}}_1\left(t\right)\\ {\stackrel{\·}{x}}_2\left(t\right)\\ {\stackrel{\·}{x}}_3\left(t\right)\end{array}\right]=\begin{array}{}\end{array}\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& a\end{array}\right]\·\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\·b+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\·w\left(t\right)$

$y\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\·\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+v\left(t\right)$

Getting state variable is: X (t)=[x ₁(t) x ₂(t) x ₃(t)] ^t, above formula can turn to

$\stackrel{\·}{X}\left(t\right)=A\left(a\right)\·X\left(t\right)+B\·b+C\·W\left(t\right)$

Y（t)＝H·X(t)+V(t)

Wherein: $A\left(a\right)=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& a\end{array}\right],B=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],C=\begin{array}{c}\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],H=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\end{array}$

W (t), V (t) is zero-mean white noise sequence independently mutually, statistical property is as follows:

E[W(t)]＝E[V(t)]＝O，E[W(t)·W ^T(τ) ^t]＝q·δ(t-τ)，E[V(t)·V ^T(τ)]＝R·δ(t-τ)

Above-mentioned continuity equation is carried out to discretize processing, obtain the identification model equation of motion in the discrete moment

X(k+1)＝Φ(k+1，k)·X(k)+U·b+Γ·W(k)

Z(k)＝H·X(k)+V(k)

Wherein:

$\mathrm{\Φ}(k+1,k)=e^{A\left(a\right)T}=\left[\begin{array}{ccc}1& T& -\frac{1}{a^2}\·(1+\mathrm{aT}-e^{\mathrm{aT}})\\ 0& 1& -\frac{1}{a}\·(1-e^{\mathrm{aT}})\\ 0& 0& e^{\mathrm{aT}}\\ & & \end{array}\right]$

$U={\&Integral;}_0^T{e}^{\mathrm{At}}\&CenterDot;\mathrm{dt}\&CenterDot;B\begin{array}{}\end{array}\left[\begin{array}{c}-\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}\&CenterDot;[T+\frac{a}{2}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})]\\ -\frac{1}{a}\&CenterDot;[T+\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\\ -\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\end{array}\right]=\mathrm{\&Gamma;}$

Q＝E{[Γ·w(k)]·[Γ·w(k)] ^T}＝Γ·E[w(k)·w(k) ^T]·Γ ^T

Application Kalman filtering, obtains following filtering equations:

$\hat{X}(k/k-1)=\mathrm{\&Phi;}(k,k-1)\&CenterDot;\hat{X}(k-1/k-1)+\mathrm{\&Gamma;}(k,k-1)\&CenterDot;b$

P(k/k-1)＝Φ(k，k-1)·P(k-1/k-1)·Φ ^T(k，k-1)+Γ(k，k-1)·Q(k-1)·Γ ^T(k，k-1)

K(k)＝P(k/k-1)·H ^T(k)·[H(k)·P(k/k-1)·H ^T(k)+R(k)] ^-1

$\hat{X}(k/k)=\hat{X}(k/k-1)+K\left(k\right)\&CenterDot;[Z\left(k\right)-H\left(k\right)\&CenterDot;\hat{X}(k/k-1)]$

P(k/k)＝[I-K(k)·H(k)]·P(k/k-1)

Filtering algorithm based on identification model is realized according to on-line identification filtering principle, utilize least square identification algorithm, by the identification of filtering Output rusults, obtain parameter a, b, by parameter a, b, determined again the state-transition matrix of object module in Kalman wave filter, cycle calculations, until precision reaches requirement;

Affiliated firing solution model:

Firing solution model mainly adopts separate to meet trajectory approximatioss, and in conjunction with the fire control common method of shipborne gun system, the prediction solution water cannon that meets is not given me a little, and takes into full account meteorological condition water cannon to impact a little, calculates firing data, and jet curvilinear equation is:

$y=A\tan {\mathrm{\&theta;}}_0\&CenterDot;\mathrm{Bx}-C\frac{{\mathrm{<figure-callout\; id="0"\; label="gx\; E\; v"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">gx</figure-callout>}}^E}{v_{}^{}}-D\&CenterDot;\frac{{\mathrm{gx}}^3}{{\left({\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_0\cos {\mathrm{\&theta;}}_0\right)}^3}$

Wherein y is for penetrating height, θ ₀for firing angle, v ₀for initial velocity, g is acceleration of gravity, and x is range, A, and B, C, D, E is ballistic coefficient, g is acceleration of gravity.

The target data that the present invention gathers sensor by fire control system, in conjunction with ship gesture information, weather information, sets up water cannon firing solution model, accurately resolves firing data, and can revise in real time, realizes the precision strike to enemy.

