METHOD AND DEVICE FOR DETERMINING STATISTICAL PROPERTIES OF RAW MEASURED VALUES

Abstract

In order to at least approximately determine statistical properties of raw measured values, e.g., measurement noise and/or average errors, without knowledge of a filter applied to raw measured values and only with the aid of a useful signal obtained from the filtering, i.e., in order to make statements regarding measurement conditions by assuming a few frequently encountered boundary conditions, statistical properties of raw measured values are determined from the useful signal, which is composed of a temporal sequence of filter output values. A filter characteristic of the filter is ascertained from the temporal sequence of output values obtained under stable measurement conditions, the ascertained filter characteristic is inverted, raw measured values are reconstructed from the inverse of the filter characteristic and from the useful signal, and the statistical properties are ascertained from the reconstructed raw measured values and/or from the inverse of the filter characteristic and from the useful signal.

Claims

1-10. (canceled)

11. A method for determining statistical properties of raw measured values from a useful signal formed as a temporal sequence of output values of a filtering operation of a filter to which the raw measured values are applied, the method comprising: ascertaining a filter characteristic of the filter from the temporal sequence of output values obtained under stable measurement conditions; inverting the ascertained filter characteristic; and ascertaining the statistical properties of the raw measured values based on the inverted ascertained filter characteristic and the useful signal.

12. The method of claim 11, wherein the ascertaining the statistical properties includes reconstructing the raw measured values based on the inverted ascertained filter characteristic and the useful signal and determining the statistical properties based on the reconstructed raw measured values.

13. The method of claim 11, further comprising identifying a presence of the stable measurement conditions by evaluating the temporal sequence of the output values.

14. The method of claim 11, further comprising identifying a presence of the stable measurement conditions by identifying that the output values change at least almost uniformly in accordance with a system model on which the filter is based.

15. The method of claim 11, further comprising identifying a presence of the stable measurement conditions by identifying that a change in the output values is at least almost constant or consistent over time in accordance with a system model on which the filter is based.

16. The method of claim 11, further comprising identifying a presence of the stable measurement conditions from an evaluation of sensor signals of sensor devices.

17. The method of claim 11, wherein the filtering operation includes a low-pass filtration.

18. The method of claim 11, wherein the filtering operation includes a Kalman filtration.

19. An apparatus comprising processing circuitry configured to: obtain a useful signal formed as a temporal sequence of output values of a filtering operation applied to raw measures values; ascertain a filter characteristic of the filtering operation from the temporal sequence of output values obtained under stable measurement conditions; invert the ascertained filter characteristic; and ascertain statistical properties of the raw measured values based on the inverted ascertained filter characteristic and the useful signal.

20. A non-transitory computer-readable medium on which are stored instructions that are executable by a processor and that, when executed by the processor, cause the processor to perform a method for determining statistical properties of raw measured values from a useful signal formed as a temporal sequence of output values of a filtering operation of a filter to which the raw measured values are applied, the method comprising: ascertaining a filter characteristic of the filter from the temporal sequence of output values obtained under stable measurement conditions; inverting the ascertained filter characteristic; and ascertaining the statistical properties of the raw measured values based on the inverted ascertained filter characteristic and the useful signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The FIGURE is a schematic block diagram of an apparatus for carrying out a method according to an example embodiment of the present invention.

DETAILED DESCRIPTION

[0020] An apparatus 100 includes a device 101, for example including a spacing radar of vehicle, for obtaining and/or delivering raw measured values 102. A filter 103 serves to obtain a useful signal 104, e.g., a spacing signal, from raw measured values 102. Useful signal 104 is transferred, via a transfer channel 107 having a low data transfer rate, to a useful signal processing unit 105 that has an evaluation unit 106 for ascertaining a filter characteristic of filter 103, reconstructing raw measured values 102, and ascertaining statistical properties of raw measured values 102. A connection 108 serves for data traffic between useful signal processing unit 105 and evaluation unit 106.

