CN103196450B - Kalman filtering method based on analog circuit and analog circuit - Google Patents

Abstract

The invention discloses a Kalman filtering method based on an analog circuit and the analog circuit. The method is characterized in that based on the continuous-time Kalman filter equation, and according to a solution method of Riccati equation, a steady-state solution of the Kalman filter equation is obtained; and after entering a steady state, filtering parameters become constants, such that various operation links can be achieved with analog devices such as an operational amplifier. Experiments show that the estimated result obtained by using the method of the invention is consistent with the result of the Kalman filter achieved in a digital form, so the method of the invention is feasible.

Description

Kalman filter method based on analog circuit form and analog circuit

Technical field

The present invention relates to Kalman (Kalman) filtering algorithm, relate in particular to a kind of kalman filter method and analog circuit based on analog circuit form.

Background technology

From measure or receive be variously called filtering with method or the technology of taking out useful signal noisy signal, or be called signal filtering.According to the statistical property of desired signal and measuring value, from measuring value, draw error performance minimum in certain statistical significance, that is optimum Signal estimation, be commonly referred to as optimal filter or optimal estimation.

Kalman (Kalman) filtering that nineteen sixty occurs is a kind of Linear Minimum Variance Filter method, is an emerging technology of getting up according to probability theory, mathematical statistics and linear algebra theoretical developments, is a main aspect in modern Control Engineering.The proposition of kalman filtering theory is widely used in engineering, especially aspect the modern projects such as control, guidance, navigation, communication.

The fundamental characteristics of signal and measuring value has been considered in Kalman filtering, and adopts the concept of state space, therefore, has following features:

(1) Kalman filtering is take the mean square error minimum estimated as criterion, and be without partially estimation;

(2) Kalman filtering algorithm is recursion, and in time domain designing filter, be applicable to the estimation of Multidimensional Processes;

(3) adopt state equation to describe by the dynamic rule of estimator, determined by the statistical information and the kinetics equation that encourage white noise by the dynamic statistics information of estimator.Because excitation white noise is stationary process, kinetics equation is known, thus by estimator can be both stably also can right and wrong stably;

(4) discrete logarithm of Kalman filtering can directly be realized on computers.

Kalman filtering algorithm all adopts digital processing unit (as single-chip microcomputer or DSP) to realize at present, and therefore the output of the analog voltage of transducer must be carried out digitlization by analog to digital converter (A/D).This system architecture is brought following limitation:

(1) reliability: system comprises simulation part, numerical portion and A/D interface, and structure is more complicated, affects system reliability;

(2) time response: response speed is limited by digital processor processes speed and A/D inversion frequency, if adopt high speed processor, will cause cost significantly to rise;

(3) cost: the use of A/D converter and digital processing unit significantly improves cost.

For simple in structure, Kalman filter that dimension is low as in the application such as inertial posture measuring, filtering parameter can be designed as normal value, therefore can consider to adopt analog circuit to realize Kalman filtering, adopt the analog components such as operational amplifier to realize the filtering such as addition, integration, feedback and calculate link.

Summary of the invention

For problems of the prior art, for the application of the Kalman filtering of lower dimension, design simulation circuit is realized Kalman filtering algorithm.

In order to solve the problems of the technologies described above, the present invention adopts following technical scheme:

Based on a kalman filter method for analog circuit form, comprise step:

S1, based on by all kinds of output signals of estimating system and with the physical relation of quantity of state, the Kalman filter model of constructing system, described Kalman filter model comprises quantity of state Renewal model, state model and the observation model of system;

S2, based on the filtering parameter of Kalman filter model acquisition system, described filtering parameter comprises the steady-state gain of Kalman filtering;

S3, the filtering parameter obtaining based on Kalman filter model builds proportional integral computing module or scale operation module and integral operation module and calculus of differences module;

S4, adopts analog component to build respectively described proportional integral computing module or scale operation module, and the analog circuit of calculus of differences module and integral operation module, obtains the analog circuit way of realization of Kalman filtering algorithm; Described analog component is mainly operational amplifier;

S5, adopts Kalman filtering analog circuit to carry out Kalman filtering to the output signal of system.

Above-mentioned steps S2 further comprises sub-step:

Described step S2 further comprises sub-step:

All kinds of output signals of 2-1 based on system, the state model of constructing system and observation model;

State model and the observation model of 2-2 based on system builds the Kalman filter model of continuous time, and obtains the steady state solution of Kalman filter model;

2-3 obtains the filtering parameter of system according to the steady state solution of Kalman filter model.