Accompanying drawing explanation

Fig. 1 is System Working Principle figure of the present invention;

Fig. 2 is that on-line identification filtering of the present invention realizes schematic diagram;

Fig. 3 is the filtering algorithm realization flow figure that the present invention is based on identification model;

Fig. 4 is water cannon jet path figure of the present invention.

Embodiment

Fire water monitor is mainly comprised of control box, automatically controlled fire water monitor, Fire Fighting Pumps, electric motor for pump or diesel engine.Fire water monitor is that the target information of utilizing control desk to send, weather information, navigation information etc. carry out the automatic track and localization of water cannon, and control that water cannon is realized rescue, fire extinguishing, explosion-proof, anti-terrorism, anti-pirate, the fixing fluidic system of the task such as fight crime.

Resolve transaction module mainly according to particle kinematics, exterior ballistics scheduling theory, on fire monitor water jet actual measurement track curve basis, derivation water cannon jet path equation, its core is that parameter relevant in water cannon work is incorporated to this equation as wind direction, wind speed, pressure, flow velocity etc., the target data gathering according to current wind speed and direction, sensor, the own warship attitude providing in conjunction with inertial navigation system solves data-out, drive fire monitor to pirate, the lawless person such as steal into another country and suppress; Data-out, on the basis of calculating, can manually be revised.First firing solution module will carry out smothing filtering to sensor information, and common method has the filtering methods such as least squares filtering, Kalman filtering, alpha-beta-γ, data message is carried out to denoising, thereby reduce error, improves system accuracy.

The present invention includes shooting Filtering Model and firing solution model.

Described shooting Filtering Model:

(1), least squares filtering model is as shown in the formula expression:

y _i＝ax _i+b

$y=-\frac{2}{n}\mathrm{\&Sigma;}{y}_i+\frac{6}{n(n+1)}\mathrm{\&Sigma;j}\&CenterDot;y_i$

$a=-\frac{6}{\mathrm{\&Delta;T}(n-1)n}\mathrm{\&Sigma;}{y}_i+\frac{12}{\mathrm{\&Delta;T}(n^2-1)n}\mathrm{\&Sigma;j}\&CenterDot;y_i$

y _i＝Y _i-S _n-i

$\mathrm{\&Sigma;}{y}_i=\mathrm{\&Sigma;}{Y}_i-\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{S}_{n-i}$

$\mathrm{\&Sigma;j}\&CenterDot;y_i=\mathrm{\&Sigma;j}\&CenterDot;Y_i-\underset{i=0,j=1}{\overset{n}{\mathrm{\&Sigma;}}}j\&CenterDot;S_{n-i}$

Sampled data sequence x _i(i=1,2,3...), the sampling period is △ T, and be ns observing time, and my warship voyage is S _ni.

(2), follow the tracks of and predict adaptive filter algorithm:

Least square identification algorithm, in conjunction with Kalman wave filter, can realize on-line identification filtering, by the identification of filtering Output rusults, obtain parameter a, b, by parameter a, b, determine the state-transition matrix of object module in Kalman wave filter, cycle calculations like this, as shown in Figure 2.

T target state equation and observation equation is constantly

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_2\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_3\left(t\right)\end{array}\right]=\begin{array}{}\end{array}\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& a\end{array}\right]\&CenterDot;\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\&CenterDot;b+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\&CenterDot;w\left(t\right)$

$y\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\&CenterDot;\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+v\left(t\right)$

Getting state variable is: X (t)=[x ₁(t) x ₂(t) x ₃(t)] ^t, above formula can turn to

$\stackrel{\&CenterDot;}{X}\left(t\right)=A\left(a\right)\&CenterDot;X\left(t\right)+B\&CenterDot;b+C\&CenterDot;W\left(t\right)$

Y（t)＝H·X(t)+V(t)

Wherein: $A\left(a\right)=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& a\end{array}\right],B=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],C=\begin{array}{c}\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],H=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\end{array}$

W (t), V (t) is zero-mean white noise sequence independently mutually, statistical property is as follows:

E[W(t)]＝E[V(t)]＝O，E[W(t)·W ^T(τ) ^t]＝q·δ(t-τ)，E[V(t)·V ^T(τ)]＝R·δ(t-τ)

Above-mentioned continuity equation is carried out to discretize processing, obtain the identification model equation of motion in the discrete moment

X(k+1)＝Φ(k+1，k)·X(k)+U·b+Γ·W(k)

Z(k)＝H·X(k)+V(k)

Wherein:

$\mathrm{\&Phi;}(k+1,k)=e^{A\left(a\right)T}=\left[\begin{array}{ccc}1& T& -\frac{1}{a^2}\&CenterDot;(1+\mathrm{aT}-e^{\mathrm{aT}})\\ 0& 1& -\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\\ 0& 0& e^{\mathrm{aT}}\\ & & \end{array}\right]$

