DE10148998A1 - Parameter estimation for information transmission involves using Kalman filter with at least two mass vectors applied to different filter inputs, a priori signal information for reduced error rate - Google Patents

Abstract

The method involves the use of a Kalman filter with at least two mass vectors applied to at least two different inputs of the Kalman filter. A second mass vector is multiplied by a correlation matrix. A priori information re received signals is used so that the error rate for decoding of the received signals is reduced. AN Independent claim is also included for the following: a parameter estimation arrangement.

Description

The invention relates to a method and an arrangement for Parameter estimation based on the use of a Kalman Filters based.

When transferring information through real, through Noise and fading disturbed channels will be transmitted Information is distorted and the signal originally sent, the can also be viewed as a parameter can only be estimated on the receiver side. The goal of an estimate is always, the smallest possible error between the estimated value and Get original value. An estimate and an original value can also be described as a vector.

One approach to estimating signals is to use a filter model described by Kalman. It models one System in which the values of past and past estimates Measured values based on the signal currently to be estimated for the estimated value to be calculated.

The Kalman filter is in the sense of the middle square Error optimal. He has the advantages of different knowledge like the statistical properties of the signal and the the associated observation / measurement values, and the rapid change of the signal to be estimated (e.g. language) to track adequately. Due to the iterative structure of the Kalman filter, this method is especially for cases suitable in which measured values are gradual or iterative be determined, as in the case of sequential decoding Voice frame in GSM (Global System for Mobile Communications) - System, or with soft-in / soft-out decoding and / or iterative decoding. It also requires a Kalman filter relatively little space.

Given the time-discrete, stochastically disturbed time variant system (system model)

X _k = Φ _{k, k} - _l X _k-1 + W _k (1)

and an associated measurement vector, the elements of which can represent different measurement values.

Z _k = H _k X _k + V _k (2)

where X _{k represents} the (n, 1) state vector at time k, Z _k the (m, 1) measurement vector, W _k the (n, 1) system interference vector and V _k the (m, 1) measurement interference vector. Φ _{k, k-1} is the (n, n) system matrix and H _{k is} the (m, n) observation or measurement matrix (the numbers in brackets indicate the number of rows or columns). The signal X _k and the disturbances W _k and V _k are uncorrelated. The disturbances are white noise and have an average of zero, ie

E {W _k } = 0 (3)

E {W _k W _j ^T } = Q _k δ _kj (4)

E {V _k } = 0 (5)

E {V _k V _j ^T } = R _k δ _kj (6)

E {V _k W _j ^T } = 0 (7)

where Q _k and R _{k are} the variance matrices of W _k and V _k . T means transposition and δ _kj the Kronecker delta.

The initial conditions (e.g. mean ≙ _0/0 and covariance matrix P _0/0 ) result

≙ _0/0 = E {X ₀ } (8)

P _0/0 = E {(X ₀ - ≙ _0/0 ) (X ₀ - ≙ _0/0 ) ^T } (9)

According to the Kalman filter theory (also known from [HW Sorenson, "Least-squares estimation: from Gauss to Kalman," IEEE Spectrum, vol. 7, pp. 63-68, July 1970], the linear, true-to-expectation value is minimal Variance for the state X _k (k = 1, 2,...) Of the system described in (1) - (9) given by the recursive calculation of the following equations (10) - (14). Filters is shown as a block diagram in Fig. 2.

I) Optimal Predicted Estimate

≙ _{k | k-1} = Φ _{k, k-1} ≙ _{k-1 | k-1} (10)

II) Covariance of the prediction error

P _{k | k-1} = Φ _{k, k-1} P _{k-1 | k-1} Φ _{k, k-1} ^T + Q _k-1 (11)

III) Gain matrix

K _k = P _{k | k-1} H _k ^T (H _k P _{k | k-1} H _k ^T + R _k ) ^-1 (12)

IV) Optimal Filtering Estimate

≙ _{k | k} = ≙ _{k | k-1} + K _k (Z _k - H _k ≙ _{k | k-1} ) (13)

V) Covariance of the filtering error

P _{k | k} = (1 - K _k H _k ) P _{k | k-1} (I ~ unit matrix) (14)

The invention is based on the object of a method and to provide an arrangement for parameter estimation which especially when there are several measurement vectors, one on using a Kalman filter Parameter estimation with improved over the prior art Quality enables.

This task is characterized by the characteristics of the independent Claims resolved. Advantageous and practical training result from the dependent claims.

The invention is therefore based on the idea of Parameter estimation with a Kalman filter at least two various input variables, in particular measurement vectors different places of the Kalman filter.

This makes it easy to add additional estimates Information is used, which improves the quality of the Estimation is increased with comparatively little additional effort.

To solve the problem is also an arrangement for Parameter estimation with Kalman filter, which can be, for example, by an appropriately programmed Processor device can be realized, specified which in particular for carrying out the method according to the invention or one of his trainings has been set up.