Above-mentioned steps S3 is specially:

Quantity of state Renewal model based on system builds the first calculus of differences module, state model based on system builds integral operation module, observation model based on system to be filtered builds the second calculus of differences module, and the steady-state gain based on Kalman filtering builds proportional integral computing module or scale operation module.

Above-mentioned calculus of differences module is specially voltage plus and minus calculation module.

A kind of Kalman filtering analog circuit, comprising:

One in proportional integral computing module or comparison operation module and the first calculus of differences module, integral operation module and the second calculus of differences module.

Systematic perspective is measured signal and the quantity of state estimated value in a upper moment is newly ceased after the second calculus of differences resume module, new breath obtains filter gain after proportional integral computing module or comparison operation module, gained filter gain and input signal carry out quantity of state renewal, obtain quantity of state latest estimated value through integral operation module through the first calculus of differences module successively, then the quantity of state that, enters next cycle is estimated.

The core devices of aforementioned proportion integral operation module, scale operation module, calculus of differences module, integral operation module is operational amplifier..

Above-mentioned calculus of differences module is specially voltage plus and minus calculation module.

Kalman filtering can be estimated the state of dynamical system from a series of observed quantities that comprise noise.The implementation more complicated of traditional digital form Kalman filtering, and be difficult to integrated, and A/D(mould/number wherein) conversion may cause the time delay of signal; And the Kalman filter system framework that analog circuit is realized is simple, reliability is high, and time response is fast and owing to having saved A/D conversion links and digital processing unit, greatly reduces cost.In addition, the Kalman filter that analog circuit is realized is easy to transducer integrated.

The analog circuit that adopts basic analog electronics to build is realized Kalman filtering, can realize the optimal estimation of analog signal, can avoid the conversion between analog signal and digital signal, has following advantage:

(1) greatly simplify system architecture, can improve reliability and antijamming capability;

(2) almost not free hysteresis of analog circuit, time response is fast;

(3) saved A/D converter and digital processing unit, only needed the analogue device such as operational amplifier and resistance capacitance, cost almost can be ignored.

Accompanying drawing explanation

Fig. 1 is the system block diagram of steady-state Kalman filter in this concrete enforcement, and wherein, figure (b) is the equivalent system flow chart of figure (a);

Fig. 2 is this concrete Kalman filtering analog circuit of implementing;

Fig. 3 is the structural representation of Kalman filtering analog circuit of the present invention;

Fig. 4 is this concrete enforcement and the filtering result contrast of the Kalman filter of traditional digital circuit, and figure (a) is both angle estimation results contrasts, and figure (b) is both angle estimation difference, and scheming (c) is gyro angle rate signal.

Embodiment

The present invention is based on the Kalman filtering equations of continuous time, and according to the method for solving of Li Kati (Riccati) equation, obtain the steady state solution of Kalman filtering equations, filtering parameter (as gain matrix) becomes normal value entering after stable state, thereby make each operation link (as addition, integration, scale operation etc.) can realize with analog components such as operational amplifiers, experiment shows, the estimated result that the Kalman filter that analog circuit is realized obtains is consistent with the Kalman filter result that digital form is realized, illustrate that it is feasible that analog circuit is realized Kalman filter.

Itself also there are some errors in analogue device and analog circuit, such as amplifier leakage current, bias voltage etc., but can, by the reasonable selection to analogue device and the appropriate design of circuit, reduce the error that analog circuit itself causes.In addition, some error even can merge and consider with sensor error, carries out On-line Estimation and compensation as the solve for parameter in Kalman filtering algorithm.

The solution procedure of Kalman filtering equations is as follows:

The state equation of supposing the system:

$\stackrel{.}{x}\left(t\right)=F\left(t\right)x\left(t\right)+B\left(t\right)u\left(t\right)+G\left(t\right)w\left(t\right)---\left(1\right)$

Wherein, the n dimension state vector that x (t) is system, F (t) is that n × n ties up sytem matrix, u (t) maintains system dominant vector for r, B (t) is n × r dimension certainty input matrix, w (t) maintains system noise vector for s, and G (t) is n × s dimension noise inputs matrix.

Observational equation is:

z(t)=H(t)x(t)+v(t) （2）

In formula, z (t) is m dimension observation vector, and H (t) is that m × n ties up observing matrix, and v (t) is m dimension measurement noise vector.

