JPH028668B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a tracking filter for predicting the position of a target in order to direct the antenna beam of the tracking radar toward the target in a tracking radar device for a moving target.

The tracking filter is a digital system that operates at a sample time Ts (seconds), and converts the estimated value of the target state vector s _k at time _k Ts (k is a positive integer) into the radar observed value vector r _k = Hs _k +n _k (1), and from this, the predicted value vector r〓 _k+1 of the radar observed value at time _(k+1) Ts is a linear combination of the observed value vectors r ₁ , r ₂ , ..., r _k This value indicates the direction in which the antenna beam will next acquire the target. However, the formula
In (1), H is a matrix for vector conversion from a state variable vector to an appearance value vector, and n _k represents an observation noise vector at time _k Ts. At this time, the predicted value of the observed value vector is determined based on a model in which the motion of the target is characterized by the following state transition equation.

s _k+1 =Φs _k (2) However, Φ in equation (2) is a transition matrix representing the characteristics of motion. Here, the target state vector
As elements of s _k , the target position coordinates x _k , y _k , z _k and the direction cosine of the target velocity in each coordinate direction x〓 k , y〓 _{k ,} z〓 _k in the orthogonal coordinate system with the radar as the origin is used. Also, the elements of the observed value vector r _k are the actual radar observed values r _k , e _k , b _k (r _k is the distance from the radar to the target, e _k is the elevation angle of the antenna beam, and b _k is the antenna beam angle). (representing the azimuth angle), the values converted to Cartesian coordinates r _k cos e _k cos b _k , r _k cos e _k sin b _k , r _k
sin e _k . In this case, the elements of each vector and matrix in equations (1) and (2) are as follows.

s _k = [x _k y _k z _k x〓 _k y〓 _k z〓 _k ] ^T (3) n _k = [nx _k ny _k nz _k ] ^T (4) r _k = [r _k cos e _k cos b _k r _k cos e _k sin b _{k r} k sin e _k ] ^T (5) H= 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 (6) Φ=1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 0T _S 0 0 1 0 00 T _S 0 0 1 00 0 T _S 0 0 1 (7) However, in the above equation, the symbol T attached to the right shoulder of the vector This symbol represents the transposition of . Also, nx _k , ny _k in equation (4),
nz _k represents each coordinate component of the observation noise vector. n _k is a white noise process with mean 0 and covariance matrix R _k .

Now, the predicted value vector r _k+1 of the observed value is found recursively by the following steps.

s^ _k = s〓 _k +K _k (r _k −r〓 _k ) (8) s〓 _k+1 = Φs^ _k (9) r〓 _k+1 = Hs〓 _k+1 (10) However, the above formula s〓 _k and s^ _k in (k
−1) Predicted value of the target state vector s _k based on the observed value vectors r ₁ , r ₂ , ..., r _k-1 , _k observed value vectors r ₁ , r ₂ , ..., r _k represents the estimated value of the target state quantity vector s _k based on Also, equation (8)
K _k in is a gain matrix obtained from calculations described later.

Next, a method for calculating the gain matrix K _k will be described.
For example, when a Kalman filter is used as a tracking filter, the value of the gain matrix K _k can be found recursively as follows.

K _k =Q _k H ^T (HQ _k H ^T +R _k ) ^-1 (11) P _k =Q _k −Q _k H ^T (HQ _k H ^T +R _k ) ^-1 HQ _k (12) Q _k+1 = ΦP _k Φ ^T (13) However, in the above equation, R _k is the covariance matrix of the observation noise vector n _k expressed by equation (4), and Q _k and P _k are the predicted state vector s〓 _k and the estimated state amount. value vector s^ _k
is the estimated covariance matrix of