[0021] The method according to the exemplifying embodiment will be described on the basis of the following designations and abbreviations:

TABLE-US-00001 Designation/ Abbreviation Description E Expected value of a random variable; obtained by integrating the random variable, multiplied by its density function, from −infinity to +infinity Variance, The variance of a random variable is equal to the square e.g., Q, R, P, F of its standard deviation, and is obtained by integrating the density function, multiplied by the square of the deviation of the random variable from the expected value, from −infinity to +infinity A Transition matrix, also referred to as a “model” H Measurement matrix I Unity matrix (i.e., only ones on the diagonal) q; Q System noise, with associated variance v; R Measurement noise, with associated variance p; P Error in system vector, i.e., difference between true and estimated value, with associated variance z Current measured value ~x/x True/estimated value of the system vector or output value P.sub.− “−” indicates the value according to the prediction P.sub.+ “+” designates the value at the end of a filter step. Values without + or − are always relative to the end of the filter step, i.e., +. Interference variables do not have a + or −. K Kalman filter return d Difference between filter result and filter prediction: x.sub.n−1 − Ax.sub.n. This difference is the so-called “filter innovation.” F Variance of the filter innovation, i.e., F = E(d,d) Statistical The expected value and variance of a random value characteristics Filter In a low-pass filter this is the filter constant; in a Kalman characteristic filter it is the additional system noise that is to be determined Output value Result of the calculations of the filter, i.e., the estimate x of a filter for the true value ~x System Synonym for the output value of a filter in the case of a position Kalman filter System Variance of the difference between the true and estimated variance P value, i.e., ~x − x.

[0022] A system model in accordance with the following equations is assumed:

.sup.˜x.sub.n+1=A.Math..sup.˜x.sub.n−q.sub.n+1

z.sub.n=H.Math..sup.˜x.sub.n+v.sub.n

[0023] The true value of the system vector is propagated using the transition matrix A, and a noise also occurs. A noise is also part of the current measured value. The noise is described as follows:

P=E(x−.sup.˜x,x−.sup.˜x)

qεN(0,Q)

vεN(0,R)

where N(0,Q) and N(0,R) are the normal distribution with an expected value and a respective variance Q and R. Any value can always be expressed as the sum of the true value and the error value. The error values are not correlated with one another.

[0024] A system of this kind can be observed, for example, by way of a Kalman filter described by the formulas below, where P.sub.− is the value according to the prediction, P.sub.+ the value after correction, and the superscript T for the variables A.sup.T and H.sup.T designates the transpose of the correspondingly characterized matrix:

x.sub.−−Ax.sub.+

P.sub.−=AP.sub.+A.sup.T+Q

K=P.sub.−H.sup.T(HP.sub.−H.sup.T+R).sup.−1

x.sub.+=x.sub.−+K(z−Hx.sub.−)

P.sub.+=(I−KH)P.sub.−

[0025] A detailed derivation of the formulas for a simple low-pass filter is provided below. The principle therein is applicable to a Kalman filter, but is simply more mathematically demanding in that context. The formulas applicable to the low-pass filter are:

x.sub.n+1=λx.sub.n+(1−λ)z.sub.n+1

P=E(x,x)

R=E(z,z)

[0026] P is the system variance, R the measurement noise, and λ the filter constant.

[0027] In periods of a stabilized state it can be assumed that the measurement noise and also the covariance of the filter are approximately constant. The filter characteristic is learned using this assumption. What needs to be determined for this purpose is the filter constant for the low-pass filter, and the system noise for the Kalman filter.

[0028] If a constant, stabilized state exists, the system variance over the course of time can be measured from the output values of the filter:

P=E(x.sub.n,x.sub.n)

[0029] The variance of the filter innovation can be measured experimentally in exactly the same way:

F=E(x.sub.n+1−x.sub.n,x.sub.n+1−x.sub.n)

[0030] This filter innovation can be rewritten as:

[00001]$F=E\left(x_{n+1}-x_n,x_{n+1}-x_n\right)=E\left(\lambda .Math..Math.x_x\left(1-\lambda \right).Math.z-x_n,\lambda .Math..Math.x_n+\left(1-\lambda \right).Math.z-x_n\right)={\left(\lambda -1\right)}^2.Math.\left(P+R\right)$

[0031] Because a stabilized state exists, however, the following is also valid:

P=E(x.sub.n−1,x.sub.n+1)=E(λx.sub.n+(1−λ)z,λx.sub.n+(1−λ)z)=λ.sup.2P+(1−λ).sup.2R

[0032] The following can be calculated:

P−F=λ.sup.2P+(1−λ).sup.2R−(λ−1).sup.2(P+R)=2λ−1)P

[0033] The filter characteristic, i.e., the filter constant in the case of a low-pass filter, can thus be determined from the equation:

2(1−λ)P=F

[0034] The filter constant can thus be calculated only with the aid of the output values, and with no knowledge of the measurement noise.