System noise and observation noise are separate, and the covariance of system noise and the covariance of observation noise are expressed as:

$\left\{\begin{array}{c}E\left[w\left(t\right)w^T\left(t\right)\right]=Q\left(t\right)\mathrm{\δ}(t-\mathrm{\τ})\\ E\left[v\left(t\right)v^T\left(t\right)\right]=R\left(t\right)\mathrm{\δ}(t-\mathrm{\τ})\end{array}\right.---\left(3\right)$

Wherein, Q (t) represents the variance matrix of system noise, and R (t) represents the variance matrix of observation noise, and δ (t-τ) represents Dirac function (Dirac Delta function).

According to state equation and the observational equation set up, can obtain Kalman filtering equations continuous time:

$\left\{\begin{array}{c}\stackrel{\stackrel{.}{^}}{x}\left(t\right)=F\left(t\right)\hat{x}\left(t\right)+B\left(t\right)u\left(t\right)+K\left(t\right)[z\left(t\right)-H\left(t\right)\hat{x}\left(t\right)]\\ K\left(t\right)=P\left(t\right)H^T\left(t\right){R_c}^{-1}\left(t\right)\\ \stackrel{.}{P}\left(t\right)=F\left(t\right)P\left(t\right)+P\left(t\right)F^T\left(t\right)+G\left(t\right)Q\left(t\right)G^T-K\left(t\right)R_c\left(t\right)K^T\left(t\right)\end{array}\right.---\left(4\right)$

Wherein,

be the estimation of quantity of state x, P (t) is estimation error variance matrix, and K (t) is Kalman filter gain.

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Take system for detecting angle of inclination as example, system comprises a single shaft gyro (model ADXRS300) and an inclinometer, inclinometer is mainly realized by the acceierometer sensor of ADXL202 model, gyro to measure represents the angular speed of dynamic change, angular speed is carried out to integration and can obtain the inclination angle that comprises angle drift.Inclinometer is directly measured static angular, and these two kinds of transducers have complementary characteristic, therefore both output signals are combined by Kalman filter, can obtain the optimal estimation of angle.

In conjunction with this example, the continuous time model of single shaft gyro output signal is as follows:

Ω _o(t)=Ω _t(t)-w ₁(t)-w _g(t) （5）

In formula (5), Ω _o(t) output signal of expression gyro, its subscript " o " represents output output; Ω _t(t) represent angular speed true value, its subscript " t " represents true value true; w ₁(t) represent white noise, w _g(t) be the zero inclined to one side of gyro, the t in bracket represents continuous time.

W _g(t) can model be variation migration immediately slowly conventionally:

${\stackrel{.}{w}}_g\left(t\right)=w_2\left(t\right)---\left(6\right)$

In formula (6), w ₂(t) be the white Gaussian noise of zero-mean.

The model of inclinometer output signal is as follows:

ψ _o(t)=ψ _t(t)+v(t) （7）

Wherein, ψ _o(t) output signal of expression inclinometer, ψ _t(t) represent true angle, v (t) represents the measurement noise of inclinometer.

By true angle ψ _tthe zero inclined to one side w with gyro _gas the quantity of state x of system, gyro output Ω _oas the controlled quentity controlled variable u of state equation, the output of inclinometer is as the measuring value z of system:

$x=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}{\mathrm{\ψ}}_t\\ w_g\end{array}\right],z={\mathrm{\ψ}}_o,u={\mathrm{\Ω}}_o---\left(8\right)$

Obtain according to formula (8):

Ω _t(t)=Ω _o(t)+w ₁(t)+w _g(t) （9）

$\left\{\begin{array}{c}{\stackrel{.}{x}}_1\left(t\right)={\mathrm{\Ω}}_t\left(t\right)=x_2\left(t\right)+u\left(t\right)+w_1\left(t\right)\\ {\stackrel{.}{x}}_2\left(t\right)=w_2\left(t\right)\end{array}\right.---\left(10\right)$

z(t)=ψ _o(t)=ψ _t(t)+v(t)=x ₁(t)+v(t) （11）

According to Kalman filtering equations continuous time, obtain the Kalman Filtering Model of the present embodiment:

State equation is:

$\left(\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right)=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\·\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)+\left[\begin{array}{c}1\\ 0\end{array}\right]\·u+\left(\begin{array}{c}{w}_1\\ w_2\end{array}\right)---\left(12\right)$

Measurement equation is:

$z=\left[\begin{array}{cc}1& 0\end{array}\right]\·\left(\begin{array}{c}{x}_1\\ x_2\end{array}\right)+v---\left(13\right)$