FIG. 1 shows an embodiment of a conventional tracking filter.
The signal line r _k represents a digital signal obtained by sampling the observed value signal observed by the radar at each sample time Ts. A difference signal e _k is obtained between this signal and the predicted value signal r〓 _k of the observed value obtained one step before. 1 is a state quantity vector estimator, and formula (8)
It consists of circuits that perform digital operations as shown in the figure below. 2 is a state quantity vector predictor, which inputs the digital signal of the target state quantity estimate s^ _k obtained by the state quantity vector estimator, and
It consists of a circuit that performs digital calculations as shown in equation (9), and as a result outputs a digital signal of the predicted value s〓k ₊₁ of the target state quantity one step ahead. 3 is an observed value vector converter, which is composed of a circuit that performs digital calculation as shown in equation (10), and converts the digital signal of the predicted value vector r〓 _k+1 of the observed value of the radar one step ahead. Output. 4 and 5 are 1 step Ts for the input signal.
This is a digital delay circuit that performs a delay of . Finally, 6 is a gain matrix calculator that performs digital operations corresponding to equations (11), (12), and (13), and outputs each element of the gain matrix K _k as a digital signal as a result. be. The digital value output of the observed value predicted value vector r〓 _k+1 of one step ahead, which is the final output of the tracking filter explained above, is converted into an analog signal by the hold circuit and is used to drive the radar antenna drive device. Used as input, etc.

By the way, in the conventional tracking filter, time _(k+1
) The predicted value r〓 _k+1 of the observed value vector at Ts is the predicted value r〓 k+1 of all observed value vectors obtained in the past r ₁ , r ₂ ,...
…, r _k as a linear combination of observation noise vectors n ₁ ,
It is obtained by weighting according to the covariance matrices R ₁ , R ₂ , . . . , R _k of n ₂ , . . . , n _k .

In prediction using this method, when the actual motion trajectory of the target matches the model shown in equation (2), for example, the model shown in equations (3) to (8) shows that the target has a constant velocity. When moving in a straight line, the tracking filter effectively removes noise, making it possible to predict observed values with high accuracy. However, when the actual motion state of the target changes and the state quantity of the target no longer follows the change shown in equation (2), the tracking filter using the model shown in equations (3) to (7), for example, When the actual target makes a turning movement, the predicted value deviates from the actual position of the target, resulting in a prediction error. This prediction error affects the state estimation of the next step and further increases the error, eventually resulting in a large prediction error within a few steps. Conventional moving target tracking filters have these drawbacks.

This invention solves these drawbacks by:
In the process of calculating the predicted value vector r _k+1 , a fading memory filter is used to weight observed values closer to the present than observed values obtained in the past. Parameters for determining weighting are adaptively determined from errors between predicted values and observed values. The purpose of this is to uniformly weight both past and current observed values when the target moves in a straight line, similar to conventional tracking filters, and when the target moves in a circular motion, to weight the observed values close to the current one. The aim is to make predictions by placing emphasis on the past observed values and to make the predicted values of the tracking filter follow the target changes.

In this invention, when calculating the gain matrix K _{k ,} a parameter ρ _k corresponding to the time average width of filtering is introduced, and the calculation method of the gain matrix K _k is improved as described later. The value is adaptively determined using the residual difference between the input and output values of the tracking filter e _k =r _k −r〓 _k = r _k −Hs〓 _k (14). As a result, this tracking filter has the observed value vector r ₁ whose value of the gain matrix K _k is the input value of the entire filter,
It becomes an adaptive filter that is influenced by r ₂ , ..., r _k .

Here, we will show an improved method of calculating the gain matrix K _k . In a tracking filter that applies a Kalman filter, the gain matrix K _k is calculated using the following calculation formula instead of formulas (11) to (13).

K _k = Q _k H ^T (HQ _k H ^T + ρ _k R _k ) ^-1 (15) P _k = ρ ^-1 _k [Q _k −Q _k H ^T (HQ _k H ^T + ρ _k R _k ) ^-1 HQ _k 〕 (16) Q _k+1 = ΦP _k Φ ^T (17) The above equation is calculated from the covariance matrix Q _k of the predicted value to the gain matrix K _k and the estimated covariance matrix P _k in equations (11) to (13). In the process of finding Q _k , we replaced ρ _k ^-1 Q _k . This means that when the predicted value r〓 _k+1 of the observed value vector is expressed as a linear combination of observed value vectors r ₁ , r ₂ , ..., r _k , each observation error vector n ₁ , n ₂ , ... ..., n Weighting the _k covariance matrix, ρ ^-(k-1) _k R ₁ , ρ ^-(k-2) _k R ₂ , ..., ρ ^-1 _k R _k-1 , R
_k (0<ρ _k 1) (18) This corresponds to the operation of obtaining the predicted value r〓 _k+1 of the observed value vector after weighting by the least squares method. The parameter ρ _k determines the weight for the observed value covariance matrix, and when ρ _k = 1, the weighting of the covariance matrix for all observed values is the same, as in the conventional Kalman filter. If 0<ρ _k <1, it means that the covariance matrix of the current observed values is given more importance than the covariance matrix of past observed values. The relationship between the parameter ρ _k and the equivalent average time width τ _k in filtering is given by the following equation.