$U={\&Integral;}_0^T{e}^{\mathrm{At}}\&CenterDot;\mathrm{dt}\&CenterDot;B\begin{array}{}\end{array}\left[\begin{array}{c}-\frac{1}{a^2}\&CenterDot;[T+\frac{a}{2}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})]\\ -\frac{1}{a}\&CenterDot;[T+\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\\ -\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\end{array}\right]=\mathrm{\&Gamma;}$

Q＝E{[Γ·w(k)]·[Γ·w(k)] ^T}＝Γ·E[w(k)·w(k) ^T]·Γ ^T

Application Kalman filtering, obtains following filtering equations:

$\hat{X}(k/k-1)=\mathrm{\&Phi;}(k,k-1)\&CenterDot;\hat{X}(k-1/k-1)+\mathrm{\&Gamma;}(k,k-1)\&CenterDot;b$

P(k/k-1)＝Φ(k，k-1)·P(k-1/k-1)·Φ ^T(k，k-1)+Γ(k，k-1)·Q(k-1)·Γ ^T(k，k-1)

K(k)＝P(k/k-1)·H ^T(k)·[H(k)·P(k/k-1)·H ^T(k)+R(k)] ^-1

$\hat{X}(k/k)=\hat{X}(k/k-1)+K\left(k\right)\&CenterDot;[Z\left(k\right)-H\left(k\right)\&CenterDot;\hat{X}(k/k-1)]$

P(k/k)＝[I-K(k)·H(k)]·P(k/k-1)

Filtering algorithm based on identification model is realized according to on-line identification filtering principle, utilize least square identification algorithm, by the identification of filtering Output rusults, obtain parameter a, b, by parameter a, b, determined again the state-transition matrix of object module in Kalman wave filter, cycle calculations, until precision reaches requirement, as shown in Figure 3.

Affiliated firing solution model:

Firing solution model mainly adopts separate to meet trajectory approximatioss, and in conjunction with the fire control common method of shipborne gun system, the prediction solution water cannon that meets is not given me a little, and takes into full account meteorological condition water cannon to impact a little, calculates firing data, and jet curvilinear equation is:

$y=A\tan {\mathrm{\&theta;}}_0\&CenterDot;\mathrm{Bx}-C\frac{{\mathrm{<figure-callout\; id="0"\; label="gx\; E\; v"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">gx</figure-callout>}}^E}{v_{}^{}}-D\&CenterDot;\frac{{\mathrm{gx}}^3}{{\left({\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="HDA0000443367780000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_0\cos {\mathrm{\&theta;}}_0\right)}^3}$

Wherein y is for penetrating height, θ ₀for firing angle, v ₀for initial velocity, g is acceleration of gravity, and x is range, A, and B, C, D, E is ballistic coefficient, g is acceleration of gravity.

As shown in Figure 4, applied shooting hits model and weeds out the old and bring forth the new and derive the trajectory diagram of water cannon, and through actual verification, through relatively the two curve is more approaching.The initial velocity of water cannon jet is 21.3m/s, firing angle is 30 °, maximum range can reach 65m, simulation and experiment result figure is compared as follows: result reflects the impact due to actual wind from the graph, there is the phenomenon of dispersing in current, actual shooting distance far away than theoretical value endways, be mainly due to the direction of wind direction and water cannon jet in the same way, when water cannon jet is reverse, penetrate apart from greatly reducing.

Claims (1)

1. a fire water monitor firing solution model, is characterized in that: comprise shooting Filtering Model and firing solution model; Described shooting Filtering Model:

(1), least squares filtering model is as shown in the formula expression:

y _i＝ax _i+b

$y=-\frac{2}{n}\mathrm{\&Sigma;}{y}_i+\frac{6}{n(n+1)}\mathrm{\&Sigma;j}\&CenterDot;y_i$

$a=-\frac{6}{\mathrm{\&Delta;T}(n-1)n}\mathrm{\&Sigma;}{y}_i+\frac{12}{\mathrm{\&Delta;T}(n^2-1)n}\mathrm{\&Sigma;j}\&CenterDot;y_i$

y _i＝Y _i-S _n-i

$\mathrm{\&Sigma;}{y}_i=\mathrm{\&Sigma;}{Y}_i-\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{S}_{n-i}$

$\mathrm{\&Sigma;j}\&CenterDot;y_i=\mathrm{\&Sigma;j}\&CenterDot;Y_i-\underset{i=0,j=1}{\overset{n}{\mathrm{\&Sigma;}}}j\&CenterDot;S_{n-i}$

Sampled data sequence x _i(i=1,2,3...), the sampling period is △ T, and be ns observing time, and my warship voyage is S _ni;

(2), follow the tracks of and predict adaptive filter algorithm:

Least square identification algorithm, in conjunction with Kalman wave filter, can realize on-line identification filtering, by the identification of filtering Output rusults, obtains parameter a, b, by parameter a, b, determines the state-transition matrix of object module in Kalman wave filter, so cycle calculations;

T target state equation and observation equation is constantly

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_2\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_3\left(t\right)\end{array}\right]=\begin{array}{}\end{array}\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& a\end{array}\right]\&CenterDot;\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\&CenterDot;b+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\&CenterDot;w\left(t\right)$

$y\left(t\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\&CenterDot;\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]+v\left(t\right)$

Getting state variable is: X (t)=[x ₁(t) x ₂(t) x ₃(t)] ^t, above formula can turn to

$\stackrel{\&CenterDot;}{X}\left(t\right)=A\left(a\right)\&CenterDot;X\left(t\right)+B\&CenterDot;b+C\&CenterDot;W\left(t\right)$

Y（t)＝H·X(t)+V(t)

Wherein: $A\left(a\right)=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& a\end{array}\right],B=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],C=\begin{array}{c}\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],H=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\end{array}$

W (t), V (t) is zero-mean white noise sequence independently mutually, statistical property is as follows:

E[W(t)]＝E[V(t)]＝O，E[W(t)·W ^T(τ) ^t]＝q·δ(t-τ)，E[V(t)·V ^T(τ)]＝R·δ(t-τ)

Above-mentioned continuity equation is carried out to discretize processing, obtain the identification model equation of motion in the discrete moment

X(k+1)＝Φ(k+1，k)·X(k)+U·b+Γ·W(k)

Z(k)＝H·X(k)+V(k)

Wherein:

$\mathrm{\&Phi;}(k+1,k)=e^{A\left(a\right)T}=\left[\begin{array}{ccc}1& T& -\frac{1}{a^2}\&CenterDot;(1+\mathrm{aT}-e^{\mathrm{aT}})\\ 0& 1& -\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\\ 0& 0& e^{\mathrm{aT}}\\ & & \end{array}\right]$

$U={\&Integral;}_0^T{e}^{\mathrm{At}}\&CenterDot;\mathrm{dt}\&CenterDot;B\begin{array}{}\end{array}\left[\begin{array}{c}-\frac{1}{a^2}\&CenterDot;[T+\frac{a}{2}\&CenterDot;T^2+\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})]\\ -\frac{1}{a}\&CenterDot;[T+\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\\ -\frac{1}{a}\&CenterDot;(1-e^{\mathrm{aT}})\end{array}\right]=\mathrm{\&Gamma;}$

Q＝E{[Γ·w(k)]·[Γ·w(k)] ^T}＝Γ·E[w(k)·w(k) ^T]·Γ ^T

Application Kalman filtering, obtains following filtering equations:

$\hat{X}(k/k-1)=\mathrm{\&Phi;}(k,k-1)\&CenterDot;\hat{X}(k-1/k-1)+\mathrm{\&Gamma;}(k,k-1)\&CenterDot;b$

P(k/k-1)＝Φ(k，k-1)·P(k-1/k-1)·Φ ^T(k，k-1)+Γ(k，k-1)·Q(k-1)·Γ ^T(k，k-1)

K(k)＝P(k/k-1)·H ^T(k)·[H(k)·P(k/k-1)·H ^T(k)+R(k)] ^-1

$\hat{X}(k/k)=\hat{X}(k/k-1)+K\left(k\right)\&CenterDot;[Z\left(k\right)-H\left(k\right)\&CenterDot;\hat{X}(k/k-1)]$

P(k/k)＝[I-K(k)·H(k)]·P(k/k-1)

Filtering algorithm based on identification model is realized according to on-line identification filtering principle, utilize least square identification algorithm, by the identification of filtering Output rusults, obtain parameter a, b, by parameter a, b, determined again the state-transition matrix of object module in Kalman wave filter, cycle calculations, until precision reaches requirement;

Affiliated firing solution model:

Firing solution model mainly adopts separate to meet trajectory approximatioss, and in conjunction with the fire control common method of shipborne gun system, the prediction solution water cannon that meets is not given me a little, and takes into full account meteorological condition water cannon to impact a little, calculates firing data, and jet curvilinear equation is:

$y=A\tan {\mathrm{\&theta;}}_0\&CenterDot;\mathrm{Bx}-C\frac{{\mathrm{gx}}^E}{v_0^2{\cos }^2{\mathrm{\&theta;}}_0}-D\&CenterDot;\frac{{\mathrm{gx}}^3}{{\left(v_0\cos {\mathrm{\&theta;}}_0\right)}^3}$

Wherein y is for penetrating height, θ ₀for firing angle, v ₀for initial velocity, g is acceleration of gravity, and x is range, A, and B, C, D, E is ballistic coefficient, g is acceleration of gravity.

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