It is the sytem matrix of the present embodiment $F=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right],$ Certainty input matrix $B=\left[\begin{array}{c}1\\ 0\end{array}\right],$ Observing matrix $H=\left[\begin{array}{cc}1& 0\end{array}\right].$

Kalman filter equation continuous time of the system equation of supposing according to formula (1), the observational equation of formula (2) and formula (4) obtains Kalman filtering gain matrix K and estimation error variance matrix P:

$K=\left(\begin{array}{c}{k}_1\\ k_2\end{array}\right)=P\left(t\right)\·\left(\begin{array}{c}1\\ 0\end{array}\right)\·R^{-1}---\left(14\right)$

$\stackrel{.}{P}\left(t\right)\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\·P\left(t\right)+P\left(t\right)\·{\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]}^T+Q-\left(\begin{array}{c}{k}_1\\ k_2\end{array}\right)\·R\·\left(\begin{array}{cc}{k}_1& k_2\end{array}\right)---\left(15\right)$

In formula (14)～(15), the initial value of system noise variance matrix R and observation noise variance matrix Q is according to the determine precision of the transducer of selecting.

Sum, by the method for solving of Riccati equation, the solution of the differential equation of above formula (15) can be expressed as:

P(t)=Y(t)Λ ^-1(t) （16）

Initial value P (the t of P (t) ₀) be:

${P\left(t\right)|}_{t={\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="130402113458.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}=\mathrm{var}\left(x_0\right)=P_0---\left(17\right)$

Wherein,

$\left[\begin{array}{c}Y\left(t\right)\\ \mathrm{\&Lambda;}\left(t\right)\end{array}\right]=\mathrm{\&Theta;}(t,t_0)\left[\begin{array}{c}Y\left(t_0\right)\\ \mathrm{\&Lambda;}\left(t_0\right)\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&Theta;}}_{11}& {\mathrm{\&Theta;}}_{12}\\ {\mathrm{\&Theta;}}_{21}& {\mathrm{\&Theta;}}_{22}\end{array}\right]\left[\begin{array}{c}{P}_0\\ I\end{array}\right]---\left(18\right)$

T ₀represent initial time; P ₀for the initial value of estimation error variance matrix P; Var (x ₀) expression state initial value variance; I is unit matrix; Λ is diagonal matrix; Θ (t, t ₀) be the one step state transition matrix of the differential equation.

Therefore the steady state solution of Kalman filtering is:

$\left\{\begin{array}{c}P\left(t\right)=Y\left(t\right){\mathrm{\&Lambda;}}^{-1}\left(t\right)=({\mathrm{\&Theta;}}_{11}{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="130402113458.png"\; state="\{\{state\}\}">P</figure-callout>}}_0+{\mathrm{\&Theta;}}_{12}){({\mathrm{\&Theta;}}_{21}{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="130402113458.png"\; state="\{\{state\}\}">P</figure-callout>}}_0+{\mathrm{\&Theta;}}_{22})}^{-1}\\ K\left(t\right)=P\left(t\right)H^T\left(t\right){R_c}^{-1}\left(t\right)\end{array}---\left(19\right)\right.$

The steady-state gain K of the Kalman filtering solving according to above formula (19).

According to above-mentioned analysis, quantity of state renewal process (seeing formula (4)) based in Kalman filtering builds the first plus and minus calculation module, state equation (seeing formula (1)) based on system builds integral operation module, build the second plus and minus calculation module based on observational equation, steady-state gain K based on Kalman filtering builds proportional integral computing module or scale operation module, thereby obtains the system block diagram of the steady-state Kalman filter of the present embodiment system for detecting angle of inclination, sees Fig. 1 (a), in figure, x ₁and x ₂for quantity of state, k ₁and k ₂represent Kalman gain.Equivalent-simplification system block diagram also converts its form in Laplace transform territory to, sees Fig. 1 (b).

Steady-state Kalman filter is mainly made up of the one in proportional integral computing module and scale operation module, plus and minus calculation module and integral operation module, above-mentioned basic module is applicable to utilizing basic analogue device to realize very much, for example, adopt the basic analogue device such as operational amplifier, resistance, electric capacity to realize.

This is specifically implemented according to the steady-state gain parameter of Kalman filtering, mainly adopts LM224 operational amplifier, resistance and electric capacity to realize respectively plus and minus calculation module, integral operation module, proportional integral computing module, scale operation module, sees Fig. 2.