The invention is more preferred below on the basis of Exemplary embodiments described in more detail to explain them Figures listed below serve:

Fig. 1 block diagram of a Kalman filter with two inputs;

Fig. 2 block diagram of a conventional Kalman filter.

Fig. 1 shows a block diagram of an enhanced over the prior art Kalman filter. This can be used advantageously in particular if, in addition to a measurement vector Z _k, a second measurement vector Z ' _k is available.

The second measurement vector Z ' _{k is present} at a second input of the Kalman filter. The additional measurement vector Z ' _k is filtered, that is to say evaluated with a system matrix Φ _{k | k} , and then weighted (weighting factor (1-α) / α)) is introduced into the estimate. Both Z _k and Z ' _{k are} taken into account as input variables or as measurement vectors. As a result, the estimate is based on more information than an estimate with a conventional Kalman filter with one input, which can reduce the estimate error.

In the following, the use of such an expanded Kalman filter based on the estimate of the a priori information for AMR (Adaptive Multi-Rate) frame bits explained. The Application of an extended Kalman filter is not, however this example is limited but can be used in all comparable estimation problems, such as those in the context of a Equalizers or a multi-antenna system occur done advantageously.

The bits of an according to a known adaptive multi Rate speech codec coded speech frames are for protection convolutionally coded against channel interference. To the receiver side Corresponding convolutional decoders are used, the best possible the original language framework reconstruct. With some - known per se - convolutional decoders, like the APRI-SOVA (Soft-Output-Viterbi-Algoritm), is a priori Knowledge (previously known knowledge) of those to be decoded Included bits in their metric, making lower Error rates in the decoding can be achieved. Important However, the prerequisite for this is the most accurate possible Determination of the a priori information because of incorrect information deterioration in decoding. It So this is an estimation problem with which the Estimation error should be minimal. Calculating an a priori Information sent to a decoder for convolutional codes Can also be made available through a Describe the filter model. Therefore, this estimate is as follows using an extended Kalman filter when using a double decoding can be solved.

In order to adapt the iteration model of the Kalman filter to the needs of the estimation of speech bits, the following assumptions are made. First, the measured variable is equal to the state variable, namely an m-value of a frame bit (an m-value here is a real value for describing a binary signal value. It lies in the interval [-1; +1]. In addition to the binary information that a 0 or a 1 is present (positive value means 0, negative value means 1) contains the amount or the amplitude information about the security that this value was received / decoded correctly.). The matrix H _k thus becomes the unit matrix and no longer has to be taken into account in the case of multiplications.

The error matrices Q _k-1 and R _k can be assumed to be a constant disturbance in order to simplify and reduce the complexity.

The last unknown size of the iteration is the system matrix Φ _{k, k-1} . The fact that information about the signal to be decoded can be calculated a priori is due to the correlation, ie statistical dependence, of the frame bits. A frame bit is correlated with bits of the same frame or with bits of a previously received frame. The system matrix is therefore nothing more than a covariance matrix of the state variable and can be calculated, for example, in the 2 × 2 case (ie two frame bits are estimated together to simplify the display and reduce complexity) as follows.

By using two decodings (two decoding steps), two measurement vectors Z _k and Z ' _k can also be obtained. Both measurement vectors are included in the filter model. To make this possible, the first iteration equation is extended by a summand.

≙ _{k | k-1} = αΦ _{k, k-1} ≙ _{k-1 | k-1} + (1-α) Φ _{k, k} Z ' _k (16)

A second system matrix Φ _{k, k is} used to use the second measurement vector. The parameter α represents a weighting of the two parts for estimation and can be optimized by simulation. Φ _{k, k} is a matrix of correlation coefficients, since the information that can be obtained from the measurement vector Z ' _k is based on the correlation of the measurement vector elements, and is calculated in the 2 × 2 case

There are therefore two measurement vectors Z _k and Z ' _k at two inputs of the Kalman filter, that is to say two different measurement vectors are used at two different locations of the Kalman filter for parameter estimation. A special definition of the system matrices Φ _{k, k} and Φ _{k, k-1} ensures that both the correlation of the frame bits to the previous frame (interframe correlation) and the correlation to neighboring bits in the same frame (intraframe correlation) are used. In the end, a usable estimate with a minimized estimation error is generated.

In addition to the embodiment variants of the invention explained above There are a number of other design variants in the frame the invention, which are not further described here, but simply based on the illustrated embodiments in the practice can be implemented.

Claims (5)

1. Method for parameter estimation, in which a Kalman filter is used, characterized in that at least two measurement vectors are applied to the Kalman filter at at least two different inputs. 2. The method according to claim 1, in which a second measurement vector with a correlation matrix is multiplied. 3. The method according to any one of the preceding claims, in which the parameter estimation within the framework of a decoding is used by convolutionally coded received signals, where a priori information about the received signals such is used that the error rate when decoding the Receive signals is reduced. 4. The method according to any one of the preceding claims, in which the parameter estimation within a Cellular transmission is used. 5. arrangement for parameter estimation, with a Kalman filter that has at least two inputs for at least two different input variables, in particular Measurement vectors.