[0035] For a Kalman filter, the derivation is as follows:

[00002]$\begin{array}{cc}\begin{array}{c}{d}_{n+1}=.Math.x_{n+1}-{\mathrm{Ax}}_n\\ =.Math.A.Math.{}^{~}x_n-q_{n+1}+\left(1-\mathrm{KH}\right).Math.\left({\mathrm{Ap}}_n+q_{n+1}\right)+\\ .Math.{\mathrm{Kv}}_{n+1}-A\left({}^{~}x_n+p_n\right)\\ +.Math.K\left(v_{n+1}\right)-H\left({\mathrm{Ap}}_n+q_{n+1}\right))\end{array}& \left(1\right)\end{array}$

[0036] This yields:

[00003]$F=E\left(d_{n+1},d_{n+1}\right)=E\left(K\left(v_{n+1}-H\left({\mathrm{Ap}}_n+q_{n+1}\right)\right),K\left(v_{n+1}-H\left({\mathrm{Ap}}_n+q_{n+1}\right)\right)\right)=K\left(R+H\left({\mathrm{APA}}^T+Q\right).Math.H^T\right).Math.K^T=\mathrm{KH}\left({\mathrm{APA}}^T+Q\right)$

[0037] The formulas for the Kalman filter were used for the derivation. The variances F of the filter innovation and P of the error in the system vector are directly measurable. P≈const in the stabilized state, and the following equation

P.sub.+=(I−KH)P.sub.−

therefore yields:

P=(I−KH)(APA.sup.T+Q)

[0038] It follows from this that:

P=APA.sup.T+Q−F

[0039] Because P and F are measurable and the transition matrix A is known from the physical model, the variance Q of the system noise can therefore be determined.

[0040] In order to ascertain the measurement noise in the second method step according to the invention, in the example of the simple low-pass filter the noise of the raw measured values can be calculated from the difference of the filter values if the filter characteristics are known. With known values for x.sub.n and x.sub.n+1 and a calculated λ, the raw measured values can be reconstructed from

λ.sub.n+1=λx.sub.n+(1−λ)z.sub.n+1

as

z.sub.n+1=(λ.sub.n+1−λx.sub.n)/(1−λ)

[0041] The statistical characteristics, i.e., the variances, etc. of the useful signal, i.e., of the output signal of the low-pass filter, are thus ascertainable.

[0042] With Kalman filters, the intensity with which the last system position and the current measurement are filtered depends on the respective covariances. If the system variance P is very large, the measured values will be relied upon more. If the measurements are unreliable, the physical system model on which the filter is based, i.e., the equation

.sup.˜x.sub.n+1=A.Math..sup.˜X.sub.n−q.sub.n+1

of the system model, will be relied upon more. It is proposed according to the present invention to use the equation of the filter innovation d, which can be measured directly in each step, in order to invert the Kalman filter. The relevant equation (see formula (1) above) is:

d.sub.n+1=K(v.sub.n+1=H(Ap.sub.n+q.sub.n+1))

where

K=P.sub.−H.sup.T(HP.sub.−H.sup.T+R).sup.−1

[0043] The random values v, p, q are to be selected here from the normal distributions N(0,R), N(0,P) and N(0,Q), P and Q being known. Only the variance R of the measurement noise v remains to be determined. A variety of numerical calculation methods, which are known in principle, can be utilized for this determination. The Monte Carlo method is recited as a preferred example of such a calculation method.

[0044] Two probable solutions for the variance R of the measurement noise v are typically obtained. Because the measurement noise, i.e., measurement error, v appears once in the numerator and once as an associated variance in the denominator, a kind of quadratic equation results with regard to v and R. A quadratic equation typically has two solutions. Which of the two is the correct one can be ascertained from a knowledge of whether, for example, the reception environment is good or bad. This knowledge, i.e., a corresponding signal, can be ascertained and transferred, e.g., by device 101 as a single additional information item and stored in a memory provided therefor, in particular a flag. The additional information item indicates only whether the actual measurement noise prior to the filtering operation is fairly good or fairly bad, and requires at most a negligibly low data rate for transfer. An at least largely exact quantitative statement regarding the measurement noise prior to the filtering operation can thus be made using the method proposed here.

[0045] The distinction between the two aforementioned solutions can also be illustrated as follows. If the filter result is very close to the expected value of the undistorted physical model, then either the measurement can be perfect and can accurately confirm the physical model, or the measurement conditions are so poor that the measurement in fact has no influence on the filter result. According to an example, a distinction is made between these extremes. Because the values of the measurement noise are known for both cases as solutions of the equation, as a rule it is easy to distinguish between the two solutions based on further heuristics.

[0046] The methods described above for processing the raw measured values, and the physical variables and signals derived therefrom, can be executed in simple and advantageous fashion in particular using digital signal processors.