In Fig. 2, operational amplifier U1 and resistance R ₁, R ₂, R ₃, R ₄composition plus and minus calculation modules A, R ₁=R ₂, R ₃=R ₄, realize the additive operation of gyro signal and estimated value:

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="130402113458.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{R_4}{R_1}(V_3-{\mathrm{\&Omega;}}_g)---\left(20\right)$

Operational amplifier U2 and resistance R ₇, R ₈, C ₉and capacitor C ₂proportion of composing integral operation module D:

$V_3=-(\frac{1}{R_8{C}_2}{\&Integral;V}_2\mathrm{dt}+\frac{R_7}{R_8}{V}_2)---\left(21\right)$

Operational amplifier U3 and resistance R ₁₀, R ₁₁, R ₁₂, R ₁₃composition plus and minus calculation module C:

$V_2=\frac{R_{11}}{R_{10}}({\mathrm{\&Psi;}}_o-\widehat{\mathrm{\&Psi;}})---\left(22\right)$

Operational amplifier U4 and resistance R ₅, R ₆, capacitor C ₁composition integral operation module B:

$\widehat{\mathrm{\&Psi;}}=-\frac{1}{R_5{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="130402113458.png"\; state="\{\{state\}\}">C</figure-callout>}}_1}\&Integral;{\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="130402113458.png"\; state="\{\{state\}\}">V</figure-callout>}}_1\mathrm{dt}---\left(23\right)$

Simplification system block diagram in circuit diagram shown in Fig. 2 and Fig. 1 (b) is equivalent, the value of amplifier model and resistance, electric capacity is selected according to obtained Kalman filtering parameter value, select and circuit design by rational device, can reduce to greatest extent the impact of the latent defect (as amplifier leakage current, bias voltage etc.) of analog circuit.

The Kalman filter that the analog circuit of design is realized is positioned on a dividing head (can produce the instrument at inclination angle) to be tested, and can obtain in real time the estimated result of the Kalman filtering of simulation realization.On the other hand, all analog signals (gyro, inclinometer, filter output) in test, with 500Hz sample rate, are gathered by the A/D capture card of 16, and the digitized signal of record is estimated by digital Kalman filter.The Kalman filter estimated result that analog circuit of the present invention is realized and the Kalman filter estimated result of Digital Implementation contrast, and comparing result is shown in Fig. 4.Fig. 4 (a) is the inclinometer measuring-signal in test, the integral result of gyro signal, the Kalman filtering estimated result that analog circuit mode realizes, the Kalman filtering estimated result that digital form is realized; The difference curve of Fig. 4 (b) Kalman filter of realizing for analog circuit mode of the present invention and the estimated result of digital Kalman filter; The angle rate signal that Fig. 4 (c) gathers for gyro.

Fig. 4 (a) shows under the condition of 10 ° of measuring range +/-, and the Kalman filter estimated result of two kinds of modes is consistent.As Fig. 4 (b) shows that the estimation difference of two kinds of implementations is relevant with angular speed size with the inclination angle scope of measurement.Three secondary figure in complex chart 4, the estimation difference of two kinds of implementations can be divided into dynamic differential (being labeled as " 1 " in figure) and (in figure, be labeled as " 2; 3; 4; 5 with static difference ") two kinds, wherein dynamic differential is main relevant to angular speed, and is mainly produced by errors of proportional factor and the time delay of signal after low pass filter of gyrosensor; Static difference is main relevant with the size at inclination angle, and inclinometer is directly using approximate the output of its accelerometer (a) as angle result in the time calculating angle (θ), and this is the main cause that produces static difference:

θ=arcsin(a/g)≈a/g

Wherein, g represents acceleration of gravity.Approximate error is as shown in table 1, and the result in Fig. 4 is consistent with the theoretical value of approximate error.When measuring range is during 20 ° of +/-, the estimated result of Kalman filter that analog circuit is realized and the difference of the result of digital form are only 0.4 °.It is pointed out that this approximate error is that this example is peculiar, is not the characteristic of simulation Kalman filter of the present invention itself.

Table 1 approximate error

Angle θ [deg]	Approximate error [deg]
		0	0.00
10	0.05
		20	0.41
30	1.35

The range of application of the present embodiment comprises but is not limited only to the estimation to angle signal, can also be applied to require high reliability, height dynamically, cheaply in dynamical system.