τ _k = 1/1 − ρ _k Ts (19) By making the average time width τ _k variable in this way, if the target moves in a uniform straight line in accordance with the model of equation (2), τ _k By setting the value of ∞ (ρ _k = 1), highly accurate estimation and prediction is possible.
Furthermore, if the target does not move in accordance with the model of equation (2), filtering that is not influenced by past observed values becomes possible by adjusting the value of τ _k to a finite value.

Next, a method for determining the parameter ρ _k will be explained. The parameter ρ _k is determined based on the following calculation.

Ω _k = ρ ^-1 _k-1 HQ _k H ^T +R _k (20) u=e ^T _k Ω _k ^-1 e _k (21) ρ _k = 1 e−c(uu ₀ ) (u−u ₀ )( u>u ₀ ) (22) Equation (20) is an equation for calculating the estimated covariance of the residual vector e _k . In this method, on the assumption that the residual vector e _k follows a Gaussian distribution, the following hypothesis H ₁ :The target motion does not match the model of equation (2).

H ₀ : The target motion matches the model of equation (2).

, and test H ₀ against the hypothesis H ₁ using a chi-square test. In other words, using the constant u ₀ that determines the rejection area based on the predetermined risk level for u obtained as a result of calculation of equation (21), if uu ₀ , then
Adopt the hypothesis H ₀ and set ρ _k =1. Also, if u > u ₀ , the hypothesis H ₀ is rejected, and depending on the value of u, 0 <
A parameter value ρ _k is set such that ρ _k <1. Here,
The value of u ₀ is u ⁰ = when the test risk is set to 5%.
It should be 7.81 (rejection region of chi-square distribution with 3 degrees of freedom). Figure 2 is obtained by (22). It shows the relationship between the chi-square value u and the parameter ρ _k for the residual vector e _k . In formula (22), c
is a constant.

Based on the above explanation, an embodiment of the present invention is shown in FIG. In FIG. 23, the gain matrix calculator 6 in FIG. 1 is replaced by another gain matrix calculator 7 and a parameter determiner 8. Another gain matrix calculator inputs a digital signal with a parameter ρ _k , performs digital operations corresponding to equations (15), (16), and (17), and converts each element of the gain matrix K _k into a digital signal. It is composed of a digital circuit that outputs . Further, the parameter determiner 8 inputs the digital signal of the residual error e _k , performs digital calculations corresponding to equations (20), (21), and (22), and outputs a digital signal of the parameter ρ _k . It is composed of digital circuits.

This tracking filter has the above configuration, so when the target moves in a straight line at a constant velocity,
It is possible to perform predictions with the same accuracy as conventional tracking filters, and even when the target moves into a turning motion, the value of the residual e _k is converted to the value of the parameter ρ _k , and this value is used as the gain of the tracking filter. By feeding back the target, it is possible to output the digital signal value of the tracking filter predicted value r〓 _k+1 that has been tracked by the target change.

[Brief explanation of drawings]

Figure 1 is an explanatory book diagram of a conventional tracking filter.
FIG. 2 is a diagram showing the relationship between the chi-square value u obtained from the residual vector of the tracking filter and the filter parameter ρ _k , and FIG. 3 is a block diagram showing an embodiment of the present invention. In the figure, 1 is a state quantity vector estimator, 2 is a state quantity vector predictor, 3 is an observed value vector converter,
4 and 5 are delay elements of one step τ _s , 6 and 7 are gain matrix calculators, and 8 is a parameter determiner. Note that the same or corresponding parts in the figures are indicated by the same reference numerals.

Claims (1)

[Claims] 1. In the tracking filter of a tracking radar device that has one tracking filter that tracks a moving target, the target is determined based on the residual difference between the target prediction information that is the output of the tracking filter and the current target position actually observed by the radar. It detects the movement state of going straight or turning, and depending on the movement state of the target, when the target is moving straight, the time average width of the tracking filter is lengthened, and when the target is turning, the time average width of the tracking filter is increased. A tracking filter comprising: means for determining an average time width that is adjusted to be shorter; and means for determining a gain of the filter based on the average time width determined by the average time width determining means.