As shown in Figure 3, Kalman filtering analog circuit of the present invention comprises following four nucleus modules: the first plus and minus calculation modules A, integration module B realize, the second plus and minus calculation module C and the steady-state gain based on Kalman filtering build proportional integral computing module or scale operation module.For the system that comprises sensor error estimation, the structure of the steady-state gain based on Kalman filtering proportional integral module D realizes the steady-state gain of Kalman filtering; For the system of estimating without sensor error, the steady-state gain direct construction scale operation module based on Kalman filtering realizes the steady-state gain of Kalman filtering.

Referring to Fig. 3, the state estimation value of observed quantity signal and last time is newly ceased, is newly ceased through proportional integral computing module or scale operation module through the second plus and minus calculation module C, and together with input signal through the first plus and minus calculation modules A and integration module B, finally obtain the up-to-date estimated value of quantity of state.

Claims (5)

1. the kalman filter method based on analog circuit form, is characterized in that, comprises step:

S1, based on by all kinds of output signals of estimating system and with the physical relation of quantity of state, the Kalman filter model of constructing system, described Kalman filter model comprises quantity of state Renewal model, state model and the observation model of system;

S2, based on the filtering parameter of Kalman filter model acquisition system, described filtering parameter comprises the steady-state gain of Kalman filtering;

S3, the filtering parameter obtaining based on Kalman filter model builds proportional integral computing module or scale operation module and integral operation module and calculus of differences module;

S4, adopts analog component to build respectively described proportional integral computing module or scale operation module, and the analog circuit of calculus of differences module and integral operation module, obtains the analog circuit way of realization of Kalman filtering algorithm;

S5, adopts Kalman filtering analog circuit to carry out Kalman filtering to the output signal of system;

Described step S2 further comprises sub-step:

All kinds of output signals of 2-1 based on system, the state model of constructing system and observation model;

State model and the observation model of 2-2 based on system builds the Kalman filter model of continuous time, and obtains the steady state solution of Kalman filter model;

2-3 obtains the filtering parameter of system according to the steady state solution of Kalman filter model;

Described step S3 is specially:

Quantity of state Renewal model based on system builds the first calculus of differences module, state model based on system builds integral operation module, observation model based on system to be filtered builds the second calculus of differences module, and the steady-state gain based on Kalman filtering builds proportional integral computing module or scale operation module.

2. the kalman filter method based on analog circuit form as claimed in claim 1, is characterized in that:

Described calculus of differences module is voltage plus and minus calculation module.

3. the kalman filter method based on analog circuit form as claimed in claim 1, is characterized in that:

Described analog component is mainly operational amplifier.

4. a Kalman filtering analog circuit, is characterized in that, comprising:

One in proportional integral computing module or scale operation module and the first calculus of differences module, integral operation module and the second calculus of differences module; Systematic perspective measures signal and the quantity of state estimated value in a upper moment obtains new breath through the second calculus of differences resume module, new breath obtains filter gain after proportional integral computing module or comparison operation resume module, and filter gain and input signal obtain quantity of state latest estimated value through the first calculus of differences module, integral operation module successively; The core devices of described proportional integral computing module, scale operation module, calculus of differences module, integral operation module is operational amplifier, and proportional integral computing module, scale operation module, calculus of differences module, integral operation module build in the following way:

All kinds of output signals based on system and with the physical relation of quantity of state, the Kalman filter model of constructing system, described Kalman filter model comprises quantity of state Renewal model, state model and the observation model of system;

Obtain the filtering parameter of system based on Kalman filter model, described filtering parameter comprises and is specially the steady-state gain of Kalman filtering: based on all kinds of output signals of system, the state model of constructing system and observation model; State model based on system and observation model build the Kalman filter model of continuous time, and obtain the steady state solution of Kalman filter model; Obtain the filtering parameter of system according to the steady state solution of Kalman filter model;

The filtering parameter obtaining based on Kalman filter model builds proportional integral computing module or scale operation module and integral operation module and calculus of differences module, be specially: the quantity of state Renewal model based on system builds the first calculus of differences module, state model based on system builds integral operation module, observation model based on system to be filtered builds the second calculus of differences module, and the steady-state gain based on Kalman filtering builds proportional integral computing module or scale operation module;

Adopt operational amplifier to build respectively constructed proportional integral computing module, scale operation module, and the analog circuit of calculus of differences module and integral operation module.

5. Kalman filtering analog circuit as claimed in claim 4, is characterized in that:

Described calculus of differences module is voltage plus and minus calculation module.

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